At Stick's suggestion, I changed the problem to a money game with the cube in the normal position. In a Pay now / Pay Later decision, you would expect the opponent to hold the cube rather than yourself.
Original problem and thread here. (http://www.bgonline.org/forums/webbbs_config.pl?read=127683)
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First, let's phone a friend and see what Stick has to say. See my post (http://bigmoneybill.blogspot.com/2012/03/pay-now-pay-later-practice.html) for more on this topic.
Stick's Pay Now Pay Later Guidelines
- How likely is it that if I don't pay now I don't have to pay at all?
- Do I have a lot of timing left?
- If we do decide to pay later are we likely to leave more or less shots than we could leave now?
- How far away is the point I'm trying to clear.
- Am I leaving 15 or more (direct) shots? 11 or 12 shots maybe, 13 is pushing it, 14 or more is too many
- From now until the time we may have to pay later, will our opponent's position (board) improve or deteriorate?
- Does our opponent have a lot of timing left?
- Does making the pay now play greatly improve our position when we get away with it?
- Are we 'virtually gin' if not hit?
- How does the roll otherwise play?
- Are we harming our position by breaking a prime or throwing too many spares behind an anchor or do we maintain a decent position?
- Is there life after death? If so, how much?
- Does his board have a blot or multiple blots? Return shots after getting hit are valuable for you.
- How do the hitting numbers play? How many hit and cover numbers are there?
- When in doubt, pay later
***************
Money Game, opponent Holds cube. 64 to play. Pay now or Pay Later?
 is The other guyscore: 0 pip: 110 | ||||||||||||||||
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  | Unlimited Game Jacoby Beaver | |||||||||||||||
| pip: 80 score: 0  is You | ||||||||||||||||
| XGID=-BABCbCB----bB-----bbcbb--:1:-1:1:64:0:0:3:0:10 | ||||||||||||||||
| to play 64 | ||||||||||||||||
| 1. | XG Roller++ | 7/3 7/1 | eq: +0.199 | |||
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| 2. | XG Roller++ | 13/9 13/7 | eq: +0.171 (-0.028) | |||
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| 3. | 2-ply | 13/3 | eq: -0.052 (-0.251) | |||
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eXtreme Gammon Version: 2.02
It looks like a close call per Stick's criteria. We get a decent discount by paying now (13 shots) and are basically home-free shold the opponent miss, which argues for paying now.
But, opponent's home board is strong as acid and we basically lose the game when hit, so we really don't want to get here, which argues for pay later.
The roll plays, not great, but it plays.
I think the key factor here is the opponent's position. He has a great position, this roll, but will have trouble holding everything together. To me, this is the deciding factor. There is a good chance that opponent will have to make a concession somewhere - either by breaking anchor, breaking the midpoint, or by weakening his homeboard. This is the main reason I like paying later.
At the table, I choose to pay later - "like a fine wine, no shot before it's time." XG shows this to be correct by a small margin.
***********
So let's say we play safe. How should opponent play his rolls? When should he break the anchor? When should he break the midpoint? When should he weaken the home board? These do not look like easy decisions to me. So let's pretend we are the opponent and play all rolls. I give my initial answers and reasons below. Normal text if my play is right. Bold if wrong followed by more discussion.
Money game. We are the Underdog, own the cube and are to play all rolls.
| is Favorite score: 0 pip: 70 | ||||||||||||||||
| Unlimited Game Jacoby Beaver | ||||||||||||||||
| | pip: 110 score: 0 is Underdog | |||||||||||||||
| XGID=--BBCBB-----bB-----cBccac-:1:1:1:00:0:0:3:0:10 | ||||||||||||||||
| on roll, cube action? | ||||||||||||||||
eXtreme Gammon Version: 2.02
General thoughts.
The race is basically hopeless. Our best attempt to win is to hit a shot. Therefore, we need to keep the board so that a hit shot is a winner, and we need to keep contact in order to maximize our chances for getting a shot.
Favorite's board is advanced, meaning that most of his builders are already past our anchor. Thus it is less dangerous than usual to abandon the anchor and play for maximum contact. Sidebar, I recall from Stick's DMP article that abandoning the back anchor is often the play to win the most games and clearly correct at DMP. (see my post http://bigmoneybill.blogspot.com/2011/12/stick-on-dmp.html which is notes from Stick's Gammon Village article, or see Stick's excellent post to Tom Keith's site, http://www.bkgm.com/rgb/rgb.cgi?view+1405)
In this position, we are unlikely to get gammoned, so can afford to take more chances. ie, running from the anchor is more likely to be correct than normal. Few point on head, or pick and pass numbers. Also note opponent only has a 41/2 point board and may not choose to hit on the midpoint with all aces (should we choose to leave a blot there).
