We are all used to playing for money or at an early stage in a match, wherethe value of a gammon is not affected by the score. Under these circumstances(assuming the cube is at 1) winning a gammon gains 1 point while losing thegame costs two points. Therefore you must win twice as many gammons as youlose games in order to justify a risky play which goes after a gammon. The match score can change things considerably. Obviously at double matchpoint all that matters is winning the game -- gammons don't count at all.This is also essentially true at the Crawford game if the trailer has anodd number of points to go. The only gain he gets from winning a gammonis a free drop, which is of very small value. Therefore, assuming a possiblebackgammon isn't in the picture (backgammons are of course very valuable forthe trailer at this score), it is correct for both players to play as though it were doublematch point. Under other circumstances, gammons may have greater value to the trailer thanthey do for money. Consider the score 1 away, 2 away Crawford. If the trailerwins a single game the match is tied, while if he wins a gammon he wins thewhole match. Of course if he loses the game he loses the match. Thereforehe can afford to play more aggressively than usual for the gammon. If a playincreases his gammon chances more than it increases his losing chances, it isthe correct play, since he stands to gain 50% match equity from winning agammon (vs. winning a single game) while he loses 50% match equity fromlosing the game (vs. winning a single game). Let's look at a simple example: 81 15 White 4* 5 point match Blue 3 Snowie rollouts: Play Cubeless equity % wins % gammons 3/0, 3/2 1.247 100.0 24.53/0, 1/0 1.165 89.7 36.1 Blue can guarantee the win by playing safe. As seen by the equity figure,this is the correct play for money. Blue does not win twice as many extragammons as he loses games. At the 2 away, 1 away Crawford score, it is another story. Blue does winmore extra gammons than he loses games, so the risky 3/0, 1/0 is thecorrect play. This may seem logical, but it is very difficult for mostplayers to suddenly shift gears and make an abnormal play such as this dueto the match score. At more lopsided match scores, such as 10 away 1 away Crawford, the numberschange. Gammons are still valuable for the trailer, of course, but theyare not as valuable as at the 2 away, 1 away Crawford score. The reason isthat the trailer will have opportunities to win a gammon later, so the gainfrom getting the gammon now is not as great. In order to simplify thediscussion, for the rest of the article I will be assuming only thescores of double match point and 2 away, 1 away Crawford in any analysis. At double match point, what should we be playing for? Gammons don't help us,but they don't hurt us either. Blitzes are clearly of less value than undernormal circumstances. On the other side of the coin, things aren't as badas we are used to if we are being blitzed. This means that we should bemore willing than usual to leave our anchor, if the alternative is stayingback and having our game crunch. We might save the gammon by holding theanchor, but we won't win the game. If we make a bold run for it we may getblitzed, but we also might survive and win. Suppose we have the strong position. At double match point, we should beplaying more of a priming game than an attacking game. If we can forceour opponent to crunch his board, he will be very unlikely to win. Undernormal conditions it might be right to attack and risk letting him get sometiming in exchange for the additional gammon possibilities. What about back games? As we all know, a really well-timed back game willwin more often than not. For money it isn't a favorite due to the gammondangers, but at double match point it is fine. Consequently it is good toget into a well-timed Backgame. Of course making sure the timing is adequateis always tricky. At double match point, the timing issue is even moreimportant than usual. The person playing the back game can go out of hisway to avoid crunching, leaving blots strewn all over the place if necessary,while his opponent must be very careful to avoid letting the timing for theback game become decent. Now let's look at the 2 away, 1 away score, where one player needs gammonsvery badly but the other player has no use for them. The player who needsgammons should be playing for gammonish positions, such as blitzes andpriming battles. It is vital for him to build up his inner board fast.Also he doesn't mind having checkers sent back as much as he might underother circumstances. True this hurts him in the race, but the gammon dangerof having checkers sent back is irrelevant. For example, consider how toplay an opening 2-1. For money, the plays of 24/23, 13/11 and 13/11, 6/5are about equal. Not true at this match score. The player who is behindmust play 13/11, 6/5. If he gets away with it he will make his five point,which will improve his gammon chances. If he is hit he will get gammonedmore often, but that doesn't matter. How about for the leader? Just as the trailer wants gammonish positions,the leader wants to avoid gammons. No blitzes for him. Just nice simpleplay. Most important is for him to form an advanced anchor. It is veryhard for you opponent to win a gammon if you have an advanced anchor. Withthat same opening 2-1, it is vital for the