but what maximizes my chances? taking the 1-sided die with my 6 sided die? or taking the 20-sided die with the 12-sided die?
OK, maybe that's too easy. But what if I was only behind by 20 sides instead of 25 [i.e. keep everything the same
in the game except pretend the 2-sided die I've captured already was actually a 9-and-a-half sided die. ok a 10 sided die,
it doesn't change the argument -- just keep the dice in play the same, but somehow give me another 7.5 or 8 points]. Would that
change anything?
3 comments:
I don't think it really matters whether you are behind 20 or 25 points. Either way, you have to be able to take the d10 and d20. The best way to achieve that is to keep your d12, and thus the obvious play is to take the d1 with your d6.
Hmmm. I think you're probably right, but I do think it's subtle: Note that if you're behind by only 20 points here, it is POSSIBLE to win by keeping just the 6 sider, so taking the 20 sided die NOW, even if it is lost -- you are hoping it either rolls 12 (best case), or that it rolls 4-11 (next best case, forcing the 10-sided die to reroll, with a 30% chance you can capture it next turn). Instead if you take the 1-sided die now, McC is certain to reroll his 20-sided die, 40% of the time he wins outright, and even if he doesn't you face a daunting series of rolls to capture it, the 10-sided die and then the 2-sided die. It's probably true that your overall chance higher here, but maybe not by that much.
In fact, doing the brute force math gives only a 5.8% chance of winning if you take the 20 sided die now, vs. a 22.1% chance if you take the 1 sided die with the 6-sided die.
And if you give me 8 more points and do the computation, the 22.1% chance remains the same, and is still the best option, but the 5.8% chance increases to 16.9%.
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