Thursday, 31 October 2013

Oracle Rulings Review - Caged Sun and Equinox

Here are two cards with Oracle text very similar or exactly the same as their printed text.  But the rulings... the rulings...

Here is a card that does something the rules don't quite explain.  The Oracle says:
Enchant land
Enchanted land has "Tap: Counter target spell if it would destroy a land you control."
But what does that mean, exactly?  I did a quick scan of the comprehensive rules and couldn't find anything, but the rules are quite large so I thought I'd ask some rules experts whether I was missing something:
Thanks to the folks at Cranial Insertion for confirming my suspicions on this one.  Basically we have to do a plain language reading of what the Oracle text.  Fortunately there are a variety of rulings to supplement the text.
10/4/2004 Equinox will not counter a spell which requires sacrificing land when it enters the battlefield, or one that requires sacrificing land as part of the cost to cast it.

10/4/2004 Equinox will not counter a spell that has a random chance of destroying a land.

10/4/2004 Equinox will not counter a spell which would indirectly cause destruction of one of your lands.

10/4/2004 The ability can target any spell, even one that would not destroy a land.

10/4/2004 When this spell resolves, it only counters the targeted spell if that spell would destroy a land if it resolved right then.

10/4/2004 Equinox will not counter a spell that deals damage to an animated land, even if it would deal more damage than the land's toughness. This is because the spell itself does not destroy the land directly. The land is destroyed by a game rule.

10/1/2008 Will not counter a spell which would destroy a land only if a choice is made.

With all of those rulings in hand I don't think Equinox is going to cause any tricky situations. I like these rulings because I don't feel like they are telling you new information about the card, but just explaining what the card means. It is quite plain to me that a Lightning Bolt does not destroy a Mishra's Factory but that instead a state-based effect destroys it after the damage applies - if that is not plain to you then the rulings help. Equinox is a little bit weird in that it asks us to check a hypothetical situation, but ultimately it's not that weird. Replacement abilities actually ask us to check hypotheticals all the time.

I give the Equinox wording...

I like it.
Caged Sun
I didn't expect to be doing Oracle reviews of cards that were printed so recently, but, as I said, this is really about rulings more than text.
As Caged Sun enters the battlefield, choose a color. 
Creatures you control of the chosen color get +1/+1. 
Whenever a land's ability adds one or more mana of the chosen color to your mana pool, add one additional mana of that color to your mana pool.
Oh, that's exactly the same as what is printed on the card, how convenient.  So what do the rulings say:
6/1/2011 Caged Sun's triggered ability is a mana ability, which means the ability doesn't use the stack and can't be responded to.
Fair enough. Oh wait, is that fair enough? This time we aren't talking about reading plain language, we are talking about apply the rules to the card.

Here is what the rules have to say about how to tell if a triggered ability is a mana ability.
605.1b A triggered ability without a target that triggers from activating a mana ability and could put mana into a player's mana pool when it resolves is a mana ability. 
605.5. Abilities that don't meet the criteria specified in rules 605.1a-b and spells aren't mana abilities.
So Caged Sun's trigger is a mana ability because it triggers off a mana ability, adds mana to your pool and doesn't have a target.

Here's the problem: We can't promise you that it triggers off a mana ability.  Suppose you have a Quicksilver Elemental in play. You activate it's ability to steal the abilities of a Witch Engine. Next, you  cast Cytoshape targeting your Quicksilver Elemental to turn it into a Dryad Arbor. According to layers copying effects come before ability granting effects, so it is now a 1/1 creature land with the Witch Engine ability. Play Caged Sun naming black. Activate the Witch Engine ability on your land. That ability is targeted so it is not a mana ability. It is, however, the ability of a land adding mana to your mana pool, so it triggers Caged Sun. Because Caged Sun's ability is not triggered by a mana ability, according to rule 605.5 it is not a mana ability and goes on the stack after the Dryad Arbor Witch Engine ability resolves.
Most triggered abilities that add mana are much safer bets. In case you are wondering, the reason why I have to use Caged Sun in this example and not other mana triggers is because most similar cards are worded differently. Right back to Mana Flare, they say that when a player taps a land for mana they trigger. This may not seem different - after all, in my example we did tap our sickening hybrid creature to get the mana - except that rule 106.10 clearly states that tapping a permanent for mana means activating a mana ability of that permanent that requires tapping as part of the activation cost. So while in my example we are tapping the Dryad Arbor to activate an ability that will add mana to our mana pool, but we are not tapping it for mana. These abilities are quite safely worded.

But no matter how safe the wording of an ability is, we can't account for the cards of the future. If a triggered ability is only a mana ability when it is triggered by a mana ability then we cannot determine if a triggered ability is a mana ability until the moment it triggers. I sent the Wizard's support team an email about this one. Of course, if you read my Mishra's War Machine review you'll know that I don't necessarily put more stock in what they say than what I think about the matter. Just because it's the rules doesn't mean it's right.

Well Wizards did get back to me and actually confirmed what I've said here. The last time I wrote in with a question like this they took over a week to get back to me and responded by telling me they would be updating the rules the next month to address the situation.

I'd be happy to give the Caged Sun wording three stars - it's a very nice wording if you ask me - but the rulings are definitely part of the Oracle, and so, until the ruling is updated to match the email I received from Wizards, I'm going to have to give it...

Come on guys

Wednesday, 30 October 2013

Path of Exile

I've been playing Path of Exile again.  I played it for a while in the beta and lost interest about halfway through the third difficulty.  I'm not really interested in losing experience when I die, especially not when lag was causing the game to report things to be in places they were not.

Anyway, it's gotten quite a bit better in that short time.  Not that it was bad before, I played plenty of it.  They added a class you can only play after winning normal difficulty that starts in the middle of the sphere grid passive skill tree.  More excitingly they added trigger materia skill gems so you can have skills automatically activate on certain events.  I haven't found these yet but it sounds really unfair.

And that's what I really like in games like this - being unfair.  Fair is boring.  If the game is totally unfair then you can play in so many different ways: look for the best build, refine your build, do broken things and make the game easy, use the worst skills and make the game near impossible.  It gives you a lot of fun ways to play.

With "balance" everything feels samey.  What the point in using the other skill if it is the same as the skill you were already using.  Sure, it may work a little differently, but ultimately the only way things are balanced is if they are almost the same, with only cosmetic difference.

This is a Diablo-like so it is actually a fair bit like Diablo and Torchlight and all those other games, but it is definitely a little more like Diablo 2 than Diablo 3.  That's a good thing here.

Tuesday, 29 October 2013

Cookie Clicker - Chain Cookies Again

Chain Cookies again.

I will refer you to my previous discussion of them to understand the basics of chain cookie analysis.  Essentially I am analyzing the choice between having Elder Wrath on and not having it on.  For a brief time that answer was that you wanted elder wrath to take advantage of huge cookie chains.  That is no longer the case.

A few things have gone into this.  First of all, the way of deciding when to spawn a cookie has changed.  The Update notes say that they are now more random, which strikes me as an odd things to say.  The graph on top compares the new probability distribution with the old one by number of seconds passed.  The lower graph is the cumulative distribution.  On both, the blue line is the new system and the red line is a uniform distribution, as it used to be.  As you can see, but about halfway through the time between the minimum and maximum times it is already nearly 100% certain that a cookie will have spawned.

