This article originally appeared in the July 2003 issue of GammOnLine.|
Thank you to Kit Woolsey for his kind permission to reproduce it here.
If your opponent plays perfectly, you will never have an advantage. Your
edge comes when he makes errors. If you can create situations where your
opponent may make an error, you will increase your winning chances.
One of the best ways to give your opponent a chance to make an error is with the cube. If you can arrange to send over the cube at a time when he might take when he should pass or pass when he should take, you have the chance for a big gain. This is a main part of my doubling rule philosophy. If I am not 100% sure whether or not he has a take he probably isn't either, which may cause him to make a cube error.
In some situations it may be better to take what you believe is a theoretically incorrect cube action, if you believe there is a good chance that this will induce a later cube error by your opponent. It is important not to overdo this. If you have a clear double and the position is volatile, you must double regardless of your opponent's tendencies and what you think he will do later on. Unless you are playing against a complete madman who will take regardless of the position, you can't afford to risk a big market loss when you roll a good number. Thus, the kind of action I am talking about is only correct in a relatively non-volatile position or when you believe the double is marginal in the first place.
I will often make a double which I consider slightly premature early in a long match just to get a reaction from my opponent. How quick he is to take, how surprised he is that I doubled, his sense of confidence in his take -- all of these things may help me size him up for the future. I think this extra knowledge about one's opponent more than compensates for what little (if any) equity I sacrifice by doubling a bit early. And who know, maybe he will pass!
Let's suppose you believe you have a pretty good read on your opponent's taking tendencies, either from long experience playing him in the past or from his actions at present. We'll examine four different types of characters:
Timid Timothy: This player drops a lot of takable cubes. If there is a threat or a degree of unfamiliarity about the position, he might let an easy take go. You want to give him every chance to make this mistake that you can. On the other hand, you want to avoid doubling when you are sure that he will take, since that sacrifices the opportunity for him to make his favorite error later.
Conservative Charlie: This player isn't as far off the mark as Timid Timothy, but he will tend to pass the close ones including some quite takable doubles. He isn't likely to shock you by passing when you were wondering if you even had a double unless it is an unusual position, but he will let some cubes slip by. With him you are hoping to reach a position where it is clear double and take, and that maybe he will make his mistake and pass.
Aggressive Andy: This player has a lot of confidence in his checker play, and will not be letting any takable doubles go. He likes complex positions, and will often take doubles he should be passing when the position has play. Against this sort of player, you are hoping to reach a position where it is double and pass and he will make a mistake and take. He isn't crazy, so you can't wait too long and hope for a ridiculous take.
Steaming Steve: This player might take anything. It is difficult to lose your market against him, but it can happen so you still have to double sometimes even when you know he will properly take. In non-volatile positions you can definitely wait a lot longer than usual, since even if you get to where he has a pass he is likely to take. Of course you are hoping to get to a position where he has a clear pass and still takes.
Let's examine a few positions and see how we might act against each of these players.
This looks to be a borderline double. Blue is ahead 7 pips in about a 90 pip race, 2 pips less than a 10% lead and neither side having any special distributional advantage. With the cube in the center, racing formulas make this a double, but the double is so close that you won't be sacrificing much theoretical equity by waiting. Let's see what the best cube actions are against each of our characters.
Against Timid Timothy, it is probably correct to wait. Even Timothy should know that this is a clear take. What you are hoping for is that you gain a pip or two on the next exchange, and now he passes what is a clear take. It is only correct to double if you believe that there is actually some chance that Timothy will pass now.
Against Conservative Charlie, you should wait. There is no question that he will take now, but if you gain a couple of pips and double next turn, there is a decent chance that he will pass when he still should be taking. The amount of theoretical equity you are sacrificing by doubing is tiny compared to the potential gain if he drops a double he should be taking in the future.
Against Aggressive Andy, it is correct to double. Andy makes cube mistakes with aggressive takes since he fancies his checker play skills, but he won't be making any mistakes in a simple race such as this. Since doubling is the theoretically correct action and there is no particular reason to expect a future mistake, go ahead and double.
Against Steaming Steve, it is naturally right to wait. Who knows how bad a take he may make in the future. Even if you gain five or six pips on the next exchange, you still may have him taking.
