To Greed or Not to Greed? by John

In the position below, it's a money game and Red is obviously very delighted with his 2-2 superjoker roll.  The question is, should he completely close his board and pretty much ensure the win, or should he leave the ace point open with the hope of getting hit, picking up more checkers and getting more gammons?

Before I give you my analysis of the situation, why don't you decide which play you think is best.






This is a money game so the gammon price is 1/2  which implies that the ratio of extra gammons/extra losses has to be a little over 2/1 for the big play to be correct.  Why "a little over 2/1"?  Because Black owns the cube and can profitably redouble when he turns the game around.

 

Is there any way the big play can meet this over 2/1 standard?  I doubt it.  Your extra gammons mostly occur when Black rolls an immediate ace and you then enter and hit a second blot.  Black however only rolls an ace 30% of the time and only 61 (which escapes and could soon get you recubed if you don't hit on the 21 or 17-points) or 51 leave you a direct shot back.  41 allows Black to enter and cover his 4-point while the other aces lift this inner board blot leaving you with a few fly shots at the 17-point blot.  If Black does enter and lift the 4-point blot, you will get a few extra gammons when you roll something that enters and hits loose on your ace point (assuming Black cooperates by dancing and you then hit Black's blot on the 17-point).  Over the board I would guess these extra gammons only amount to around 1.5 in 36 games, around 4%.  It's actually a little less than this since the big play can cause White to get gammoned as well.  The big play can still be correct, but only if it creates no more than around 2% additional losses.  I'm pretty sure the extra losses from this play will exceed 2%, but let's take a look.

 

If White closes his board, he only loses about 3.6% of the time.  The big play will therefore only be justified if it raises Black's winning chances to no more than 5.6%.  Black's winning chances when he rolls an ace have got to be at least 10% and they're over 3.6% when he dances since White doesn't cover with 66,64, and 63 as is left with an awkward structure with 62,61,52, and 51.  If we give Black 4% when he dances (which seems a little low to me), we're already over the 5.6% loss figure for White so the obvious play of closing the board is correct in this position.


Below is the ExtremeGammon eval which confirms my estimations and shows that it would be an 11% blunder to play for the gammon








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