Strategy for the game of Buttonmen. Maybe other buttonmen-related topics.
Monday, October 12, 2020
Priorities
It's AD's turn. Which move(s) will maximize his chance of winning? Which move(s) will maximize his chance of not losing?
1 comment:
Scipio
said...
I'm still working on a more complete analysis, but I'm favouring p(X=8) takes (2) for at least one of those two goals. This forces you to take a poison die. If you take zp(12), you can't use your (4):1, so the p(8) can capture that later. If you take the p(8), zp(12) has at least another capture. If you take the second poison die afterwards, AD captures your remaining non-Stealth die with his (20) giving him a 19/20 chance of winning. If you don't, AD captures your remaining non-Stealth die with his poison die, giving him a 100% chance of winning/drawing, depending on which poison die you took. So all in all, a better than 19/20 chance of not losing.
A similar move would be capturing (4):3 with zp(12): This allows guarantees a possible capture with a poison die later. I think those moves are actually (almost?) equivalent in terms of success probability. I suspect that this is the best (type of) move to avoid losing: Capturing with the (20) immediately exposes it, obviously. Other captures with a poison die risk leaving one poison die low, allowing the other to be captured and thus forcing a capture with the (20).
The chance of winning isn't extremely high here though, there might be a better strategy for that.
1 comment:
I'm still working on a more complete analysis, but I'm favouring p(X=8) takes (2) for at least one of those two goals. This forces you to take a poison die.
If you take zp(12), you can't use your (4):1, so the p(8) can capture that later.
If you take the p(8), zp(12) has at least another capture.
If you take the second poison die afterwards, AD captures your remaining non-Stealth die with his (20) giving him a 19/20 chance of winning.
If you don't, AD captures your remaining non-Stealth die with his poison die, giving him a 100% chance of winning/drawing, depending on which poison die you took.
So all in all, a better than 19/20 chance of not losing.
A similar move would be capturing (4):3 with zp(12): This allows guarantees a possible capture with a poison die later. I think those moves are actually (almost?) equivalent in terms of success probability.
I suspect that this is the best (type of) move to avoid losing:
Capturing with the (20) immediately exposes it, obviously.
Other captures with a poison die risk leaving one poison die low, allowing the other to be captured and thus forcing a capture with the (20).
The chance of winning isn't extremely high here though, there might be a better strategy for that.
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