leader to play 24/23, 13/11. Thesplit greatly improves the chances of making an advanced anchor, as well asmaking it more difficult for the opponent to make inner board points. There issome danger of being blasted away with 4-4 or 5-5, but you have to live withthat. Once the leader has made that advanced anchor, he should be reluctant to giveit up unless he sees a clear route home. The game plan is to sit on thatanchor until he rolls big doubles, and then run away for the win withouttaking any risk of being gammoned. It should be noted that the leader doesn'tmind complicated games where both sides have a lot of checkers back. Theseusually reduce to mutual holding games, which is fine. What he wants to avoidare games where he is being attacked. I thought it would be useful to look at a few positions from the latest matchof the month, which went to the Crawford game and a couple of games beyond.I will list Jellyfish rollouts of the plays in question, giving the percentageof wins and gammons for each side as well as the cubeless equity. In this waywe can see how certain plays might differ depending on the match score. It must be noted that the Jellyfish rollouts for this sort of problem havea reliability problem other than the usual problems associated with rollouts.The difficulty is that if we are analyzing a double match point problem, theprogram doesn't realize that is what we are doing. Thus in the rollout itplays aggressively for the gammon if it thinks that is correct, not knowingthat it shouldn't be doing that. Consequently, we may get some misleadingresults for that reason. However we can still look at the rollouts andget an idea of what is going on. 150 123 White 10* 11 point match Blue 4 Rollout results: Play Equity Win gammon Win game Lose Game Lose gammon 24/18, 8/4 -.551 10.0% 35.8% 64.2% 35.9%10/6, 10/4 -.562 7.8% 30.3% 69.7% 23.8% This is a classic position which is affected by the score. White can run oneback checker and risk getting blitzed, or hang back and die a slow death. The equity figures show that for money this is a very close decision. At doublematch point, it is another story. The running play wins more than 5% more oftenthan staying, so it is clearly correct. Since Blue has an odd number of pointsto go at the Crawford game, 24/18, 8/4 is correct since the play should bethe same as at double match point. Suppose instead Blue had an even number of points to go, so gammons countedextra for Blue. The running play loses far more gammons than staying. Italso wins more gammons, which is useless to White. Thus 10/6, 10/4 would bevery correct. Of course if it were Blue who were ahead in the match thenrunning would be even more correct since that play generates both more winsand more gammons, and losing a gammon wouldn't matter. 132 120 White 10* 11 point match Blue 4 Rollout results: Play Equity Win gammon Win game Lose Game Lose gammon23/20, 16/10 +.637 20.6% 73.5% 26.5% 4.7%20/11 +.625 24.3% 72.2% 27.8% 7.3%23/14 +.610 26.2% 71.3% 28.7% 9.5% Blue wins more games by locking up the anchor, largely because he can't beattacked so there isn't much White can do. However Blue both wins and losesmore gammons by making one of the other plays. These plays mix the checkersup more. When gammons don't matter Blue should play 23/20, 16/10, but ifBlue can use gammons while White can't then he should play either 20/11 or23/14. 129 107 White 10* 11 point match Blue 4 Rollout results: Play Equity Win gammon Win game Lose Game Lose gammon 13/9*, 9/7 -.731 4.5% 24.3% 75.7% 24.7%6/2, 4/2 -.743 3.1% 22.0% 78.0% 20.5% White can hit and pray, or he can make the two point and hope something goodhappens later. Hitting is surely the best shot at winning the game. Bluemight stay on the bar for a while giving White a chance to win frontwards,or Blue might hit something after which White might be able to time anace-point game. At the match score where gammons almost don't matter, Whiteshould clearly hit. However if the score were 2 away, 1 away, then the gammonswould cost. Since White loses more extra gammons after hitting than he winsgames, it would be correct to make the two point. Note that the plays arepretty close in money equity, but at the different match scores it is quiteclear which play is superior. 111 92 White 10* 11 point match Blue 4 Rollout results: Play Equity Win gammon Win game Lose Game Lose gammon 10/8, 10/4 -.759 2.0% 17.8% 82.2% 13.2%24/16 -.835 5.0% 21.0% 79.0% 29.6% If gammons mattered it would clearly be folly for White to play 24/16. Therollouts demonstrate what we already knew -- that running considerably increasesthe gammon danger. However if White's only care is winning the game, then24/16 is the best shot. If White doesn't run now he will almost certainlybe saddled with a poorly timed ace-point game, and those just don't win veryoften. White has a strong enough board to be a contender if he hits a shot,so if he runs and survives the first salvo he is right in the game. This playlooks intuitively so awful that it is difficult to find at the table, butwhen winning is everything it is the right play. 86 64 White 10* 11 point match Blue 4 Rollout results: Play Equity Win gammon Win game Lose Game Lose gammon6/3, 2/0 +1.017 15.0% 93.2% 6.8% 0.0%6/4, 6/3 +1.010 13.0% 93.9% 6.1% 0.0% The safest play is 6/4, 6/3. That play gives Blue very good distribution,with spares on the four and three