Sunday, January 12, 2020

Is this subtle? I don't want to do the math.


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:

James said...

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.

Ted said...

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