I have four possible attacks here. *probably* I should use the #(8), as I really have to get the 10-sided die to reroll to have any chance of victory -- but should I take the 4-sided die or the p(6,6)?
I can afford to lose one of my dice if I capture all of his, or even *both* of my dive do long as I capture the 10-sided die but NOT the poison.
2 comments:
The route to capturing all irilyth's dice except his p(6,6) is awfully difficult in my brief assessment when compared to trying to capture all his dice.
But note that if I take the (4) with my #(8) and roll 6,7,8, i. would have to capture with his (10) and if he rolls 1-6 I'll take the (10) with my #(6) and hope to roll 1-5. Not great odds, just 3/8 * 6/10 * 5/6 = 3/16 = 18.75%
Still, the other way is not so great, either. if I want to capture ALL his dice without losing more than one, I have to first take his p(6,6) with my #(8) and roll 4-8... then he takes one of my dice with his (10) [though which should he take? if the #(8) rolled 6,7,8 he'll take it for sure and win for sure if he rolls 7-10, if he rerolls 4,5,6 I'll take his (10) with my #6 and must then roll 4,5,6 to win; but if his (10) rolled 1,2,3 I could take the (4) and hope to roll higher than the (10). On the other hand, if my #(8) rolled 4 or 5, it might make more sense for him to take the #(6) and hope to reroll hgiher than my #(8), though I get once more chance after taking the (4)... the cases are monotonous, and I don't want to do the math, but I think there's a good chance this comes in below 3/16.
I mean consider my initial roll of the #(8) after capturing the p(6,6). 3/8 of the time I lose outright by rolling 1-3. another 3/8 of the time I roll 6-8 and he recaptures with the (10): of these, I lose outright 40% of the time when he rolls 7-10, and another 40% of the time he rolls 3-6 and I'll go one to lose half of those, and then 10% of the he rolls 2 (and I'll lose only 1/3 of those) and 10% of the time he rolls 1 (and I'll lose only 1/6 of those)... overall, when I roll 6-8 on my #(8) I go on to lose (40 + 20 + 10/3 + 10/6 = 65% of the time). so I'm already losing 3/8 * 100 + 3/8*65 = 61.875% of the 75% of the time I roll either 1-3 or 6-8 on the #(8). I don't have the patience to finisht he math for the times I roll a 4 or 5 on the #(8), but it must be WORSE than 65% (he could just take the #(8) even though taking the #(6) is probably better) -- this is CLOSE, but I need to do the math to be sure: the threshold is 77.5%, if it's worse than THAT, then the other approach is better
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