This is a typical five-point holding game. White has an easy take with racing chances, hitting chances, and little gammon danger. Blue barely has a proper double due to the potential large market loss if he rolls big doubles combined with the fact that he will retain his advantage for a while pretty much whatever happens.
Against Timid Timothy, I believe it is correct to wait. Even Timothy isn't going to be afraid to take this one. What you are hoping for is a small improvement, such as gaining more ground in the race, making the bar point, or clearing the midpoint but not to safety (2-2 for example). If one of these things happen you just might get a pass out of Timothy when he still has a pretty easy take. The equity gain when this happens easily compensates for the tiny theoretical equity loss from not doubling now.
Against Conservative Charlie, double. Charlie isn't likely to make a future mistake here. He will still be taking if Blue makes a small improvement, since this isn't the type of position which Charlie will be afraid of. If Blue rolls his big doubles Charlie's drop will be correct, and Blue will lose his market. Since doubling is theoretically correct, go for it.
Against Aggressive Andy, double. Andy makes some bad takes, but not in this sort of position where there will be little checker play skill left if Blue rolls a good number. If Blue rolls well he will lose his market to Andy, so he should make a proper double now.
Against Steaming Steve, wait. You never know what may happen. Even if Blue rolls 4-4, he may find Steve taking later. Any theoretical loss which comes from failing to double now will be more than compensated for if Steve later makes one of his steaming takes.
This is a typical early development double. Blue has the jump in devleopment and a small racing lead, and that plus the potential of a few jokers is sufficient to give him a cube -- but not by much. White has a fairly easy take.
Against Timid Timothy, double. Not only is the double theoretically correct, but this is the sort of position which Timothy just might surprise you and pass. Since it is possible to get the big mistake out of him now, there is no reason to wait.
Against Conservative Charlie, double. Charlie will definitely take now, but he probably won't be taking if Blue makes another improvement. However, Charlie's future pass is quite likely to be correct. If Blue makes one more improvement in this sort of position, he could easily lose his market and Charlie won't be making any mistakes. Just go ahead and make the theoretically correct double.
Against Aggressive Andy, wait. Andy will see a lot of play in this position, even if Blue gains on the next exchange. It is possible for Blue to roll a great attacking number and lose his market, but more likely Blue will make another improvement. After that happens White will probably have a pass, but Aggressive Andy will still be there taking.
Against Steaming Steve, wait. Even on some of Blue's best sequences, Steve just might be taking.
A very typical 1-3 backgame. White has great timing -- maybe. If White can spring a back checker on his next roll he will have as perfect a 1-3 backgame as one could want. In fact he would be a clear favorite to win the game, although the gammon danger makes him a money underdog. If White fails to spring a back checker next roll, his position starts to crumble, and if he doesn't get out in two rolls his board will probably disintegrate beyond repair. White's winning chances are so good that he has an easy take if doubled. Blue just about has a double due to the huge market loss if White's board collapses.
Against Timid Timothy, double. There is a very realistic chance that Timothy will crawl into his shell and pass. He may think: If I don't escape I'm doomed, and if I do escape I still have to hit a shot and win, while all my losses will be gammons. That's the way he thinks. You can't afford to wait, because after Timothy sees the result of the next roll he will definitely get it right -- passing if he doesn't escape, and taking if he does.
Against Conservative Charlie, double. Charlie also isn't going to make a mistake in the future -- he will pass if he doesn't escape and take if he does. The actual double is borderline in theory, but there has to be some slight chance that Charlie will turn more conservative than usual and let it go. That argues for doubling.
Against Aggressive Andy, wait. This is the kind of position Andy loves, since he thinks his superior checker play will see him through. If Andy rolls something like a 4-3 on his next roll he would have a clear pass, yet it wouldn't be at all surprising if he takes. He will be looking at things in the following optimistic manner: Yes, my board is partially busted, but it isn't beyond repair. All I have to do is escape a back checker next turn, and then I will have my timing and should have no difficulty remaking my six point and being right in the game. This is all true. What Andy fails to see is just how badly things go if he doesn't escape on that second roll. That possibility makes it a clear pass after White's 4-3 roll, but Andy may still be with us.
Against Steaming Steve, wait. Everything said about Aggressive Andy holds true vs. Steve, and even more so. The only question vs. Steve would be whether or not to pull the trigger if he doesn't escape next turn, or to wait thinking he will still take even if his board does collapse.