Nothing against Orteil - actually, big thanks to Orteil for making such a great game and for inspiring me to work on my own projects - I just disagree with the idea of "more random."  To me, uniform distribution is as random as it gets.  If the goal was to prevent the prediction of cookie spawns then this change makes them less predictable in the sense that we can no longer get the time remaining to spawn from the variable it is stored in, but it is more predictable in the sense that the window in which the spawn will happen is much narrower and the spawns are more clustered around a certain number of seconds.  Personally I think the old method was better, but if a check is to be made every tick then uniform distribution could be easily recreated by just using the right check.

Because of the way the cookie spawns cluster, the chance of getting a lucky cookie while your frenzy cookie is still going on is very close to 100%.  If you can click the cookie within 1.5 seconds of it spawning then you'll only miss your high value lucky cookie about 2.3 out of every 1000 times.  Now 80% of your click frenzy time will be during frenzy time - up from 39% under the old system.  That dramatically increases the value of golden cookies while not under elder wrath, to about 48 times your listed CpS.

Anyway, I wanted to talk about chains.  Every chain generates at least 5 digits.  Starting with the fifth, the chain has a 1% chance to end randomly, and it will also end if it is more than 25% of your current holdings or more than 6 hours of your current production.  As I discussed the last time I wrote about this, it's a little tricky to set a cut-off when each successive click multiplies your returns by ten.  If you get a chain that is 26% of your current holdings then it ends.  If you get one that is 24.9% then it doesn't, and then the next one is 249%, which is a lot.  Similarly, 6 hours of production is plenty while nearly 60 hours is pretty fantastic.

I asked a for a friend's CpS to benchmark my numbers.  The number I was using was 885.8B.  At that CpS you qualify for a 77 quadrillion chain without wrath or a 66 quadrillion chain with wrath.  To get that you need at about 27 quadrillion in the bank as well, but that's easily attainable.  When you have 885.8B CpS, though, 77 quadrillion isn't all that much.  A lucky/frenzy combo will be worth 7.5 quadrillion, and you get those every four and third minutes like clockwork.

My big spreadsheet matches my intuition.  Giving up on those big lucky cookies, as well as those insanely huge click frenzies, just isn't worth it to pick up extra chains.  Because the chains for wrath use 6's and the ones without use 7's, you could have enough CpS to qualify for a 17 digit chain with wrath on and only a 16 digit chain without wrath.  But even then no wrath is better.  Chain cookies, after all, are only a small part of that 48 times return when not on wrath.  The majority is lucky cookies.

Personally I'd like it if wrath was better now that there are things attacking you during the wrath.  It seems like if you have to defend yourself you should be getting more reward.

Monday, 28 October 2013

Candy Box 2

Candy Box 2 came out.  I'm not sure it should be called Candy Box 2 so much as it should be called Candy Box: Origins, or Candy Box: Revelations or something.  It is not a sequel to the original game, but rather a reimagining of it.

I don't mean to criticize, this is a great game.  The original felt a little bit cobbled together and this is more of a cohesive whole.  It offers a great feeling of exploration, very much like A Dark Room.  But also, like a Dark Room, it is not actually very long.  I started playing and won it in the same day, and in fact I started over again near the end of the day to do something a little differently, so my final winning game was probably only four or five hours old.

I don't really mean that as a criticism either.  The game offers more in that short time than a lot of games offer in more, and obviously it doesn't cost you anything to play.  After winning I did some reading about different ways to approach the challenges in the game and I was very happy to see that there are actually multiple ways to get past certain encounters.  There isn't even one way that feels like the right way, instead there are lots of tools available and you can put them to use.  The game doesn't punish you for doing things "wrong".

So I like Candy Box 2 and I would definitely play a sequel (as in actual sequel) or another game by aniwey.  It's a has a nice old-timey feel to it.  I might even play this game again one day to see if I can win without using a certain strategy.

Sunday, 27 October 2013

Mad Myth Sunday? - The Computer

Some children play a game, rolling rocks down a hill to see which one goes furthest.
A scientist decides to model the game to see which child will win.  To do so he builds a computer.  He gives the computer a model of gravity and of the hill, but it is unable to predict the winner.
He takes takes pictures and measurements of every bit of earth and stone, and adds more processors and memory to his computer to interpret the improved model.
He adds high speed cameras to measure how the children throw the rock.  He scans every rock before it is thrown to know exactly how it will bounce and roll.  Every time he improves the modelling he must add more components and the computer becomes larger and larger until it towers high above him.
Some children play a new game, rolling rocks down a massive computer to see which one goes furthest.
Candy Box 2 came out, so I'll have a post about that for you this week, but you might want to try it out first.

Thursday, 24 October 2013

Oracle Review - All Hallow's Eve and Clergy of the Holy Nimbus

Oh yes, it's time!

All Hallow's Eve
Some of you might not realize how wonderful this is, but here is the oracle wording:
Exile All Hallow's Eve with two scream counters on it. 
At the beginning of your upkeep, if All Hallow's Eve is exiled with a scream counter on it, remove a scream counter from it. If there are no more scream counters on it, put it into your graveyard and each player returns all creature cards from his or her graveyard to the battlefield.
If you didn't play way back, if you didn't follow the Oracle over the years, you may not know that All Hallow's Eve was an Enchantment for a long time. Yeah, they errata'd it to an enchantment because you couldn't have a sorcery sit around with counters on it. Sure, you can flip a card onto the battlefield and deal damage based on what it lands on, but having a sorcery sit around with counters is right out, right?

Well, that made sense to me at the time, but we all know it's total nonsense now. It makes me so happy to see this has been corrected at some point in the last decade. I give this sorcery...

Clergy of the Holy Nimbus
That's a pretty big name for a such a low impact card.
If Clergy of the Holy Nimbus would be destroyed, regenerate it. 
1: Clergy of the Holy Nimbus can't be regenerated this turn. Only any opponent may activate this ability.
Alright, where did that come from? I'll tell you where it came from, it came from errata that made sense of the card in a time when they couldn't figure out how to word the original card. Of course the card is pretty easy to word right now:
When Clergy of the Holy Nimbus would be destroyed, instead any opponent may pay 1.  If no player does, regenerate Clergy of the Holy Nimbus.
Yeah, it's pretty close to the text of the original card.

The astute reader may notice a meaningful juxtaposition here. Two cards that were reworded - despite never being reprinted - to make them work within the rules at the time. Both are very easy to word to keep the original intent of the card. One did have it's wording restored to match the card, the other did not. It should not be any surprise, then, that I give the clergy...

Wednesday, 23 October 2013

Raiding By Myself

I was playing Aarklash last night and it really reminded me of raiding.  In particular there was an enemy that had an ability that killed everyone who was more than three meters away from him.  Then he also used area attacks against people close to him.  I'm pretty sure on harder difficulties you would need stand just outside the area and run in to not be killed.  He also had an attack where he hit someone and everyone close to them for a bunch of magic damage, so you had to spread out around him or run people away when they were targeted.  Again, on medium difficulty there was room to make mistakes, which I was glad about because it took me a few tries anyway.