points. This is the play to make atdouble match point, since if Blue doesn't get hit he wins. However if gammonsare pulling extra weight then Blue should play 6/3, 2/0. The extra checkeroff can swing the gammon, and keeping the spare on the six point may enableBlue to hold the point for an extra roll, which may be enough to contain theWhite checkers so Blue can win a gammon. Blue will get hit more often andlose more games, but the extra gammons are worth it. 79 59 White 10* 11 point match Blue 4 Rollout results: Play Equity Win gammon Win game Lose Game Lose gammon 4/0 +1.040 14.7% 94.5% 5.5% 0.0%6/5, 6/3 + .996 8.9% 95.3% 4.7% 0.0% This is very similar to the previous position. If gammons counted, 4/0 isclearly the best. The extra danger is minimal, and the increase in gammonpotential from the extra checker off and the held six point is considerable.However if only winning matters than clearing the six point is best. 173 144 White 10 11 point match Blue 5 Rollout results: Play Equity Win gammon Win game Lose Game Lose gammon 20/10(2) +.458 14.0% 68.3% 31.7% 5.1% 20/15(2), 6/1(2)* +.411 15.6% 65.8% 34.2% 6.4% 8/3(2), 6/1(2)*. +.376 19.7% 61.9% 38.1% 6.3% 20/10(2) is clearly the best overall play. This brings the checkers aroundtogether and properly takes advantage of Blue's big racing lead. The playswhich attack on the ace point leave Blue with a divided game, and if Whiteenters quickly Blue will have problems. Even with the gain from winninga gammon equal to the cost of losing the game it turns out that 20/10(2) isbest, but 8/3(2), 6/1(2)* comes in a very close second -- 5.7% more gammons,and 6.4% more losses. It is only the relatively low general gammon threat(because of White's advanced anchor) which makes the blitzing play lose outwhen gammons pull extra weight. 168 169 White 10 11 point match Blue 7 Rollout results: Play Equity Win gammon Win game Lose Game Lose gammon B/21, 20/16, 8/4(2) +.317 21.4% 59.5% 40.5% 9.5% B/21, 20/16, 11/7(2) +.304 18.2% 60.1% 39.9% 8.6% This is a very typical result for an early position. The purer play of makingthe bar point both produces more wins and loses fewer gammons, so for theplayer ahead in the match it is clearly correct. However if the player behindin the match had this play to make, making the four point would be the rightidea. It is inner board points which produce gammons, since they lead tofuture blitzes. Primes are nice to lock up games, but they won't get thegammons which blitzes get. 161 161 White 10 11 point match Blue 7 Rollout results: Play Equity Win gammon Win game Lose Game Lose gammonB/20 +.211 15.7% 57.2% 42.8% 9.4%B/23, 6/3* +.211 18.0% 56.6% 43.4% 10.5% It should be no surprise by now that hitting on the three point stirs thecheckers up and produces more gammons for both sides (and fewer wins for White).While for money the plays are close, at this match score it appears clear forWhite to play B/20. 148 164 White 10 11 point match Blue 7 Rollout results: Play Equity Win gammon Win game Lose Game Lose gammon 13/10, 8/5, 4/1(2)* +.945 49.3% 73.8% 26.2% 5.9% 13/7(2) +.876 36.9% 76.6% 23.4% 4.7% This is an excellent prototype position illustrating the difference betweenvarious plays depending upon the match score. For money, 13/7(2) would bea serious error. The plays which involve shifting to the ace point areclearly superior. White has excellent chances to blitz Blue off the boardwith the shifting play, and this play will produce a lot of extra gammons.However when gammons don't help White, then the quiet 13/7(2) is the bigwinner. The solid five prime makes it very difficult for Blue to win the game.He doesn't figure to have timing to play a satisfactory ace-point game, yetwinning frontwards will be very difficult. It is to be noted that the pureplay also loses fewer gammons than the blitzing play, which is no surprise.If the positions were reversed and the player behind in the match had thedouble-threes to play, then failing to blitz would be a monstrous error. 121 168 White 10 11 point match Blue 7 Rollout results: Play Equity Win gammon Win game Lose Game Lose gammon 21/16*, 16/14 +1.100 45.1% 81.8% 18.2% 2.4% 10/3 +1.063 39.5% 83.5% 16.5% 2.4% When your opponent is playing a deep anchor or back game, every checker yousend back increases your gammon chances. In this position, hitting theblot is the money play or the play if White is behind in the match andcan use the gammon. However for just winning the game, the simple 10/3completing the prime is the winner. 87 131 White 10 11 point match Blue 7 Rollout results: Play Equity Win gammon Win game Lose Game Lose gammon 14/11, 13/12* +1.504 59.2% 92.7% 7.3% 0.1% 14/10 +1.200 32.8% 92.9% 7.0% 0.1% If gammons mattered, it would be a huge blunder to not hit the blot. Howeverif White is just playing for the win, it appears that not hitting is better.By hitting White gives Blue a chance to time his ace-point game if Blue can stayon the bar for a while. If Blue is forced to play, his timing is almostcertain to be shot. The above positions are some illustrations of the big differences in checkerplay which can occur at double match point or when one side can use a gammonbut the other can't. When you reach such a match score it is important tobe aware of your goal and play accordingly. Seemingly obvious plays mightbe very wrong due to the match score.

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