And is this situation any muddier? Would you take my 10-sided die or my 20-sided die? Does it make much difference?
* Next Turn * Player: Gryphon * Next Turn *
Button Man: CynCyn Score: 34 (3.3 sides)
Rounds Won/Lost/Tied: 0 / 1 / 0 (out of 3 round(s))
Captured Dice: 12-sided die, 6-sided die
| Dice | 6-sided die | 20-sided die | 6-sided die |
| Value | 3 | 20 | 1 |
| Dice | 10-sided die | 20-sided die | |
| Value | 9 | 6 | |
Button Man: Sailor Jupiter Score: 29 (-3.3 sides) Rounds Won/Lost/Tied: 1 / 0 / 0
Captured Dice: Doppleganger 10-sided die, X Swing 4-sided die
Results from last turn:
ElihuRoot is performing a power attack with a 20-sided die showing 10,
targeting Gryphon's X Swing 4-sided die showing 4.
The 20-sided die is rerolled and the new value is 6.
3 comments:
Good one. Intuitively, it looks like you should take the higher value (the D10).
If you take the D20:
- reroll 10-20 you win (55% chance)
- reroll 1-9, he takes your D20
- If his D10 rerolls 5-10, it's likely he wins
- if his D10 rerolls 1-4, you win.
So, approximately, you have about 75% chance of winning.
If you take the D10:
- reroll 1-6 you're pretty likely to lose (>75% chance)
- reroll 7-10 you're still likely to lose (>50%) since he'll take your D6 showing 3 and could roll higher than you
- reroll 11-20 you're likely to win (>50%); the higher you roll, the more likely.
Without doing the calculation, this feels like about 50-60% chance of winning. (Ted?)
So I'd take the D10.
Whenever it's a D20 v. D20 rerolling match I always think of it as about a 50% chance. Since his D20 has a way out to reroll, it's not really at a "6". I'd consider it as being at a "10.5", an average roll for a D20. That's why you should take the D20 first.
Correction:
"So I'd take the D10."
I meant the D20, of course!
-dvs-
Devious is absolutely right, and his approximations for the math are about right, too -- (you have about 74.35% chance of winning by taking the 20-sider, and 57.75% if you take the 10-sider. There are a few subtleties in getting it exact, but they don't make any difference in the decision.)
I sort of knew to take the 20-sider instinctively, but until I worked it out, I thought the two were fairly close -- but a difference of 16.5% is substantial.
If you want to see the full computation:
take D20
11/20 roll 10-20 he has no chance of winning
1/20: roll 1, he has a 8/10*9/10 chance of winning
1/20: roll 2, he has a 7/10*9/10 chance of winning
7/20: roll 3-9 he has a 6/10*9/10 chance of winning
overall:
HIS chances are
(72+63+54*7)/2000 = 513/2000 = .2565%
so you have 74.35% chance of winning
===========================================
take D10
1/20 roll 1: he has 18/20 * 19/20 chance
1/20 roll 2: he has 17/20 * 19/20 chance
4/20 roll 3-6 he has 16/20*19/20 chance
14/20 roll 7-20: he must outroll you+1 on first roll,
(would it ever make sense for him to take the "1" first?
YES -- if you rolled a 19, he's sunk unless he does this
but for 18, he's better off taking the "3".
then if he succeeds, 19/20 chance on final roll.
so his chance of outrolling you + 1 is 12/20, 11/20, 10/20, ... ,1/20 (roll 18), handle 19 separately,
20 he's got 0 chance
19: he takes the "1", has 1/20 chance of rolling a 20,
then 17/20 on last roll
so his overall chance is:
[(18+17+16*4+12+11+10+...+1)*19 + 17] /8000
[(sum(1...18) + 6)*19 + 17]/8000
[(19*9 + 6)*19+17]/8000
3380/8000
169/400
he has 42.25%, you have 57.75% chance of winning
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