But then I started to realize how much the other parts of the game are like raiding as well.  There are stationary packs with patrols nearby so sometime you want to pull a pack away from where they are standing to fight them.  You fight large numbers of enemies with diverse abilities and have to decide which to fight first and how to control the dangerous ones.  One fight that took me a few of tries had the following composition:

A melee fighter with a stunning charge and a small aura that shuts off attack abilities.
A melee fighter who buffs himself with high criticals and who comes back to life a few seconds after the first time he dies.
A melee fighter who buffs itself with increased attack speed and mana drain and can heal himself to full by banishing himself and slowly regenerating.
A caster who casts a long duration stun and a charm and who, a few seconds after his death causes an area effect fear around his corpse.
Three archers who have an instant cast heal on a long-ish cooldown.

The tank I have relies on an attack ability to keep himself alive - he can blind enemies in a small area around him about 25% of the time, so that no-attack aura makes him take a lot more damage.  One of my damage dealers is melee range but he has one ability that he can use every 30 seconds that makes his next three attacks do a huge amount of damage, so he could activate that before running in to get a lot of damage on the no-attack aura guy but that ability is also my only silence effect and that charm/stun caster is obviously a huge problem.

My mage character has an area knockdown but it affects allies.  I could use that to interrupt the caster once at the beginning of the fight to hold off his charm for a while, or I could use it with good positioning to knock down the melee and save a bunch of damage from the tank.  I can customize her to either have a lightning spell that hits multiple targets or a single target one that does a lot of damage but not both.  She also has a heal spell but the way mana works means trading off heals for damage done.  My healer character has two heals, one targeted and one that infects an enemy and then heals allies in an area around that enemy when it ends.  The targeted heal can't target herself.  She can also steal buffs from enemies every 25 seconds.

I started off by trying to take out the no-attack-aura guy but I decided the caster was just too dangerous so I used the silence ability of the rogue and lightning bolt to take it out first through the heals from the archers.  I tried taking out the no-attack aura guy next but it was just too hard to take him down with the healers and the rogue not being able to be fully effective.  So I ended up using the multi-target lightning bolt spell to work on one of the healers at the same time as fighting the caster and finish it off before the healing cooldown came back up.  The rogue then went to take out another healer while the mage switched to healing duty to keep the tank alive while the healer's AoE heal ability cooled down.  Once I got the healers down and just had the melee left it wasn't that hard anymore but my resources had been depleted to the point that the fight wasn't really won until I had one of the melee down as well.  It took me several tries to get there.

If I'd been able to choose my party for that fight - it was at a point in the game where you have to split up - then it would have been much easier because I could have used the other tank who wouldn't have their survivability hurt by the no-attack aura.  Well, also the other tank just seems like a better tank to me, though I think she's just more my style.

In another fight there were two casters with damaging ground effects and two others who shot slow-moving, piercing missiles along with four or five weak melee guys and they all appear in a circle around you.  That fight wasn't nearly as hard but I had to move my team around a lot.

If this sounds like an awesome game then you have good taste.  It's like raiding but there are no other people.  It makes me want a version of this game where you have a 10-person party.

Tuesday, 22 October 2013

Come Dine With Me

Maybe it's silly to analyze the game of a reality show.  Reality shows have a lot of bad games.  Survivor, the first big reality TV hit, was the ultimate in bad game.  Supposedly it is a test of survival but we all know that they aren't going to let anyone die on TV, so really the title of the show might as well have been "Petty Politics".  The game where the players of the game elect a winner is a really lousy game.

But this show, Come Dine With Me, takes this bad game to a new low.  In Come Dine With Me five competitors take turns hosting a dinner party for the other four.  At each party each person scores them on food, fun, or whatever other factors they find important.  At the end, the person with the most points wins.

"So why doesn't everyone just give everyone else one out of ten?" you may ask.  As far as I can tell, the only reason is that they want to be seen as playing fairly when they appear on TV - or alternately they don't actually understand how the game works.  Giving everyone else one out of ten is *the* strategy in this game.  What's more, if you go have your dinner party first, your scores are already locked in, so you can be as awful and destructive at everyone else's party as you like, bringing the mood down and making sure everyone has a bad time.  Presumably you can't go so far as to directly sabotage others as I assume that is prohibited - murdering the competition is a successful strategy in nearly all competitions but it is allowed in remarkably few.

What's so stomach-churning about this particular game is that it is so easily fixed.  Simply add the average score each person gives to their own score and the reward for giving a bad score to others is eliminated.  Sure, played properly the corrected game is a weird game of deceit where you want to give the best score to the person with the lowest overall score and the worst score to the person with the highest overall score to try to make all of your opponent's scores exactly equal to one another, but that game is hardly even worth playing.  If you give the highest score to the person with the worst food you have no idea if everyone else did that too.  The system becomes largely un-game-able.

The idea of a game where you lose becuase one of your own competitors claims that you did badly is very distasteful.  And it's televised in 43 countries!  Yuck.

Monday, 21 October 2013

A Game I Like - Aarklash: Legacy

Recently I've been playing plenty of games for their graphics and sound.  I think that's a little hard for me to admit.  Shortly after FFX came out I remember commenting that I would play it just as much if graphics were as simple as the mini-map in the corner that represented you as a triangle.  I used to care very little for graphics and sound and much more about gameplay.

It isn't so much that I've changed as that games have changed.  The kind of gameplay that I loved has mostly just gone away.  I never played XCOM but Ziggyny's recent post about it, and about it's recent re-imagining, reveals a great deal about what has happened to games.  The depth of system mastery available with two actions a turn is so much less than with action points.  The amount of customization is equipment sets is less.  The number of characters on the field is smaller.  So without being terribly engaged in any game, the one with the better graphics simply seems more enjoyable.

It took me very little time playing the Aarklash: Legacy demo before I realized it was the kind of game I like.  This is a game that I would enjoy if it was stick figures or blue dots instead of pretty 3D people.  At the same time, this is a game that actually merits the use of those little 3D people because where they are in their little 3D world matters.

In Aarklash you are mercenaries for some banker guild sent to retrieve some forfeited collateral when the king decides that the bankers are no longer desirable and declares them outlaws.  You don't know this so you are surprised when you are attacked by knights.  Of course you are super-awesome so you smash all the "bad guys", take their stuff, and start to make your way to a guild hold.  I'm sure there is something mysterious going on behind the scenes and you'll save the world or whatnot.

But forget all that, this game has a real-time combat system that I - as a turned-based junkie - was surprised to really like.  Essentially they hybridized real-time and turn-based by simply giving you a pause button that you can press whenever you want.  You can stop at any time to think about the situation and enter commands, including sequences of commands.  As I implied above, where your units are on the battlefield matters, so you actually spend some time moving them around.  There are eight different characters - I've only found six so far - with different sets of abilities.  Each has a skill tree of sorts where you can make a pair of branching choices for each skill.  You can re-form your party and re-choose your skills any time you want, so you can customize the people and skills you have for each fight.

And I actually expect to be doing that.  I was given a choice of four difficulty settings - easy, medium, hard and something above hard - and chose medium to see what the game was like.  I've died several times now, and I can easily imagine how choosing the right people for the fight could matter in the future.  I've even died against trash pulls, not just bosses.

I like that the second setting from the bottom is hard enough that I'm not just breezing through the game, smashing everything.  It's not really too hard, and I haven't had to try a fight more than twice, but it's a nice contrast from something like Dungeon Siege 3 where if I didn't have it set to the hardest difficulty the game was a joke.  The second time I played through the opening sequence I smashed fights that seemed a little tricky the first time, so there is definitely space for me to get better and try to play the harder settings later.  For now I'm quite content to be a little stronger than my opponents and to get by on decent tactics rather than having to be perfect.

