slightly later in the same round

 

Tournament #15120: Friday like Soldiers Current Round: Round 2. (organized by TheUniverse)

Skills in this game: X Swing

Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: RandomBM (4 8 10 20 X)   Score: 38 (0.6 sides)   Rounds Won/Lost/Tied: 0 / 0 / 0 (Out of 3 wins)
Your Captured Dice: 20-sided die, 6-sided die

4-sided die	20-sided die		8-sided die
2	5		6 Captured last turn
4-sided die	20-sided die	X Swing (with 4 sides)
3	19	2

Opponent: TheUniverse *My Birthday*
Button Man: RandomBM (4 6 20 20 X)   Score: 37 (-0.6 sides)   Rounds Won/Lost/Tied: 0 / 0 / 0
Captured Dice: 10-sided die, X Swing 5-sided die, 8-sided die

two obvious options -- 

ONE: take his d4(2) with MY d4(2), hope to roll  a 4

force him to roll his d20. I'd then have 1 chance in 5 he'd roll low enough to be captures.

that gives me 1 chance in 20 -- actually, still more, since even if my d(4) rolls low, he has to either

roll his d20 or give mine one last chance of rolling above 19  -- this is 3/4* 1/20, for a grand total of 

7/80, or 8.75%

TWO:  take his d4(3) with my d20(5).  1/10 of the time I roll 1 or 2 and it's over; 1/20 I roll 3. He'll take my d4 and 3/4 of the time I'll have one more chance to roll the d20, with 1/20 chance of winning.

 15/20 I roll 4-18, and then I'll certainly get one more chance to roll above 19, with 1/20 chance of winning;

1/20 I roll 19 and he has to take me, I could win if he rolls 1 or 2 [1/10 chance], or if he rolls a 3

and my next attack rerolls to a 4 [1/20 * 1/4 chance];

and the final 1/20 I roll 20 and I win.

what's that?  1/20*(3/4*1/20) + 15/20 * 1/20  + 1/20[1/10 + 1/20*1/4]  + 1/20 = 38/400 = 9.5%
that's pretty close!