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A little brainteaser for all you 'elite' Kdice players out there :p
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the brain wrote
at 2:34 PM, Thursday April 23, 2009 EDT
Ok, this is given: you are playing a 1vs1 version of kdice with only 2 lands. Each player starts with 2 dice.
You are the first to take a turn. Assuming that your opponent will play optimally, what is your best move? (attack 2vs2, wait for an 8 stack, or maybe something else? :D) I have a statistical proof of the best strategy, I just thought it might be an interesting challenge for you people who claim to 'know' the game ;). (And yes, I know that this is hardly a realistic situation, but if you give it a try you might appreciate the complexity of the statistics involved) |
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lesplaydices wrote
at 2:38 PM, Thursday April 23, 2009 EDT Wait for him to attack you.
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saetep wrote
at 2:44 PM, Thursday April 23, 2009 EDT And then? Assuming he knows you're waiting then he will wait to have dice saved up. You have to 8v8 eventually.
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Mazaman wrote
at 2:58 PM, Thursday April 23, 2009 EDT wait for 8 stack and +6 dices, then attack
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Shivan Dragon_ wrote
at 3:03 PM, Thursday April 23, 2009 EDT you should attack first. you have a 44% chance of winning the attack. if you lose, you still have a 2 stack then your opponent will only have a 44% chance of winning if he attacks. if your opponent builds, he can never use his +1 advantage in dice, and the game will advance to a 8v8 outcome where your opponent is at a disadvantage if he attacks first. your chances of winning are much better than your opponents, essentially you get a free turn and just lose your first-player advantage. assuming that your opponent will play optimally, the only attack that will be a 2v2. but i dunno. i haven't done any game theory stuff in a few years.
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Angryhat Samuel wrote
at 3:09 PM, Thursday April 23, 2009 EDT what top guy said.
if you have a 2v2, you always take it. |
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Mr.Eko wrote
at 3:41 PM, Thursday April 23, 2009 EDT 2v2 and hope for a decent restack :)
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montecarlo wrote
at 4:29 PM, Thursday April 23, 2009 EDT 2v2 is 44% chance. 8v8 is 47% chance. so wait for the 8v8, with the +6.
infinite 2v2s chance of winning = 0.44 + 0.56^2*0.44 + ... + 0.56^2n*0.44 = 64.1% infinite 8v8s (+6) chance of winning = 0.47 + 0.53^2*0.47 + ... + 0.53^2n*0.47 = 65.4% if you 2v2 then he doesnt do shit, then you 2v3, you have a 59.6% chance, but you get more street cred. in the end, though, kdice isnt full of impersonal robots. if you wait for the 8v8 (+6), then the gallery will hate you, and heckle you to death, and it will have repurcussions in future games (negative ones). if you take the 2v2, then the 2v3 afterwards, it will have positive repurcussions. and, lets be honest, the only reason you would wait 12 turns to gain a +1.3% chance is if you really hate the person or if you direly need to win (i.e. if you lose, you lose out of a tourney or something). god i wasted too much time thinking about this. and i bet im still wrong. |
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wiggin1 wrote
at 4:44 PM, Thursday April 23, 2009 EDT Shivan is right. I almost missed it, funny question.
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wiggin1 wrote
at 4:51 PM, Thursday April 23, 2009 EDT To all those who think it's better to wait for +6 dices. Let's play a hypothetical game:
Situation 1: I go first I 2v2. 44% chance of winning. You build until you have 8 stack and + 6. When I have an 8 stack I 8v8 you. If I win I win, otherwise, I lose. 8v8 has 47% chance of winning. So overall I get 1 -.56*.53 = 70.32% chance of winning Situation 2: You go first You build to an 8 stack with + 6. As soon as you get an 8, I 8v8 you. You have 1 - .47 = 53% chance of winning |
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r0n wrote
at 5:19 PM, Thursday April 23, 2009 EDT The answer is...
FOUR!? |