This game definitely isn't for everyone.  Even on the easy setting a tactical novice could easily get shut down by the first boss and be unable to progress.  I mean, I tried it and it wasn't hard at all, but judging by the "What happens if I just let my guys auto-attack" test, I think a five-year-old would lose hard.

Friday, 18 October 2013

Mad Myth Friday - Predicting the Future

Scientists discover a gene linked to a particularly deadly form of breast cancer.  The gene cancer is so aggressive and comes on so suddenly that it is seen as a death sentence.  A woman discovers she has the gene and decides that she will have a double mastectomy to live.  At first this is considered rash or even crazy, but gradually over time, and with public awareness campaigns society comes around to the idea.  More and more women decide to take this route until it becomes the norm.
What is the gene?  It is a gene that prevents breast cancer. 
A quick note on the above parable, it was written in 2005 or 2006, before I had heard of BRCA1 and BRCA2 and mutations of those.  It was long before Angelina Jolie brought the concept of having a preventative mastectomy into the public spotlight.  Rather, I dreamed the example up myself as a plausible future.

Of course in reality there will never be a gene that definitively causes or prevents anything.  But the message of the parable is the same.  At the time I was very up-in-arms about people with the idea that we are vehicles for our genes.  But the reality is that long before contemporary genetic engineering we stopped being controlled by out genes and started controlling them instead.  Evolution is results-based thinking, laws with predictive power surpass it.

Thursday, 17 October 2013

Oracle Review - Tawnos's Coffin and Basalt Monolith

A pair of artifacts which have been updated to meet the current rules. Neither have been done right.

Tawnos's Coffin
It's fair to say that instead of Tawnos's Coffin I could be reviewing Oubliette. My commentary applies equally to both.
You may choose not to untap Tawnos's Coffin during your untap step. 
3, Tap: Exile target creature and all Auras attached to it. Note the number and kind of counters that were on that creature. When Tawnos's Coffin leaves the battlefield or becomes untapped, return that exiled card to the battlefield under its owner's control tapped with the noted number and kind of counters on it. If you do, return the other exiled cards to the battlefield under their owner's control attached to that permanent.
Here is what Tawnos's Coffin should say:
You may choose not to untap Tawnos's Coffin during your untap step. 
3, Tap: Target creature phases out.  That creature cannot phase in as long as Tawnos's Coffin remains tapped.  When Tawnos's Coffin leaves the battlefield or becomes untapped, that creature phases in tapped.
I'm here to argue that Phasing the creature out is closer to the original wording of the card than exiling it and bringing it back. So let's go through the actual card.

The coffin did not say that it removed a creature from play, it said that the target creature was considered out of play. It did not say to note the number of counters on the creature and then put that many counters on when it returned, it said to leave the counters on. It did say to return the creature to play at the end, though I would argue that this was just the easiest way they could think of to say the effect ended.

What do these differences mean?

If a creature has a "When this leaves the battlefield" trigger, does the original wording of Tawnos's Coffin suggest it would trigger? To me the answer is no. The creature does not leave the battlefield, it is merely treated as though it is no longer there. Score one for phasing.

If a creature has a Paralyzation counter from a Dread Wight and it targetted with the coffin, when it comes back into play we know it should have the counter, but should it still be unable to untap? Should it still have the ability "4: Remove a paralyzation counter from this creature"? The original coffin says that you leave the counters on, so I would say we should expect it is still affected by the wight. The Oracle text says that the creature would get the counter but that the counter would have no effect. Score two for phasing.

Regarding entering the battlefield at the end of the effect. Was the intent of the original wording, for example, that a Clone would get to copy a new creature when it came out of the coffin? Is that how your play group would have understood it in 1994? To me, this is another point for phasing.

What about if you had Magical Hacked your Shanodin Dryad to Islandwalk, would the Tawnos undo that? The original card mentions only enchantments and counters, not changed words on the card. But then it also mentions only some of the ways the creature is out of play. It says the creature can't attack or defend, that it can't be targeted. It does not say that it won't be counted as a creature in play if Congregate is cast. The list description of what it means to be out of play on the card is meant to trigger our intuition. If counters remain on it and enchantments remain on it, then we would have suspected that alterations to the wording were meant to stay as well. A fourth point for phasing.

But wait, if it phases out that means that equipment and, sigh, fortifications on it phase out too.  The original coffin said nothing about that. Surely I can't advocate phasing out equipment when the card says nothing about that, can I?

Tawnos's Coffin was printed in 1994. Phasing was introduced in Mirage in 1996. Equipment was introduced in Mirrodin in 2003. That is seven years during which the coffin could have been phasing creatures out before equipment, let alone fortifications, ever came on the scene. Taniwha didn't start phasing out fortifications attached to your lands until 2007. If we can make the case that the coffin phases creatures out, then it has as much right to evolve with the phasing mechanic cards that actually have the word "phasing" printed on them.

The thing is that either way the wording of the coffin isn't right. It is trying to do something that the rules don't explain. That thing, however, is so similar to phasing that I would advocate having it be phasing rather than adding an additional section to the rules explaining what it means to treat a permanents as though it isn't in play - a section that would basically be a repeat of the rules for phasing, without the bit that things phase in during your untap step. But adding another section to the rules would be my second choice. Exiling and returning to play is too much of a departure from the printed coffin when better alternatives exist. Oubliette is a lot like Oblivion Ring in concept, but "when this deals damage you gain that much life" is a pretty similar concept to lifelink and they haven't gone and changed all those cards. In the end I score phasing 5 and exiling 0. I think there is room for argument on my points but it even being as charitable as I can I still get 3 to 2. That still gives phasing a lead by one point, and speaking of "one"...

A poor wording

Basalt Monolith
This wording looks simple enough, so it may be hard for you to figure out what I'm going to laud or deride:
Basalt Monolith doesn't untap during your untap step. 
Tap: Add 3 to your mana pool. 
3: Untap Basalt Monolith.
But take a look at all printings of the card and tell me what is wrong:

Do you see an activated ability to untap the monolith on any of these?

Okay, wait a minute, we update old wordings all the time. Scavenging Ghoul didn't have an activated ability on it's original printing either, but the rules team saw that it was really an activated ability to they reworded in that way in Fourth Edition. Surely they would do the same with the monolith.

Maybe they would have, but they never did. We saw with Mana Vault that when they reworded its untap ability to an activated ability they eventually went back and undid that. Of course Mana Vault's ability was clearly an upkeep trigger, not an activation. But the Monolith says you can untap it at any time. That sounds like an activated ability.

Except that's what Nafs Asp says as well. It's an ability that says someone can do something at some time.

One problem with old cards is that they didn't have the same kind of line breaks as we do today. But this is a formatting issue, not an issue of meaning. The old formatting was ambiguous, which is precisely the opposite of being certain. We can't say that Tawnos's Coffin wasn't supposed to gain the ability to untap until you use its ability the first time, we have to use our heads and think about how to read the card.

It seems like I'm arguing that the monolith should have an activated ability to untap it. After all, you are reading the original card and using your head and concluding that it has three abilities, just like the Oracle wording says.  I haven't convinced you.

