(ML)"My gammon value is huge here and I want to increase my chance of gammons."
(NK) Forgive me for being blunt as I am trying to get you to expand your thought processes. The above is the only correct thing you stated pertaining to this problem. However, the same play that is correct here should also be correct for $ play if you hold the cube.
(ML) "I have an even amount of checkers left, so taking one of would not decrease the amount of rolls I need to get off that much."
(NK) This is one of the causes for your blunder and a rather common missconception. The even/odd thing applies when you have something very close to a pure roll oriented speed board bearoff. After playing 4/3 4/1 you have 8 checkers left and a persistant gap on the 2 pt. You're quite likely to waste a turn by rolling a missing 2. Compare with playing the clearly speedier 4/0. Now you still have that 2 gap, but you have 7 checkers left and can afford to miss once with a 2, which currently fills the gap from the 4 pt and likely prevents further misses. 4/0 is probably close to half a roll quicker than 4/3 4/1. So if we ignore shot potential we see that 4/0 is much better than 4/3 4/1. We can't totally ignore shot potential, but after 4/0 with your opp having only a 2 pt board and you having cube access to cash or still play on if hit, just how often do you think he's staying around on your 2 pt to wait for a blot?
(ML)"I would like to bear off without leaving a shot, although I may still be a favorite to win a game (not a gammon) if I get hit and come around."
(NK) Here's another big missread on this position that contributed to you choosing a blunder. Leaving a shot here is no where near as bad as it usually is when bearing off since your opp has only a 2 pt board and other blots and you have many checkers off and cube access and can basically cash at will for a couple turns after being hit. If you get hit, you probably still can play for a G for a turn or two. I think if you play 3/0 1/0 leaving an ace shot, and hoping to not roll miss later and gain a full turn and get hit with a "joker" 31 or 11 making his 6 pt, you still may be a bit TG since you can still fluke him with a G and cash later. The same applies after 3/0 3/2x if he jokers with 32. I think you're still TG and of course, if you cautiously cash, you only lost your G chances by getting hit, but not the game. However, most of the opp's hits leave at lease one blot on his side of the board and you may be able to rehit at some point and then G him. Safety in this posted position is only a minor consideration. Speed of bearoff is most important as he has only a 2 pt board and you have many checkers off and you can cash if you get scared after getting hit.
(ML) "Therefore, I played 4/1 4/3. This helps clear the last point on the next roll."
(NK) Clearing the point doesn't matter here, speed to bearoff does! As we seen, nearly any other play is superior to 4/1 4/3 here. 4/0 clearly is better and 3/0 1/0 and 3/0 3/2x are probably still better. Taking two checkers off is fastest and runs no risk of losing due to cube access. Hitting (my original choice here) is somewhat slower than even 4/0 but sets the opp back two pips and one crossover. Hitting gains huge if he dances with 44 which otherwise usually saves G, and gains big on any of the other 3 dances. I think it is slightly correct to hit.
OK here's a spoiler RO for money play and with our opp owning the cube, and we see what we expect to see and that is that we can only very rarely lose this game no matter what we play. For money I'd probably have played 4/0 to be honest and in practical play may gain on some opp mistakes in whether to stay or go with his next roll.
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| XGID=-BaBD-----------a--a---ci-:1:-1:1:13:0:0:3:0:10 | |||||
| Blue to play 13 | |||||
| 1. | Rollout1 | 3/Off 3/2* | eq: +1.2064 | |||
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| 2. | Rollout1 | 4/Off | eq: +1.1994 (-0.0071) | |||
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| 3. | Rollout1 | 3/Off 1/Off | eq: +1.1887 (-0.0178) | |||
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| 4. | Rollout1 | 4/3 4/1 | eq: +1.1498 (-0.0566) | |||
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| 1 5184 Games rolled with Variance Reduction. Dice Seed: 67389374 Moves and cube decisions: XG Roller+ | ||||||
eXtreme Gammon Version: 2.00