not really a problem, but an observation about null dice

I didn't want to make this one a puzzle -- it's too easy! isn't it? But it's a perfect illustration of a point that's worth making about the utility of null dice. Where they really shine is in protecting your large dice -- disrupting skill attacks against them or keeping them from having to be rerolled.

TheUniverse here will probably win no matter what, but the instinctive "avoid using null dice whenever possible" idea is wrong: 1/12 of the time it will result in a tie -- if he (or she) instead attacks with the null die first, he (or she) is certain to win.

Viewing Game #680455

Tournament #13749: Revenge on the Stats- lephantman13 Current Round: Round 4. (organized by lephantman13)

Everyone but me must choose randomly, please.

This game was last modified on Sat Sep 26, 2009 19:15:28

* Next Turn * Player: TheUniverse *My Birthday* * Next Turn *
Button Man: inundator Score: 42 (0.6 sides) Rounds Won/Lost/Tied: 0 / 0 / 0 (out of 3 round(s))
Captured Dice: Fire Shadow 20-sided die, Morphing Trip 6-sided die, Speed 10-sided die

Dice	Plasma {Chance} 12-sided die	Plasma {Null} 12-sided die
Value	9	3
Dice	Focus 8-sided die	Stinger 10-sided die
Value	7	1

Player: ElihuRoot *Dead Dude* *Fanatic*
Button Man: BlackOmega Score: 41 (-0.6 sides) Rounds Won/Lost/Tied: 0 / 0 / 0
Captured Dice: Plasma {Trip} 12-sided die, Plasma {Focus} 12-sided die, Plasma {} X Swing 8-sided die

playing it safe (pretty easy)

One plausible move will is certain not to lose, but might draw; another move has a better chance of winning, but could lose. Which should you chose? or is there another option?

Yes, I know this is actually not that tricky. I still like how the choices present themselves in this example.

Button Men Game #680299
Tournament Legal challenge, copying communication from game 679964

Skills in this game: Option, Morphing, X Swing
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Jingjing (m4 8 10 20 X) Score: 45 (-2 sides) Rounds Won/Lost/Tied: 1 / 1 / 0 (Out of 3 wins)
Your Captured Dice: Option 20/24 20-sided die, 8-sided die, Option 8/16 8-sided die

Morphing 8-sided die	10-sided die
7	10
8-sided die	Option 2/12 (with 2 sides)
5	1

Opponent: alaric *Sci-Fied* *Silver Medal in Men's Boxing* *Silver Medal in Men's Marathon* *Silver Medal in Men's Synchronized Swimming* *Gold Medal in Men's Wrestling*
Button Man: Apples (8 8 2/12 8/16 20/24) Score: 48 (2 sides) Rounds Won/Lost/Tied: 1 / 1 / 0
Captured Dice: 20-sided die, X Swing 15-sided die, 8-sided die

the SECOND largest number?

We always know that the goal in these circumstances is to maximize the SECOND largest number, i.e.

what will be left to attempt the recapture after the opponent captures your largest die and rerolls.

On the other hand, if he will have to make TWO attacks, maybe the THIRD largest number matters.

(though in this case, maybe that isn't true, since R. only needs to capture the 10 and 12 sided dice in order to win.

Oh, but wait -- does that mean R. should ignore the 6 sided die? That's not true in ALL circumstances, is it?)

In any case, the question isn't what R. should do, but what *I* should do. If the goal is to maximize the expected value of my SECOND largest die, I might be better off rerolling the 12 sided die. But doesn't rerolling the 10 sided die make more sense?

Doesn't it?

Button Men Game #679774 [some values tweaked to make the question more interesting]
Tournament Legal challenge, copying communication from game 679239

Skills in this game: Focus, V Swing, X Swing, Speed

Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Ken (8 10 z12 20 V) Score: 38 (-0.6 sides) Rounds Won/Lost/Tied: 0 / 0 / 0 (Out of 3 wins)
Your Captured Dice: 10-sided die, 10-sided die, X Swing 4-sided die

10-sided die	Speed 12-sided die	V Swing (with 6 sides)		8-sided die
2	3	5		1 Captured last turn
Focus 6-sided die	16-sided die
2	16

Opponent: Russian *2^12th game cookie* *Ngozi's Disciple*
Button Man: Tsusuko (f6 10 10 16 X) Score: 39 (0.6 sides) Rounds Won/Lost/Tied: 0 / 0 / 0
Captured Dice: 20-sided die, 8-sided die

eat the poison?

This one may be more subtle than it appears to be!

What do you think? I have to take either the 10-sided die or the 20-sided die.
which should I take? and should I do a skill attack or a power attack?

Button Men Game #679217
Tournament Legal challenge, copying communication from game 679082

Skills in this game: Poison, X Swing
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Ngozi (4 6 8 10 X) Score: 52 (22 sides) Rounds Won/Lost/Tied: 2 / 2 / 0 (Out of 3 wins)
Your Captured Dice: 20-sided die, 20-sided die

6-sided die	8-sided die	10-sided die		4-sided die
1	2	5		1 Captured last turn
10-sided die	Poison 20-sided die	X Swing (with 20 sides)
3	3	17

Opponent: alaric *Sci-Fied* *Silver Medal in Men's Boxing* *Silver Medal in Men's Marathon* *Silver Medal in Men's Synchronized Swimming* *Gold Medal in Men's Wrestling*
Button Man: Crusher (10 p20 20 20 X) Score: 19 (-22 sides) Rounds Won/Lost/Tied: 2 / 2 / 0
Captured Dice: X Swing 20-sided die, 4-sided die alaric's Response