So let's take another look at the original card.

Yes, Basalt Monolith is a Mono Artifact. There were four kinds of artifacts back in limited edition and through to antiquities. There were mono artifacts, poly artifacts, continuous artifacts and artifact creatures. What did all this mean? An artifact creature meant the same thing it means today. A continuous artifact and a poly artifact can basically just be read as "Artifact" with no changes to their wording. But mono artifacts have to be read differently. A mono artifact was one that you had to tap to use. That's why Mox Emerald doesn't say that you tap it to add one green mana to your mana pool. It's why Nevinyrral's Disk didn't say to tap it in limited edition but got a tap symbol in revised.

Strangely, Basalt Monolith does say that you tap it to use it, but it's not like the formatting crew were on the ball back then, as we've already discussed. It also says you can pay three to untap it. But if that were an activated ability then you would have to tap the monolith to use it. The monolith is a mono artifact.

So we know that in limited that was not an activated ability. While Revised brought in the tap symbol and did away with mono artifacts, it did not add untapping as an activated ability, despite the fact that we know that using the same formatting only a month later the Mana Batteries were printed in Legends with multiple activated abilities on the same card. There is nothing about revised monolith to suggest that there was a change from the limited edition that could not have had an activated ability to untap.

That means the untap ability of Basalt Monolith should be a special action and hence should not use the stack. Reasonable people might disagree as to whether the action could only be used once each time the monolith was tapped or whether it could be used any number of times after the monolith has been tapped once, but if your monolith comes into play tapped then you definitely shouldn't be able to untap it. Then again, since you haven't activated it, maybe it should untap during your untap step as well. You could try to make that point.

As a result of all of this, I am forced to give Basalt Monolith...

I mean, come on, I am being outrageous here

Wednesday, 16 October 2013

Heroes of Loot

This game sucks.  Okay, so I've been playing it a lot lately and I guess I'm having fun doing so, but really, it kind of sucks.

Heroes of Loot is a gauntlet-like with randomized levels.  People like to call everything with "permadeath" a rogue-like these days, but let's face it, back in the day *every* game had permadeath.  And aside from randomized dungeons this game has nothing to do with rogue.  By contrast, choosing whether you want to play the warrior, the elf, the wizard or the valkyrie and then entering the top-down-view dungeon and throwing your weapon at eveything you see is a lot like Gauntlet.  There are no monster generators and your health doesn't count down over time, but it's only like Gauntlet, it isn't actually Gauntlet.

You go through the dungeon killing things and collecting coins which you can spend at shops that appear one-per-floor unless there is a quest instead.  One of the monsters has a key which opens the door to the next level.  You can get a small number of items like a shield that gives you an ablative health bar, a cloak that makes you temporarily invisible and a regeneration potion that permanently allows you to recover health over time.

Yeah, how about that last one, eh?  Your health comes back *fast*, by the way.  This game is two games.  There is the game of no regeneration potion where you try as hard as you can to survive but ultimately die trying to fight your way into a room full of shooting attackers from a narrow hall.  Then there is the game of regeneration potion where eventually you die because you stopped paying attention when a minotaur spawned on top of you.  There is a cup of life which allows you to regain full life by standing next to a well for a while once per level that has a well.  It costs 399 and heals you to full every now and then, the regeneration potion costs 200 and heals you to full repeatedly every floor of the dungeon.  There is also the lens of secrets that allows you to see secret rooms.

About those secret rooms.  They have nine spaces each with a treasure on them.  The treasures regularly include a cloak and very frequently include a regeneration potion.  As far as I can tell there is no way to detect them by the appearance of the dungeon except in certain lighting so you basically get to run around every level of the dungeon looking for the hole in the wall that gets you your regeneration potion so you can be invincible.  Then when you get the lens of secrets you spend half the game basically invulnerable as well as invisible.

Except for the minotaurs will kill you in less than a second if you stand near them and sometimes spawn out of nowhere, so you have to constantly pay attention.

There are five classes, including the unlockable barbarian, which all basically play
the same.  Some classes have more strength but they appear to attack slower so its barely a noticeable difference.  Some classes have more magic but magic is pretty lame in any event since you can't die anyway and magic doesn't stop those minotaurs from appearing on you or help you react quickly to them.  Some classes need more or less experience to go up a level but after a few levels the only way to go up a level anymore is to get an experience scroll which puts you exactly up the next level - rather than say, giving you some fixed amount of experience.  Theoretically you could go up levels by killing monsters but you find enough scrolls that any progress you make towards a level will be wiped out before you get there unless you specifically avoid taking the scrolls.

After unlocking all the features of the dungeon, none of which make much of a difference at all, you get the ability to collect collection items.  And when you get six for the same class you get to start one level higher with that class!  This doesn't really mean anything.  It appears you can only collect one such item per playthrough since I almost always get one by dungeon level 10 or so and didn't get another by dungeon level 56.

So nothing in this game really means anything.  That's fine since you are just going through a dungeon killing things.  I'd just rather you started with the regeneration potion so I didn't have to hunt secret rooms every time I started a new game.

Alternatively I wish that playing well mattered, that there were real differences between the classes, and that there were more than three items that affected your game - more than two really since the cup of life doesn't change anything.  Oh well, I'll probably keep playing it anyway.

Tuesday, 15 October 2013

SolForge Creature Types

I had never paid much attention to SolForge creature types.  Dr. Frankenbaum cares about Abominations, Xrath cares about Zombies, there are a couple of legendary cards that care about Robots, and then there is cultivate, but other than that you could ignore what creature types things have.

First, there is, to me, the most egregious.  Spring Dryad is a Dryad, Lifeblood Dryad is an Elf Druid.  Oops?

There are several cards that are "Zombie"s and there are three different  "Zombie Necromancer"s, but then there is also Darkheart Wanderer who is just a "Necromancer."  Not a zombie or a human or anything.  Similarly, there are lots of humans, a few humans with jobs and a few jobs that have no race when the picture seems to suggest they are human.

Speaking of creatures that have a "class" but not a "race" type, Zimus is just a soldier at level one.  He is, however, one of two creatures that changes types as he goes up levels.  At level two and three he is a Zombie Solider.  The other creature that changes types is Chrogias who goes from seedling to plant to treefolk.  That means you can Cultivate a level one or a level three Chrogias, but you can't cultivate a level two one, even though it is clearly a seed.

Then there are the cycles of cards that seem to have mismatched types.  The savants are a Zombie Necromancer, a Technomancer Wizard, a Pyromancer Wizard and a Geomancer Wizard.  I find these types kind of outlandish, but shouldn't the Darkshaper be a Wizard as well?  Presumably "technomancer" "pyromancer" and "geomancer" aren't really going to be meaningful types in the future.  Perhaps they could just be wizards.  Or human wizards.  Or maybe a dryad wizard, a fire asir wizard and a human wizard.

The Avatars are a manticore, an abomination, a cyborg and a human druid.  That seems like an odd mix.  Manticore and Cyborg are both unique creature types.  The Rootforged Avatar is the only one with a job, and he's also one of only two humans in Uterra.  He also hardly looks human at higher levels.  Hellforged Avatar, on the other hand, has a relevant creature type that interacts with another Nekrium card.

Since this is a digital game, it is relatively simple for them to update card types if it becomes desirable to do so.  There are a few things that should probably be sorted out before they get out of beta.

