Game 3 Move 16 Zorba cube?

[ah_clem]

We rolled a 6-5 and were forced to leave a shot.  Z now has a cube decision.

NOTE: gnubg crashed this morning and I lost the last three or four  moves. That's ok, I entered them by hand. Consequently, the move numbering in the sgf file is now wanky.   I think I lost a rollut or two.

[Zorba]

To consider doubling at this score and cube value, I need at least 50% winning chances, somewhat less if you factor in the occasional gammon win by me.

I have 11 fives plus 3-2 that hit, for 13 shots. If I miss, I may get a shot later, or even win the race. It looks like another shot won't come up soon very often, so a hit is not a winner then, with a crunched board. Chances to win the race are rather remote too, with a 37 pips deficit. Together, it doesn't look like I got much GWC left if I miss this shot, I'd say it must be less than 15% and probably more than 10%.

So that makes 13/36 ~= 36% GWC for the hits, and (100-36)=64% chance that I won't hit for another ~13% GWC for an additional 0.64*13= ~8% GWC, giving a final estimate of 44% wins for me from here.

Even with a few gammon wins for me, that can't be enough to get in the doulbing window I think, so NO DOUBLE.

[ah_clem]

rollout

Spoiler

First of all, if any of the Herd were thinking about dropping this, think again.  It's a massive take, and dropping would be an epic blunder.  

On the other side of the board it's a tough cube decision.  Perhaps the toughest part for this intermediate is seeing that it's worth considering a double in the first place. I had rolled for Z and was in the middle of posting the thread when a lightbulb went off maybe this is a double?  Over the board I probably would have missed it altogether.

I'm impressed at Zorba's GWC estimation of 44% - gnubg pegs it at 41 to 43 percent, so he's awfully darn close. But at this match score you apparently don't need 50% to double - a single point loss puts Z at 0-4  crawford (about 15% MWC) so he's not risking all that much with a double and the rewards (4-2 Crawford or 75% MWC) are substantial.  Lot's of market losers here, so doubling as soon as you get into the theoretical doubling window should be correct.  Max Frii has the minimum double point at 46% at this match score (http://xfriis.dk/maxfriis/bg/double.html#3-5) which is less than 50%, but this still doesn't explain why gnubg thinks this is a double.

I need to look at this one a bit longer - I think this is a position worth studying and remembering.  One interesting aspect is that by turning the cube Z increases his GWC by about a point (43% vs 42%) - since he won't care about gammons, he can play more agressively for the win.  




//////////////////// 2-ply analysis ///////////////////////////
Cube analysis
2-ply cubeless equity  -0.149 (Money:  -0.157)
 0.425 0.014 0.000 - 0.575 0.021 0.000
Cubeful equities:
1. Double, take         -0.041
2. Double, pass         +1.000  ( +1.041)
3. No double            -0.047  ( -0.006)
Proper cube action: Redouble, take

/////////////////0-ply rollout ///////////////////////

Rollout details:
Player Zorba owns 2-cube:
 0.413 0.013 0.000 - 0.587 0.021 0.000 CL  -0.173 CF  -0.090
[0.001 0.000 0.000 - 0.001 0.001 0.000 CL   0.002 CF   0.003]
Player The Herd owns 4-cube:
 0.430 0.012 0.000 - 0.570 0.090 0.001 CL  -0.024 CF  -0.024
[0.001 0.001 0.000 - 0.001 0.005 0.000 CL   0.006 CF   0.006]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 905458359 and quasi-random

dice
Play: 0-ply cubeful prune [expert]
Cube: 0-ply cubeful prune [expert]


Cubeful equities:
1. Double, take         -0.024
2. Double, pass         +1.000  ( +1.024)
3. No double            -0.090 ( -0.065)
Proper cube action: Redouble, take


///////////////2-ply rollout ///////////////////////////

Rollout details:
Player Zorba owns 2-cube:
 0.422 0.013 0.000 - 0.578 0.021 0.000 CL  -0.155 CF  -0.082
[0.001 0.000 0.000 - 0.001 0.002 0.000 CL   0.002 CF   0.002]
Player The Herd owns 4-cube:
 0.434 0.011 0.001 - 0.566 0.080 0.000 CL  -0.007 CF  -0.007
[0.001 0.000 0.000 - 0.001 0.006 0.000 CL   0.005 CF   0.005]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 905458359 and quasi-random

dice
Play:  2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.1
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]


Cubeful equities:
1. Double, take         -0.007
2. Double, pass         +1.000  ( +1.024)
3. No double            -0.082 ( -0.074)
Proper cube action: Redouble, take

[close]

[Zorba]

Thanks for the rollout ah_clem, interesting stuff. Did you realize it's a redouble to 4 in your comments and is this what maxfriis's numbers are for?

In hindsight, I think this might be a redouble because of the Herd's gammon wins, which I didn't factor in. They will lose me the match, even if I don't redouble. So the "risk" part of redoubling is actually lower than what I used, pushing the start of the doubling window below 50%. Then my own gammon wins push it even lower, although I win very few of those. Apparently, it's enough to redouble with only 43% wins, although I have some doubts about the size of the error GNUBG's 2-ply rollout dings me for. I'd like to think that if this is a redouble, it has to be very close.

[ah_clem]

Thanks for the rollout ah_clem, interesting stuff. Did you realize it's a redouble to 4 in your comments and is this what maxfriis's numbers are for?

In hindsight, I think this might be a redouble because of the Herd's gammon wins, which I didn't factor in. They will lose me the match, even if I don't redouble. So the "risk" part of redoubling is actually lower than what I used, pushing the start of the doubling window below 50%. Then my own gammon wins push it even lower, although I win very few of those. Apparently, it's enough to redouble with only 43% wins, although I have some doubts about the size of the error GNUBG's 2-ply rollout dings me for. I'd like to think that if this is a redouble, it has to be very close.

Yes, I realize that it's a redouble to 4.  No, I wasn't thinking about that when I quoted the theoretical double point of 46% - that number is for an initial double and not applicable here.  Good catch.  (c:

I'm not seeing an explicit redouble point on his site, so I guess I'll have to try to calculate it myself.  The calculation goes something like this...

#1) Your MWC if you double and win (score 4-2) is 75
#2) Your MWC if you double and lose (score 0-6) is 0
#3) Your MWC if you hold and win (score 2-2) is 50
#4) Your MWC if you hold and lose (score 0-4) is 16

(using g11 MET rounded to nearest integer)

risk = #4 - #2 = 16 -0 = 16
gain  = #1 - #3 = 75 - 50 = 25

double point = risk/(risk+gain) = 16 / (16 + 25) = 16/41 = .39

So this calculation says that your theoretical double point is 39%.  This gybes with gnu saying it's a double with only 43% GWC.  I'm still struggling a bit with the idea of the double-point, so take this with a grain of salt...

[Zorba]

Thanks! Yes, that calculation looks right to me, I used 15% instead of 16% (from the old Woolsey MET, nice round number), but that's a detail.

I must've messed up my own calculation then, as I ended up with the doubling window opening up at 50%. It should be 38-39% indeed, and then with the huge volatility it's obviously a redouble. Oh well.

[ah_clem]

This position made me realize that recubes in short matches are more tricky than I had thought and that I really don't understand them very well.  The immediate takeaway is that the trailer should double aggressively at 5-away 2-away (and even more so at 4-away 2-away) especially if ti's gammonish.  I need to study up on recube takepoints and min re-double points at various match scores.