Monday, June 27, 2011

Never reroll a 30-sided die that is safe from attack.

That seems like a sound instinct, doesn't it? But is it always true?

Can you see the justification for rerolling the d30 with value 30 in this situation? Is the
argument compelling? What if the mood swing were just a regular d12? or a d4?


Viewing Game #719620
Tournament Legal challenge, copying communication from game 716780
This game was last modified on Thu Jun 23, 2011 10:40:03

* Next Turn * Player: theAlmighty *heavenly* *Silver Medal in Men's Basketball* *Silver Medal in Men's Fencing* *Silver Medal in Men's Judo* *Gold Medal in Men's Table Tennis* * Next Turn *
Button Man: Vincent    Score: 33 (-14.6 sides)   Rounds Won/Lost/Tied: 1 / 0 / 0 (out of 3 round(s))
Captured Dice: None

Dice 30-sided die30-sided dieOption 6/30
(with 6 sides)
Value 8305
Dice 4-sided dieKonstant
6-sided die
8-sided dieOption 10/20
(with 20 sides)
X Mood Swing
(with 12 sides)
Value 113171
Player: ElihuRoot *Dead Dude* *Fanatic*
Button Man: Fan Chung Graham    Score: 55 (14.6 sides)   Rounds Won/Lost/Tied: 0 / 1 / 0
Captured Dice: 30-sided die

1 comment:

Gryphon said...

The argument for taking your 20-sider now is quite simple: if you take his 6-sider and either of his 30-siders, he can only win if your mood swing rerolls to have 16 or 20 sides. Since he can't guarantee you'll need to roll that die and the 6-sider is pretty much impossible to protect, his best move is to try to protect both 30-siders now. Taking your 8-sider with the die showing 8 gives him a 1/3 chance of rolling it too high for you to take. Taking your 20-sider with the other 30-sider, on the other hand, gives him a 4/5 chance of rolling to a safe number. Without crunching the numbers, his odds seem far better if he has both 30-siders than if he has a 30-sider and a 6-sider.

If the mood swing were a regular 12-sider, he will lose if he loses two of his remaining dice and win if he only loses one. If it were a 4-sider, he wins if he keeps both 30-siders, ties if he keeps a 30-sider and the 6-sider, and loses otherwise. Either way, the need to keep two dice to avoid losing and the relative difficulty of protecting the 6-sider would make the argument for taking the 20-sider now even stronger.