Also, my imgur SolForge Album has some new shots in it if you are interested in that sort of thing.

Friday, 11 October 2013

Mad Myth Friday - The Shadow

A child sees a monster in the corner of his room and calls to you for help.  You arrive and reassure, "There have not seen a monster, it is only a shadow."  But the child has seen a monster.  True, there is no monster, but there is no shadow, either.
The easy part of coding it coming up with algorithms that do what you want.  The hard part of coding it putting in the semi-colons.  The even harder part of coding it counting pixels.

I'd like to have more facility to do original art, but it seems extremely difficult.  Particular sprite sheets.  The idea of making things that look right when flashed every 30 milliseconds is really daunting, and will probably never be within my capacity.  Code for user interfaces offends my sensibilities.  I think that for now it is good for me to be coding in html/javascript because the entire system is designed around what is displayed on the screen so I am forced to work with that early on.  Instead of thinking of abstract objects that have to have graphics attached to them at the end, I think of graphics and attach actions to them.

Thursday, 10 October 2013

Oracle Review - Mishra's War Machine

I don't get actively angry about old card wordings very often - by which I mean I probably do it as much as the rest of the human population put together - but we've got one today that is downright insane.

Mishra's War Machine
Let's get right to it:
Banding (Any creatures with banding, and up to one without, can attack in a band. Bands are blocked as a group. If any creatures with banding you control are blocking or being blocked by a creature, you divide that creature's combat damage, not its controller, among any of the creatures it's being blocked by or is blocking.)
At the beginning of your upkeep, Mishra's War Machine deals 3 damage to you unless you discard a card. If Mishra's War Machine deals damage to you this way, tap it.
Hello, Banding reminder text!

"If"?  If it deals damage in this way then tap it?  Are they serious?

This is a situation where a later printing is overwriting an earlier printing. Mishra's War Machine was inexplicably reprinted in Revised and Fourth Edition and this "if" nonsense was added. Now I know I admitted in an earlier review that more recent printings take precedence over older wordings, so there is a sense in which this is the right wording for the card. But I just can't condone it.

Remember Mana Vault? In that case they didn't use the most recent wording because that wording was flawed. The wording was flawed in part because it was just flawed - and I believe it was errata'd at the time - but the errata did not make it match the current oracle wording. They didn't errata it from an activated ability to untap to a triggered one.

Things are different now
So why go back to the earlier wording in the case of Mana Vault? The answer is fairly clear. The wording of the fifth edition printing was done the way it was because they were trying to work with the rules and the direction that they had at the time. If I have my dates right, power level errata were all the rage at the time, and it was sixth edition that brought in rules that we would recognize as the rules of Magic. Fifth edition rules were still mired in Interrupts and Mana Sources.

I can't tell you exactly why Mana Vault got its fifth edition wording, but I can tell you exactly why Mishra's War Machine got it's Revised and subsequent Fourth Edition wording.

My Personal Struggle With the Early Rules of Magic
I started playing Magic the summer of 1994. The Dark came out and for some reason it was crazy expensive in my town. I bought a few packs and got an Inferno and a Maze of Ith.

My play group instituted a house rule that if your mazed a Thicket Basilisk it wouldn't kill things over my objections. I was the first one to really build a deck instead of just playing with all cards of two colours plus all artifacts. Those really were the days. I could understand their objection that the maze was intended to remove the creature from combat. From a flavour perspective I get it - if the basilisk is lost in a maze then it's petrifying gaze isn't going to affect anything. Even still, in flavour draft I'd give this one to the basilisk. If the block already happened then its victim already saw its eyes before it was whisked away into the extra-dimensional pulsating-sphere maze.

What really ground my gears, though, was that in The Duelist magazine, our point of contact with Wizards in those pre-internet days, there was a rules question about using Maze of Ith on Serra Angel. To my amazement, the rules team - that is, Tom Wylie - said that you could not use the maze on an angel because it was already untapped.

Tapped = Full?
This floored me. It made no sense. If the maze was only supposed to target untapped creatures then it should have said, "target untapped creature" the way the Royal Assassin said, "target tapped creature." The ruling was based on their general rule that you can't tap something that is tapped and you can't untap something that is untapped. Well, of course you can't, but it seemed to me that if you couldn't do something then you just didn't do it. That didn't negate that the card said to do something else. After all, if you cast a Fireball on two creatures and then one of them gained Protection from Red, the fact that you couldn't damage that one didn't stop the Fireball from damaging the other. Surely, if your Demonic Hordes was tapped for some reason you still needed to pay {BBB} to avoid losing a land!

Well, no, you did not. For a while if your Demonic Hordes was tapped you did not have to lose a land, because you couldn't tap it so you stopped the ability cold, the rules team decided.

Of course I convinced my friends that you could use the maze on the Serra regardless of what the company who made the game thought. I used various examples to show that their ruling made no sense. The basilisk thing continued for a while, but really just until other people started making decks and realized that you could deal with stuff like that.

Just because something was the rules doesn't mean it was right. Like Ghandi and Martin Luther King Jr. before me, the tide of history was on my side. The rules eventually came to reflect my understanding of it.

Back to the War Machine
If the fifth edition Mishra's War Machine used the Antiquities wording, it would not have attempted to do 3 damage to you if it was already tapped. Of course the way they changed it had a different problem. If you prevented the damage then it would not become tapped. Either way they were altering the card - something they worried about less back then - but I guess they figured that the "if it does" wording was less confusing since their entire idea about how tapping worked was confusing to a lot of people - being totally wrong and all.

So as you can see, the Revised wording of Mishra's War Machine came out of a defect in the rules. They were trying to work around Tom Wylie's insistence about how tapping worked, and so they had to compromise the card. Well, those rules got fixed, and there is no reason to keep a bad wording that was the product of Magic's dark age.

This wording stings me, not just because I feel it is a product of bad rules, but because it was a product of what for me was the original sin of bad rules. My memories of the tapping rules are generally those of triumph, but this wording is still there, a final vestige of those rules, clinging to the great rump of Magic: the Gathering. We have nearly completed our second decade of this mistake, I wish I could say that I had hopes that we would not see a third.

Also, my lord this card is bad.

The worst of the worst (except for Chaos Orb, the actual worst)

Last week I said I'd have two antiquities artifacts this week. I'm conscious that this review is already quite long and that I might go on a very long rant about the next card too, so I'm going to leave this review here. The other card was Tawnos's Coffin, so feel free to speculate in the comments about what I'm going to say about that one.

Wednesday, 9 October 2013

Temporal Slices of Pirates with no Past or Future buying T-Shirts to avoid Infinite Loops

A long time ago Ziggyny had a post about pirates killing each other - or in this scheme choosing not to kill each other - for money.  Specifically the captain - pirate A - chooses a scheme for divvying up 100 coins.  The pirates vote - including the captain - and the captain wins in the event of a tie.  If the captain's scheme is voted in then it is executed.  If the scheme is not voted in then the captain is executed and the deputy captain - pirate B - takes over.  The pirates are named A, B, C, D, and E and decide who replaces a dead captain based on seniority.  Thankfully their seniority is coincidentally the same as the alphabetical ordering of their names.