65. If we run from the anchor, 20/9, we lose big on 13 and 11 and lose a bit on 44. 44 the other way we get a shot but are not in the air. We gain big on 65, 64, 63, 62, 61, and 54. We also gain a bit on other small numbers since our escaped runner gives us spare pips to stall next time with most rolls.
If we run one from the midpoint, 13/2, we lose big on 13, 12, 14, 11. We gain big on 65, 64, 63, 62, 61, and 54. Compared to running with the anchor, it looks like 14 is the big difference. A small difference is that one small numbers we lack the spare pips to play next time. We will likely abandon the anchor leaving two blots or abandon the midpoint, giving only indirect shots next time.
Two down from the midpoint, 13/8, 13/7 just seems anti-thematic. I think we need the midpoint contact to try and generate a direct shot. I dismiss this play.
I like 20/9.
64. I like 20/10 for same reasons as above
63. Run 20/11 for same reasons.
62. This roll doesn't escape.
Is the cold-blooded 20/14, 4/2 too loose? We get crushed on 14, 12, 13, and 11 as above, but also on 24 and 22. I'm not sure how likely it is but there are disaster variations where two blots get scooped up and we get gammoned. Is there an upside? Well, 65, 64, 63, 61, and 54 are now double shots. Before we were getting ace's and eight's or 17 hitters. Ace's, Eight's and Deuce's would be 23 hitters so more but shots but not huge more. I suppose it could be right but I doubt I would have the stones to make that play.
I choose to come down from the midpoint. I like just 13/5. Saving the six with 13/7, 4/2 doesn't really save much. 61 I suppose. It's unclear to me if you should even make the ace on 65 so I would count that as a saved six.
** note ** XG had all three plays essentially tied 13/5 best by a nose over 20/14, 4/2 and 13/7, 4/2.
61. 20/13 seems like the thematic play - keeping contact at not too much risk.
54. 20/11 for same reasons as above.
53. There is an argument for 13/5 to preserve the better board but why give those hit and cover aces for free? Lets make the ace 6/1, 4/1.
** 13/5 is correct by a small margin (.01). I guess you need the board. **
52. 20/13 again playing for maximum contact to win at the price of not too much risk.
51. 6/1 followed by some other ace is the safest and could be right but our gameplan requires a good board to win. I can't do that. I play 13/7 and stick to the program.
** Best is a play I didn't even consider. 20/14. Maximum contact and hold the board is the order of the day. The risk isn't that great. We only get G-balled 5.5% with the two blot play compared to 4.9% gammons on the one blot play. So the "extra gammons" from the risky play are mostly a mirage in this case. That said my play 13/7 is essentially tied and only a smidge worse.
43. Once again run to the midpoint, 20/13.
42. That roll sucks . I am going with 13/7 on the same logic as per 51. We need the board.
** Once again the best play is 20/14 and I didn't see it! Exact same reasons and numbers as with 51 above.
41. Same as 42. I come down 13/8 and cross my fingers.
** And again The agrressive, max contact play that I didn't even see is correct. The computer likes 20/15. This time my play, though OK, is off by .01
32. I make the ace 4/1, 3/1.
** Are we seeing a theme yet? 20/15 is best, even though we diversify his numbers. As per the general discussion above, we need the board to win. A 5-point board with the ace open is just so much stronger than any other 5-point board that it is a real concession to weaken the board by shifting. Also, the gammon danger isn't too bad. Even though we diversify his good rolls and levae two blots, we only get gammoned 14% by leading with the chin. Interesting.
My play, 4/1, 3/1 is only 4th best and costs .016 in equity.
31. Again make the ace, 3/1, 2/1.
** This time making the ace is right but I am not sure I understand what is different compared to 32.
21. Stall ball. 4/1.
66. We were down 40 pips before the roll so the race is still unlikely even after this huge roll. I think our main gameplan is still to get a hit so we need to keep contact somehow.
13/1(2) makes the board but only gives us indirect shots in the best case scenario.
20/13(2), 13/7(2) is too easy for opponent to escape, and we are down too much in the race.
