So: In the below situation, you are me ("ElihuRoot"). [And, for those unfammiliar with buttonmen.com notation, the 20-sided die on the top right has just been captured by Anders]. You have eight different possible power attacks, and one possible skill attack. What is the move that maximizes your probability of winning this round?
Button Men Game #599271
Skills in this game: Reserve
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Diamond (4 6 12 20 r8 10 r10 20) Score: 52 (1.3 sides) Rounds Won/Lost/Tied: 1 / 2 / 0 (Out of 3 wins)
Your Captured Dice: 20-sided die, 12-sided die
| 4-sided die | 6-sided die | 20-sided die | 10-sided die | 20-sided die | |
| 3 | 3 | 17 | 10 | 1 Captured last turn | |
| 6-sided die | 10-sided die | 20-sided die | |||
| 6 | 1 | 19 |
Button Man: King Endymoin (6 10 20 20 r6 r10 12 r20) Score: 50 (-1.3 sides) Rounds Won/Lost/Tied: 2 / 1 / 0
Captured Dice: 12-sided die, 20-sided die
5 comments:
Right or wrong, this is how I would play it -and why. Assume your d20 showing 17 is lost. You could power with it and hope for a 20, but you're better off keeping it a high value and not giving Anders the opportunity to take it with a lower die. Keep your d10 showing 10, so you have the best odds of beating his d20 (after he takes yours). That brings us to the question of 3 & 3 vs. 6 & 1. I would skill attack the 6, as it is easier to outroll the 1 (in fact, you could not outroll the 6 at all).
Ah, very interesting. Ordinarily, I would have done as muda said. But given that it's posed as a puzzle, I noticed that the skill attack gives you a 37.5% chance of rolling a 1, whereas power attacking with the 10 showing 10 only gives you a 10% chance of rolling a 1.
Since you need to capture the twenty-sider to win, and it seems the best way to do that is to force him to re-roll it, we want to avoid letting him attack with his other die -- thus, power attacking with the 10 seems like the best choice.
I would skill attack with the two 3s and take his 6 sider hoping that my dice would both roll higher than a 1 forcing him to roll his 20 sider on his next turn.
Of course, you are playing against Anders which means you're probably going to lose anyway.
The path towards winning is to capture Anders' D20, and to force him to reroll it with our dice as high values as possible. If the D20 and D10 stay 10 and higher, then when he rerolls the D20 we win (at least) 50% of the time. That seems like the best scenario.
Jota's comment suggests rerolling the D10...but I think that would leave us with very low valued dice when he rerolls his D20.
Others suggest skill attacking the 6, giving about a 1-in-3 chance of rolling a 1, which lets him reroll the D10, which probably would force us to reroll the D10 or D20. Probably not great. So it's a 2-in-3 chance of giving us a 50-50 chance of winning.
What about using our D20 and capturing the D6? If we reroll 10 or higher, we have our 50-50 win again. If we reroll 1, we're probably hosed. But if we reroll 2-9, he has to reroll his D20.
If he takes our D10, we can still reroll our D20 by taking his D10. (Don't know odds, but it feels 50-50 as well.) If he takes our D20, we win again 50% of the time.
So it seems like a 1-in-20 chance of losing, 19-in-20 chance of having about 50% win.
So, I recommend D20 captures D6.
What did you do?
Interesting responses, all! I'm pretty sure devious's move is the best choice, and his reasoning is fairly sound (though the math is only approximate). You should take Anders's 6-sided die with a power attack from your (my) 20-sided die.
You VERY much want Anders to have to reroll the 20-sided die, and the sooner the better, while you still have a moderate number of dice. rolling the 20-sided die will turn out badly 5% of the time (you roll a 1: he can then recapture with his 10-sided die. You still have some chance of winning, since you'll be able to capture his 10-sided die no matter what and he'll then have only the 20-sided die left -- but you'll only have a few small dice and not much chance of catching him).
Another 5% of the time, you'll roll a 20, and he'll have to capture you with a skill attack with his last two dice -- this is not the best outcome, since you'd rather his 10-sided die stayed with its value of 1 -- but it's still fairly good, with at least a 60% chance of taking the 20-sided die (if you go for it: if his 10-sided die rolls a 10 and his 20-sided die rolls a 1, you might consider taking the 10-sided die first, etc.). Even in the worst case, you can capture the 10-sided die and he'll have to reroll the 20-sided die in the final rolls against your small dice.
the remaining 90% of the time you force him to reroll the 20-sided die and leave his 10-sided die with a value of 1. if he takes your 20-sided die at this point, you've got a 60% chance of being able to capture his 20-sided die on the next turn -- and again, even if it doesn't happen, you have a chance on subsequent turns. [the calculation is a little more complicated because you still have consider his 10-sided die; for that matter, if, when you reroll your 20-sided die in capturing his 6-sider, it rolls low, Anders might be better off taking your 10-sided die and allowing you to reroll your 20-sider in capturing HIS 10 sided die... maybe that's for a future post...]
I actually won this round (but then lost the match in the fifth round). Still, you're actually in a fairly good position here -- IF you capture the 6-sided die with the 20-sided die!
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