Now we start talking about rational, self-interested beings.  The pirates all want to get as much loot as possible and know that the other pirates want to get as much loot as possible.  Also, in this story, the pirates value their lives at precisely nothing - rather than valuing them at quite a lot - so I don't really know why the bit about them getting killed is included.  It seems like the puzzle would be less confounding if, upon losing a vote, pirate A simply was excluded from this round of treasure allotment.  After all, that would remove the implicit gain to be had by killing a colleague and thus having fewer people to split the loot next time - the game doesn't say its iterative, but the set-up makes it easy to think of it that way.

To find the solution we think back from the two pirate scenario.  With two pirates the captain splits the loot 100-0 and votes for the split and wins the tie so D gets all the loot and E gets none.  Clearly, E must avoid this scenario, so E should be willing to take even one coin to make sure it doesn't happen.  Induction quickly brings us to a split of 98-0-1-0-1 because C and E will be forced to take it.

For a while I've had a bit of a problem with the concept of a "rational, self-interested" being.  Obviously in real life rational self-interest probably leads to a more equitable split since the captain knows he is going to have to work with these other pirates in the future.  How motivated is pirate B going to be to plunder when he knows he never gets anything?  But we are supposed to limit ourselves to the assumptions stated in the game so the pirates are temporal-slices of pirates who have no future and no past but nonetheless care about how much gold they get.

I said it was odd that the game includes the detail that the pirates die since clearly we are not meant to think of them as valuing their lives.  In the analysis here the value of their life doesn't matter, but it's still a little strange.  I also find games like this don't specify certain details, like that time flows forward.  Okay, so we normally assume that time flows forward in most situations, and maybe it would be up the game to specify that it doesn't.  But let's consider what it means for time to flow forward.

Newcombs paradox is a scenario that specifically questions our notion of time flowing forward.  A super-intelligent alien claims to be able to perfectly predict human behaviour based on a brain scan.  To prove this he sets up a game.  Box A is a clear glass box with $10,000 in it.  Box B is an opaque box.  The human has two choices: either pick box B or pick both boxes.  If the alien predicted that the human would pick just B then there is $1M in box B, otherwise there is nothing.

Again, if we assume time flows forwards then there is a very obvious solution for the human.  Both boxes always contain more money together than box B does alone, so the human always picks both.  But the alien being able to predict the human's behaviour calls that idea into question.  Let's make this clearer.  The "predicting behaviour" thing is a specifically intended to raise philosophical questions.  Instead of claiming to be able to predict behaviour, the alien demonstrates before the game is played that it can travel through time and explains how time travel works in a way that satisfies you that it will effectively - by your understanding of time - be making the choice of whether to put the money in box B after you choose which option to take.  Now it is obvious that the human should just pick box B.  The idea that picking both is better relies heavily on time going in one direction - that how much is in box B is completely determined before you make your choice.

So back to the pirates.  By time flowing forward, we mean that the pirates can choose their strategy based on information in the game at each turn.  Just like in Newcomb's paradox, as long as you have information about the past - that the money is either there or not - you can make a decision based on that information.  If you can't rely on that information you use a different strategy.

So suppose that all pirates agreed ahead of time to strategy S1: [If they get floor(loot/#pirates) then they vote yes, anything less they vote no.  If they get to split the split it evenly {here evenly will mean giving any extra that cannot be divided evenly to the person dividing it}.]  One clever pirate realizes that the game takes place over time.  Can that pirate improve his lot by changing strategies?  Pirates B through E can't.  Pirate A can: simply give two other pirates 20 and 60 to themselves.

What if they use S2: [Vote yes for floor(loot/(ceiling(#pirates)).  Split by randomly giving that amount to two other pirates and keeping the rest.]  Now pirate A, C, D and E can't improve their strategy by noticing how time works, but pirate B can.  Pirate B can decide to vote no.  Then when he gets to split the loot he splits it 50-50 between himself and one of the others and gets 50 instead of 33.

This means that these strategies are not in "Nash Equilibrium."  A strategy is in Nash Equilibrium if no player can improve upon it by unilaterally changing their own strategy.  Note that Nash Equilibrium doesn't mean good result.  In the game of two cars driving in opposite directions on the street, there are three Nash Equilibria: both go left, both go right, and both flip a coin.  That last one results in a head-on collision 50% of the time.  A Nash Equilibrium means that no player can better their payoff without another player also changing their strategy as well.  I have every reason to suspect that by allowing each pirate to iteratively change their own strategy we could end up with the 98-0-1-0-1 split given in the simple analysis.  That *is* in Nash equilibrium.  If anyone changes their strategy unilaterially then they get equal or fewer coins.

So why would we talk about Nash Equilibria instead of simply solving the question as we do above.  The answer is basically because of Nash's Existence Theorem that proves that in games with finite players and finite choices there *is* a Nash Equilibrium.  The problem with doing analysis in an ad hoc way, no matter how convincing, is that with time flowing forward and players being able to make decisions based on information in the game and based on what they believe other players will do, you cannot actually prove that there is a solution.  The proof above looks pretty good, except that I could ask, "But what if pirate E votes no to the first vote?"  Well, that's easy, you say, then pirate B splits 99-0-1-0 and E gets nothing so it's worse for E.  

But now everyone has the information that E voted no.  How does that change B's assessment of the right way to split now that he knows that giving a pirate 1 coin doesn't necessarily buy their support?  We don't know that there even is a solution.  By voting no player E may put the pirates into an infinte loop.  The rules of the game didn't say that they were given a finite amount of time to make up their minds how to vote, so that may destroy the entire game.  At any rate, we don't know what would happen, and if we don't know what would happen we can't promise that it is a worse result for pirate E, who is the one who has to make the decision.  The problem with the solution that I outlined is that it both assumes time flows foward *and* relies on not getting certain kinds of disturbing information about the past.  If it gets to just pirate D and pirate E then pirate E gets 0 - that's for sure, but how sure are we that taking one coin instead of zero is the strategy that gets you the most loot?

After all, isn't a better strategy for E to demand 2 coins instead of one?  If that is E's strategy and player A knows it and plays rationally then player A gets 97 and player E gets 2.  Sure, you can say that E knows the split wasn't 97-0-1-0-2 by the time it gets to him so he should go ahead and take his one.  But if pirate A is Newcomb's alien then Pirate E has to be ready to vote no to one coin in order to get his two.  The pirates don't have to be able to communicate ahead of time to realize this possibility, and assume that there is perfect information and a perfect ability to reason out the other pirates' strategies they all already know this problem.  They are at a standoff and pirate A never splits at all.

Suppose that all pirates play S3: [Split the loot evenly.  If it's an even split, vote yes, otherwise vote no.]

Now can any pirate improve their standing by fixing their strategy?  No, they can't.  If player A doesn't split it 20-20-20-20-20 then he gets zero and everyone else gets 25.  If any other player changes their strategy it doesn't matter because they will just be outvoted on the first round anyway.  This is a Nash Equilibrium.

So, suppose our temporal slices of pirates show up in the game wearing T-shirts printed with "Even split or I vote 'no'."  The opening problem didn't say anything about how the pirates were dressed, but we were meant to assume something, so I guess it's up to me.  Giving up their strategy in advance and sticking to it gets players B through E 20 instead of 0.5 each - just like knowing that the alien can actually see the future gets you a million dollars instead of just $10k.

