Game 2, move 16: herd cube decision

[diane]

Position ID: jZ5vAAC2bQGADQ
Match ID: cAmgABAAAAAA

[ah_clem]

Spoiler

20 numbers hit the blot. That gives us about a 55% chance to hit, and it sure looks like we win all of them, plus a fair number of gammons.  So that's basically a 55% chance to win, with lots and lots of market losers and some gammon chances.  Is this enough?

Lets try some math:

Assume that we win 55% of games and that slightly more than half of those are gammons.  Say, 25% single wins & 30% gammon wins.  Also assume that when we don't hit we lose a single game (this is not entirely correct - we lose some gammons and win some games, so call it a wash for simplicity.  Or he might just cube us out which gives the same result.  OTOH, If we miss, he doubles and we take, the calculation gets too complicated so I'm just going to ignore that possibility.)

Let's add up the match equity:

Cube centered
Win single -> score 1-1  -> equity == .5 * .25 == .125
Win gammon -> score 2-1 -> equity ==  .57 * .3 == .171
Lose single -> score 0-2 -> equity == .35 * .45 == .1575
Equity with cube centered == .4535

gaspar owns cube
Win single -> score 2-1  -> equity == .57 * .25 == .1425
Win gammon -> score 4-1 -> equity ==  .81 * .3 == .243
lose single -> score 0-3 -> equity == .26 * .45 ==  .117
Equity with cube centered == .5025

So the math says double, but the math is only as good as the assumptions.  I'm not entirely sure about neglecting our gammon losses, so take all this with a grain of salt.  My gut says hold.  I'm going to go with the math, but I'm far from certain.

[close]

[gaspar]

in my early days i would have cubed in a heartbeat..but although half numbers hit...half of them also miss!!!  cube decisions are like revenge..best served cold.  anyway early in match i would hold the cube more because of rewhip if you miss and although clem's calculations on the spoiler comment looks at your gammon equity in considering the cube what about possible gammons if you miss !!!.

let's look at a situation where you would CUBE in this position ...let's say down 5-1 in a 7 pt match for example (or 5-2) ....for money i dont think you could blame your opponent if he decided to beaver. 

matches present us with a whole different dynamic in cubing than in money play.  most early cube decisions are easy for money since usually if you have a high anchor (even 3 pt) then usually a take since gammons are rare the match equities are a lot different... Kit woolesleys book is high on my list of must reading.  it's in some respects a boring technical book..like holding game take point etc.  but a must read for regualar match players.   one mistake i see quite often is opponents who hold the cube when opponent is 2 away.  let's say losing 3-1 in a 5 pt match.... If you dont cube early (almost any slight advantage will do) and your opponent wins then it's 4-1 for him at crawford. you win crawford (4-2) then assuming no gammons you have to win 2 more games.  in other words 3 straight games to win match.....a tall order....

[ah_clem]

 ...one mistake i see quite often is opponents who hold the cube when opponent is 2 away.  let's say losing 3-1 in a 5 pt match.... If you dont cube early (almost any slight advantage will do)

Interesting.  What I seem to see alot is the opposite side of that coin - when I get to two-away first my opponent doubles way too early.  I'd say that about half the time on FIBS against a sub 1800 player the cube comes whipping across right away.  I strongly disagree that "almost any slight advantage will do" - I've seen way too many rollouts where the trailer was >50% to win, cubed, and got dinged with a double whopper.  This "double at the slightest advantage" seems to be a pervasive myth, and I'm not sure where it comes from.

Granted, the doubling window is smaller than usual for the trailer when the leader is 2-away, so the trailer should double slightly earlier.  Emphasis on slightly.

[ah_clem]

rollout

Spoiler

It's a whopper with cheese to hold the cube here, and enough burger to feed a family of five if you pass.

BTW, I underestimated the single wins, overestimated the gammon wins, and completely neglected the 5.5% of gammon losses, so my calculation above is just so much GIGO even if it did come up with the right answer in spite of itself.

What seems to make this a double is the abundance of market losers and white's bad structure.  Move a single checker from the 17 to the 16 so gaspar isn't stripped/stacked and the double is too close to call. 

More discussion over at Stick's site.




Rollout cubeless equity   +0.352   (Money: +0.350)
Cubeful equities:
1.   Double, take       +0.475   
2.   Double, pass       +1.000     +0.525
3.   No double           +0.313     -0.162
Proper cube action:   Double, take


Rollout details
   Win   W g   W bg      Lose   L g   L bg   Cubeless   Cubeful
Centered 1-cube   0.607   0.191   0.004   -   0.393   0.055   0.003   +0.352   +0.313
Standard error   0.001   0.002   0.000   -   0.001   0.001   0.001   0.004   0.007
Player gnubg owns 2-cube   0.616   0.200   0.003   -   0.384   0.071   0.007   +0.840   +0.475
Standard error   0.002   0.002   0.000   -   0.002   0.003   0.002   0.010   0.013
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 881799873 and quasi-random dice
Play: world class 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

[close]