Game 3, move 11: Herd to move 5-2

[diane]

Choices...choices...

3DYHCwA7cyrAAA:UYmqAAAAGAAA

[stiefnu]

Spoiler

Is it wise to hit now?  If he doesn't dance and gets a return, we're in trouble.  Having moved deep into our home board, I'm thinking our best strategy now is to hold the bar point, try to fill gaps in our board and hope to hit later.  So I prefer something like 10/3 or maybe 9/7, 10/5

[close]

[ah_clem]

Spoiler

If we hit, I count 15 return shots (51 53 54 55 56 31 33 36).  Any whiff gives us a great chance to close him out and win a gammon, not that gammons do anything for us..  OTOH, if he makes any of the shots, we risk being gammoned ourselves , and at this match score that's a problem - the aggressive play risks gammmons both ways, but they only help our opponent.

Normally, the hitting play would be a slam dunk, but maybe not here.  Let's try to put some numbers on it.  The following are rough estimates, so take them with a grain of salt.

If we play passively, the holding game gives us about a 45% chance to win with gammons being negligible.
If we hit, we're roughly a 55% chance to win (21/36 or 58% he misses, and add back a bit for fudge factor)

Figure he wins a gammon half the time he hits, giving a gammon loss chance of 21%.  How to put this all together?  Add up the partial equities for each possibility:

Win -> win match -> match equity == 1 so   partial equity is .55
Lose single -> 3-2 score -> match equity == .6  so  partial equity is .6(.34) = .2
Lose gammon -> 3-4 score -> match equity == .41 so  partial equity is .41(.21) = .087

Adding up the partial equities, we get .55 + .2 + .087 = .8361 for the hitting play

How about the passive play

win -> win match -> match equity == 1 so  partial equity is .45
lose -> 3-2 score -> match equity == .6 so  partial equity is .6(.55) = .33

Adding them up we get .78 equity.

.836 is bigger than .78, so let's hit.

18/11*

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[NIHILIST]

Spoiler

I count 14 return shots, which only serves to enhance our winning percentages, conceding the adjusted accuracy of your calculations.  it's a frightening looking board after we hit, but the numbers seem to say hitting is best.
But............ maybe my biggest concern is the checker we momentarily strand on his bar point. This complicates our task in the sense that we have two objectives, closing the board and safely bringing the blot on his bar point home.

A sequence  like FAN, 1-6 still leaves him the favorite to enter with unduplicated 1s and 6s hitting the stranded blot on his bar point. How do you like the sequence FAN, 6-6 ?

I count 16 point making numbers for us if he fans plus 4-4 and 5-5 which, though not making a point, cleans up some of the mess.

If the cube weren't in play I'd hit, but here,at the end of the day, I think I'm going to play the chickenly 10-5, 9-7 and wait for a better opportunity. It's worth remembering that even the bravest Kamikaze pilots wound up dead.

Bob

[close]

[stiefnu]

Spoiler

It's worth remembering that even the bravest Kamikaze pilots wound up dead.

Nice one!  Must remember that one for my next chouette.   Anyway, to bring the votes closer, I have switched mine from 10/3 to 9/7, 10/5.  Now, any of you brave Kamikaze pilots like to reconsider?

[close]

[ah_clem]

Spoiler

I count 14 return shots,

yes 14, not 15.

A sequence  like FAN, 1-6 still leaves him the favorite to enter with unduplicated 1s and 6s hitting the stranded blot on his bar point.

It does?  I'd make the 5 point with 1-6 , leaving him on the roof against a five point board - definitely not a favorite to even enter, let alone enter and hit.  What am I missing here?

How do you like the sequence FAN, 6-6 ?

It sucks.  But I'm not going to base my play on one bad sequence.

I count 16 point making numbers for us if he fans

My count: 61 63 64 65 51 53 54 41 43 11 and 33 all make the 5 point - that's 20
In addition 42 31 21 32 and 22 all make the bar point.  That's another 9.
Plus 62 52 44 and 55 make an outfield point for what that's worth. 

If the cube weren't in play I'd hit

The cube is in play?  Looks to me like the cube is dead, what with us two away holding the cube at two.  What am I missing?

[close]

[NIHILIST]

Looks like I cant count either. Yes, the cube is in play, we have it at 2 meaning gammons cost us 4 points instead of 2 if the cube werent in play. Pretty big swing, wouldn't you say ?