Most games seem to favour the player who goes first.  There isn't a particular reason that this is true, it can be a lot of different things.  As we've seen here, sometimes the reason is that the first player gives information to the second player that the second player can act on.  It seems strange that this might put the second player at a disadvantage, but in Newcomb's paradox - and possibly also in the pirate game - it actually makes the second player much worse off to know about the first player's play play.  Fortunately in a game where time does flow forward the second player has an out - they can predetermine their actions or determine them at random up the point that having the extra information is no longer a detriment.

The non-first players can only actually gain this advantage, however, by sticking with the plan.  A being of rational self-interest has no ability to stick to a plan even when it is rational and self-interested to do so.  Ultimately for such beings there is Nash Equilibrium and there is nothing.  Of course, for these pirates, perhaps an infinite consideration of the problem is the best outcome: as soon as the problem ends they wink back out of existence.

Monday, 7 October 2013

Cookie Clicker - Chain Cookies

I did an little analysis of cookie clicker before to explain how the late game is dependent on clicking.  Well, here comes some more, and it's really good news - kind of.

Generating cookies in end game was heavily dependent on alternating between Frenzy and Lucky cookies to get massive quantities of cookies when the duration of frenzy overlapped with the effect of a lucky cookie.  I ignored chain and click frenzy because they were rare and basically bad.  But they aren't bad at all any more.  Let's talk about them for a moment.  I'm going to talk about these new calculations using 12B Cps, which is about how much you will have with the current upgrades in the game assuming you are at end game and just trying to get your last 10 or so condensers before acquiring your last 20 or grandmas with 250 heavenly chips.

Click frenzy multiplies your click value by 777 for 26 seconds.  Thanks to a new upgrade, your click value is 5% of your Cps plus 4 plus 132.6 times the number of non-cursor objects you own which will be around 900-ish so that's 119344.  If your Cps is 12B then your 5% of that is 600M so... oh, right, your click value is 5% of your Cps.  In a quick test I think it's pretty reasonable to click 5 times a second for 26 seconds - we'll call it 25 because you probably miss a second realizing you've hit the rare event - so that's 125 clicks at 5% of your Cps is 6.25 times the 776 bonus you are getting is 4850 seconds of production.  That's a lot.

Of course, like lucky, click frenzy can overlap with a frenzy, which would multiply its effect by seven because your click value is just a fraction of your Cps.  Unlike lucky, though, you need the frenzy to last beyond the instant you get the click frenzy or it may just apply partially.  If you click frenzy with 12 seconds left of frenzy then you get times-seven for 11 or 12 seconds and no times-seven for the remaining 14 seconds.  Thanks to Markov chains and uniformly distributed probabilities, I can say that 39% of your click frenzy time will be under the effect of a frenzy.  So the total value of a click frenzy is about 16,243 seconds of production.

That's a lot and not to be missed in the calculation even though it is infrequent.  At this level, assuming you have the requisite cookies in the bank to maximize your lucky clicks, you are producing about 18.9 times your Cps while actively playing without considering Click Frenzy.  Click Frenzy brings that up to 26.6 times.

What about chain?  Chain used to have a 10% chance of stopping every chain cookie that appeared after the fourth one, and at maximum gave 13 chain cookies, the last of which was worth 6.66 trillion cookies.  That sounds like a lot but it isn't.  At 12B Cps a lucky cookie is worth 14T without an overlapping frenzy, over 100T with one.  Since just over 50% of lucky cookies have overlapping frenzy, the chain is prety miserable.  Especially since a chain only has 43% chance of paying that much.

But the 13 digit limit has been upped to 17, which is 66 quadrillion.  To compensate the chance of ending went up to 13% and if the cookie gives you more than 25% of your current holdings then the chain automatically ends.  Of course that means if the cookie gave you 24% of your current holdings then the chain might continue, and the next cookie would be worth about 240% of your current holdings, with no limit by Cps.  Does that sound insane?  Sure it does.

So, if you have 12B Cps you ought to have over a quadrillion cookies in the bank.  Since one quarter of that is 250T, a cookie with a value of 666T would automatically end the chain.  Still, that means getting 740T cookies out of the chain.  That's more than 60k seconds of production, which is the first time I've felt the need to abbreviate the number of seconds of production an event generates with a "k".  Of course each link in the chain is only an 87% chance, so the value of a chain cookies is actually only 17,923 seconds of production.  But that's still a lot.  The chance of getting a chain cookie is only about a half percent, though, so that only brings out total production up to 27.5 times your list Cps.  More, but not a lot more than the value without chains.  But what if you stored up 2.67 quadrillion cookies so that the 666T cookie did not automatically end the chain and instead had an 87% chance to lead to the 6.66 quadrillion cookie?

Instead of averaging just shy of 18k seconds of production, the value of a chain cookie expands to just shy of 156k seconds of production.  This increases your golden cookies adjusted Cps to 34.3 times your list Cps.  That's about 25% more than if you didn't save up the massive bank.

But all of this math has always had the unstated assumption that you were not in grandmapocalypse mode.  That makes sense because your cookies used to come from frenzied lucky cookies.  You can't even get frenzy in the grandmapocalypse, and more than half the time you are going to get a cookie that is actually bad.  How could this possibly be good?  Well, it increases your chances of getting a chain dramatically from half a percent to 9.3%.  Of course get can get clot which can halve your lucky cookies and click frenzies.  You can get ruin which loses you 10 minutes of production.  All of this adds up so that if you have minimum frenzy/lucky cookies in the bank with 12B Cps then turning on the grandmapocalypse reduces your cookie production from the 27.5 times list mentioned above to only 17.7 times list.  That's not good.  What about if you save up 2.66 quadrillion cookies and activate the grandmapocalypse?  Then your production, instead of the 34.3 times list mentioned above is 104.5 times list.  That is good.

Okay, let's just go over that again.  If you have 12B Cps, and you all in full on grandmapocalypse with all upgrades, then the actual amount of cookies you take in per second of play is not 12B but 1.2T.  That means if you play for an hour you'll rack up 4.3 quadrillion cookies.  Of course, what that really means is that if you play for an hour you'll get an average of 24 chances at a 9.5% shot to get a 25% shot at getting 7.4 quadrillion cookies.  The rest of what is happening is kind of miniscule by comparison, accounting for only about 6% of your total income.

But if you can average 4.2 quadrillion in an hour, then you could reasonably bank 26.67 quadrillion cookies so that you could hit a 66 quadrillion chain.  That would multiply your income by about 8.1 times, meaning you could average more than 32 quadrillion an hour.  Even 100B Cps would account for less than 5% of the total cookies per hour at this level.  The breakpoint is actually around 466B Cps.  At that amount you should ditch the chains and return to lucky/frenzy.

At the beginning I said this was all good in a way.  The way it is good is that all we care about is making a lot of cookies.  But this kind of destroys the game.  You don't need hundreds of condensers or kittens or new upgrades or forthcoming dungeons.  All you need is a psychotic hivemind of old ladies and a couple of quadrillion to kickstart your efforts.  Once you have that, your Cps basically doesn't matter anymore.  Plus progress is unbelievably random.  It is quite possible that one person will hit two max chains in an hour while another person goes on hours and hours without getting a single one.

You can see how that is a problem.  Wait did I say you can get more cookies?  Oh yeah, no problem.

And speaking of no problem, it took a couple of days between when the 13 digit limit was removed and when the 17 digit limit was implemented.

Count those digits again