I like 20/2, 13/7 keeping maximum contact while duplicating aces.
** my play is correct but by a tiny margin. Both 13/1(2) and 20/8, 13/1 are very close. I didn't even see 20/8, 13/1 which duplicates aces.
55. 20/5, 13/8 duplicating aces is a possibility (like with double sixes above) but I am not sure we are this desperate. We could also try 20/10, 6/1(2) keeping a 5 point board with less risk. I am not sure, but choose this safer play.
44. 20/16(2) coming into direct contact with the guys onthe midpoint is a possiblity. Then we could try 13/9(2) or 5/1(2) with the other 4's. Both plays have merit. 5/1(2) yields a double on 61 or 64 but I hate to make the 5 point a gap when we don't have to. 13/9(2) keeps the best board should we get a shot. Coming out gets diret contact but gives 65 as an extra clearing number and also we only get one shot by coming closer. Staying back on the 20 point we might get multiple shots if say, he breaks the midpoint, we miss, and then he can't come to safety next time. Another factor may be that opponent can stall on 5's.
Another play is 13/1, 5/1 preserving a 5 point board for one roll but giving the ace jokers. Once again I am not sure, but like the idea of max contact so I will go for this.
** my play was right, but is tied with 20/16, 13/9. 13/5. The bot has no fear. Any play that advances the back anchor with 20/16(2) is a significant error.
33. Once again stepping into direct contact is a possiblity. This gets double shots on 65 and 61 but allows opponent to stall on 5's. We also suffer the one shot and done should we get a shot.
I am going to stick with the main plan and bolt from the anchor, 20/8.
** This time advancing the back anchor 20/17(2) is a whopper sized error.
22. In this case, we step into the ideal contact range, six away from his midpoint anchor. This is too juicy to pass up. I am going for this one. 20/18(2), 13/11(2).
** Advancing the anchor is correct but the bot likes to leave a blot with either 13/9 or 13/11, 4/2 with the other two two's. again I didn't even see this play. My play is OK, only a .01 error. The blottly play gains double shots on missing sixes.
11. Shift or make the ace? Since there is a good chance we get a shot next roll let's stay blot free in the inner board. 3/1(2).
************
Variant #1. move opponent's spare from the 4 point to midpoint.
We are favorite, have doubled and have 64 to play. Pay now or pay later?
| is Opponent score: 0 pip: 119 | ||||||||||||||||
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| | Unlimited Game Jacoby Beaver | |||||||||||||||
| pip: 80 score: 0 is You | ||||||||||||||||
| XGID=-BABCbCB----cB-----bbbbb--:1:-1:1:64:0:0:3:0:10 | ||||||||||||||||
| to play 64 | ||||||||||||||||
| 1. | XG Roller++ | 13/9 13/7 | eq: +0.194 | |||
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| 2. | XG Roller++ | 7/3 7/1 | eq: +0.090 (-0.103) | |||
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| 3. | 2-ply | 13/3 | eq: -0.061 (-0.255) | |||
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eXtreme Gammon Version: 2.02
Compared to the first position, this time the opponent has spare timing. He plays from the midpoint next time and holds the anchor, the board, and the midpoint - everything. So his position does not deterioriate next time.
Our situation is the same. We arelikely to leave a shot anyway, and since we are getting a discount, we might as well go for it. 13/9, 13/7 Paying now is clear.
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Variant #2. Same as position 1 but we have 65 to play instead of 64.
Pay now or pay later?
| is Opponent score: 0 pip: 110 | ||||||||||||||||
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 | Unlimited Game Jacoby Beaver | |||||||||||||||
| pip: 80 score: 0 is You | ||||||||||||||||
| XGID=-BABCbCB----bB-----bbcbb--:1:-1:1:65:0:0:3:0:10 | ||||||||||||||||
| to play 65 | ||||||||||||||||
| 1. | XG Roller++ | 7/2 7/1 | eq: +0.295 | |||
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| 2. | XG Roller++ | 13/8 13/7 | eq: +0.275 (-0.020) | |||
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| 3. | 2-ply | 13/2 | eq: -0.039 (-0.334) | |||
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eXtreme Gammon Version: 2.02
Once again the opponent is in a bit of a dilemna. He cant hold everything next turn and must make a concession. This agrues for Paying Later. Also, compared to 64, 65 plays better as we make a 5-point board. If opponent chooses to hold the midpoint next turn, then all of our aces are real killers next time.