Bob

[ah_clem]

Spoiler

Looking at this again, I think wy analysis is flawed. There's the obvious 14 return shots v 15 shots that Bob pointed out, but the real flaw is the assumption that 58% misses turns into 55% gwc.  With five blots hanging around, we need to shave off more than 3% - I'd say more like ten (maybe more).  Let's run the numbers again with 51% GWC (14 return shots gives 61% missses minus ten for "fudge actor")  

If we play passively, the holding game gives us about a 45% chance to win with gammons being negligible.
If we hit, we're roughly a 51% chance to win

Figure he wins a gammon half the time he hits, giving a gammon loss chance of 24.5%.  How to put this all together?  Add up the partial equities for each possibility:

Win -> win match -> match equity == 1 so   partial equity is .51
Lose single -> 3-2 score -> match equity == .6  so  partial equity is .6(.245) = .147
Lose gammon -> 3-4 score -> match equity == .41 so  partial equity is .41(.245) = .108

Adding up the partial equities, we get .51 + .147 + .108 = .765 for the hitting play

How about the passive play

win -> win match -> match equity == 1 so  partial equity is .45
lose -> 3-2 score -> match equity == .6 so  partial equity is .6(.55) = .33

Adding them up we get .78 equity.

Pretty close.   The question is: how good is that 10% fudge figure?  Hard to say.   I'm going to stick with the hitting play, but I'm much less certain now.

18/11*

[close]

[stog]

Spoiler

a possible gammon?.... let's develop a little b4 considering hitting -->10/5 9/7

[close]

[diane]

This was a difficult one...I saw the hit right away, and almost 'nexted' it...

As usual, I checked with gnu first....and did a double take when it wasn't the best move...nor the second best.... nor the third...

At that point - I checked the dice to see I had the roll right!!

I went back to the list of possible moves ranked from best to worst, and was astonished to find I had to scroll down to the second page to find the hit move!!  It seems almost anything is better than this hit!! 

Anyhoo...we have chosen this path - and I still think there is some discussion here, because clearly I was not the only one confused by this roll!

[ah_clem]

rollout

Spoiler

Well, I really screwed the pooch on this one.  Hitting is a triple whopper here. 

So what did I get wrong?  I had estimated our GWC with the hit at 51%, and gnu rollout pegs it at 50.3%, so that's not too bad.  My estimate for gammon losses was 24.5% and gnubg has it at 22.4% so that's not too bad either.

The big mistake was underestimating the GWC of the passive play.  I saw our poor timing as reducing our GWC to 45%, but even with our poor timing we're still over 49% according to gnu.  Holding games are not the most interesting, especially from a cubing perspective - since the chances are about equal  I've had no real reason to study the GWC of various holding games.  This position is more even than it seems - I'll have to look into it to see how wide this trend is.

BTW, hitting is still about a .1 error at 0-0 to 5, so the hit is not the "slam-dunk" that I thought it was.  At gammon-go, gnu 2-ply analysis likes the hitting play, but by the slimmest of margins.

    1. Rollout          10/3                         Eq.:  -0.050
       0.493 0.036 0.000 - 0.507 0.026 0.001 CL  -0.050 CF  -0.050
      [0.001 0.003 0.000 - 0.001 0.001 0.000 CL   0.003 CF   0.003]

    2. Rollout          9/7 8/3                      Eq.:  -0.055 ( -0.004)
       0.492 0.031 0.000 - 0.508 0.026 0.001 CL  -0.055 CF  -0.055
      [0.001 0.003 0.000 - 0.001 0.001 0.000 CL   0.003 CF   0.003]

    3. Rollout          8/3 6/4                      Eq.:  -0.058 ( -0.008)
       0.489 0.034 0.000 - 0.511 0.026 0.000 CL  -0.058 CF  -0.058
      [0.001 0.003 0.000 - 0.001 0.001 0.000 CL   0.003 CF   0.003]

    4. Rollout          10/5 6/4                     Eq.:  -0.065 ( -0.015)
       0.488 0.034 0.000 - 0.512 0.028 0.001 CL  -0.065 CF  -0.065
      [0.001 0.003 0.000 - 0.001 0.001 0.000 CL   0.003 CF   0.003]

    5. Rollout          10/5 9/7                     Eq.:  -0.071 ( -0.021)
       0.485 0.032 0.000 - 0.515 0.029 0.001 CL  -0.071 CF  -0.071
      [0.001 0.003 0.000 - 0.001 0.001 0.000 CL   0.003 CF   0.003]

    . . .

   18. Rollout          18/11*                       Eq.:  -0.346 ( -0.295)
       0.503 0.225 0.003 - 0.497 0.224 0.028 CL  -0.346 CF  -0.346
      [0.002 0.007 0.000 - 0.002 0.002 0.002 CL   0.007 CF   0.007]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 900960086 and quasi-random dice
        Play: 0-ply cubeful prune [expert]
        Cube: 0-ply cubeful prune [expert]
 

[close]

[NIHILIST]

Great learning position, lots of nuance to this one.

Bob