On the other hand, if we pay now we leave the minimum shots (11 compared to 13 hitters with 64). This should be roughly 5.5% extra win chances. We should expect it to be close, and it it.
Pay Later is right, since as discussed above, the roll plays well and opponent must break next time somewhere. But paying now is only a small error.
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Variant #3.
Move opponent's spare from 4 point to midpoint and give us 65 to play.
| is Opponent score: 0 pip: 119 | ||||||||||||||||
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| | Unlimited Game Jacoby Beaver | |||||||||||||||
| pip: 80 score: 0 is You | ||||||||||||||||
| XGID=-BABCbCB----cB-----bbbbb--:1:-1:1:65:0:0:3:0:10 | ||||||||||||||||
| to play 65 | ||||||||||||||||
| 1. | XG Roller++ | 13/8 13/7 | eq: +0.293 | |||
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| 2. | XG Roller++ | 7/2 7/1 | eq: +0.098 (-0.195) | |||
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| 3. | 1-ply | 13/2 | eq: +0.010 (-0.283) | |||
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eXtreme Gammon Version: 2.02
Once again pay now is clearly correct. Paying Later is a double whopper.
*********
One last exercise.
Let's contune from Variant #2. We play safe and make the board. Now let's switch sides and try playing those rolls again. When do you abandon the anchor? When do you leave a blot on the midpoint? When do you break the home board?
Underdog to play all rolls.
I am not going into detail on every single roll this time. Instead, I will group the rolls into categories.
| is Favorite score: 0 pip: 69 | ||||||||||||||||
| Unlimited Game Jacoby Beaver | ||||||||||||||||
| | pip: 110 score: 0 is Underdog | |||||||||||||||
| XGID=--BBCBB-----bB-----cBcbbc-:1:1:1:00:0:0:3:0:10 | ||||||||||||||||
| on roll, cube action? | ||||||||||||||||
eXtreme Gammon Version: 2.02
General thoughts.
Opponent has a 5 point board - this must be respected. It is very unlikely that these extravagant two blot plays are likely to be right. There is no inner board blot so the upside is less and the risk is obviously more.
Similarly, leaving a blot on the midpoint is unlikely to be correct. Opponent will freely hit with any ace, that's 11 immediate rolls where we lose bigtime. and where is the upside? Well we gain a direct shot on 65, 64, 63, 54 as well a double on 62. That just seems like too much risk for not enough gain.
Even though opponent has a 5 point board, he only one has one builder above us. So he can only hurt us pick and pass aces as well as 44. Not good, but our gameplan is still to preserve the board and seek contact so bolting from the anchor may well be right. Not too many G's and he only has one builder to work us over.
So ....
Big numbers ...
Me.
65, 64, 63, 54. I run from the back anchor. Once again, the logic is try and hold the midpoint to get a direct shot. While the risk is greater, with his 5 point board, it's still not horrific since he only has one active builder.
XG. Running is correct in all cases but it is quite close. By about .01 in most cases.
Sevens ...
Me.
61, 52, 43. Run to the midpoint but make the ace on 43. Same logic as above.
XG.
Make the ace with 43.
Run to mid with 61 (there is nothing else)
Two down with 52 (run to mid is .015 error)
Mid-Size numbers ...
62, 53.
Me.
Two down from the midpoint on 62. Leaving a direct shot is too deadly.
Make ace with 53. Keep the contact since the roll plays OK.
XG.
Agrees with me.
Small numbers ...
51, 42, 41, 32, 21
Me.
51. Breaking the board is just too ugly. Come down from the mid. 13/7
42. sucks. can't break the board and can't leave a shot so two down by default 13/11, 13/9.
41. Down from the mid. 13/8.
32. Make the ace, 4/1, 3/1
21. Stall with 4/1
XG.
Only right to leave a shot from the mid on 51 and 41. You just can't break the board and expect to win. My plays are OK.
Doubles ...
Me.
66. 13/1(2). Safe.
55. 20/10, 6/1(2)
44. 13/1, 13/9
33. 20/8
22. 20/18 (2), 13/11(2)
11. 3/1(2)
XG.
My 55 is a whopper. Best is to move from the mid 13/3(2). I guess this way you get the indirects without leaving the pick and pass jokers and 44 - must be just too risky.
On the other hand, my 33 play is correct though it is close. Both 20/17(2), 13/10(2) and 13/7(2) are almost correct. I wonder what the difference between this and double 5's is?
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