White has a huge take on the race alone. Blue is ahead only 4 pips, and Blue's bearoff structure is less efficient than White's. In fact, the crossovers are equal. The danger of getting hit isn't sufficient to turn this into a pass, particularly since it is possible for White to recover from a hit. White has a very easy take. Blue can lose his market big time if he hits and White flunks. That plus Blue's small racing lead is enough to give Blue a borderline double.
Against Timid Timothy, double. He just might pass. His thinking could be: If Blue hits I'm dead (which he isn't, of course), and if Blue misses I'm still an underdog since I'm behind in the race. Therefore, I'm not going to win 25% of the time. Since the double is borderline correct anyway, that slight chance that Timothy might pass makes the double clear. It can't be right to wait for a later error by Timothy when it is possible that he will make a huge error right now.
Against Conservative Charlie, wait. Charlie will definitely take now, of course. The key variation occurs when Blue hits with something like 3-1, and White enters with a six. Now White still has a take (though close), but Charlie may think it is a pass due to the race and Blue's pick and pass numbers. Charlie may underestimate the possibility of White rolling a joker to hit an indirect shot, along with the various other good things which may happen.
Against Aggressive Andy, double. Andy isn't going to be making any future mistakes in this position. If he is hit and enters with a six he will not be afraid to take, and if he doesn't enter with a six his pass will be clear. Doubling is theoretically correct, so double.
Against Steaming Steve, wait. As always, it is never correct to make a marginal double against Steve. He is quite likely to take something later which is a clear pass. You really have to roll a joker to lose your market against him.
Clearly White has an easy pass if Blue doubles. The question is whether or not Blue should play on for the gammon. There is plenty of gammon potential, but White's anchor cuts down on the danger considerably. There will be plenty of danger down the road. In addition, Blue doesn't even have a free ride on his next roll -- look at how 6-4 plays, for example. For these reasons, it is borderline correct for Blue to double now and cash his sure point.
Against Timid Timothy, wait. The key is that against Timothy, you may be able to bluff him out with the cube later if things go badly. That potential makes playing on for the gammon much safer. Timothy will know that you are playing on for the gammon, so when you double later he will tend to assume that you have just given up on your play-on and are cashing, and he may drop a double which is a clear take.
Against Conservative Charlie, double. It is not clear what turn the game will take, nor whether you are likely to arrive at a position where Charlie may make a mistake. Since cashing is the theoretically correct action, that is what you should do.
Against Aggressive Andy, double. The reasons are largely the same as with Conservative Charlie. Aggressive Andy isn't too likely to make a disastrous blunder in upcoming positions, so it is right to cash.
Against Steaming Steve, it is probably right to wait. Even Steve isn't going to take this cube -- there is a difference between steaming and being a total maniac. By waiting, there are two things which can happen, and both are good. If you roll a good number, you continue to play on for the gammon of course. However, if you roll a moderately poor number but the roof doesn't cave in you can double next turn, and now maybe Steve will take when he should pass.
This is a deceptive position. White is in trouble, but offhand it may seem as though White has some play. He has an anchor, and all of his men are in play. It is easy to see White suriviving and getting back into the game.
The truth of the matter is that White's position is hopeless. The problem is that Blue has too much control. Blue can play an attacking game or a priming game depending upon what his dice tell him, and either way White is likely to get crushed. Even if White wins the fight for Blue's three point, White's timing will be awful for a back game, and with Blue owning White's four point White isn't going to make any progress frontwards for quite a while. If Blue doubles, White has a very easy pass. In fact, Blue's position is so solid and it is so difficult for Whtie to snap back into the game quickly that in theory Blue has a borderline play-on for a gammon. But what should Blue do in practice?
Against Timid Timothy, wait. Timothy will correctly pass if doubled, of course, and playing on is reasonable. Furthermore, if things go badly for Blue he is likely to be able to bluff Timothy out later on anyway. It is a win-win proposition.
Against Conservative Charlie, wait. The same arguments apply as with Timid Timothy, although not as strongly. Charlie isn't going to make a mistake now -- he will certainly pass -- but he might make a mistake in the future. Since the decision of whether or not to play in is close anyway, that factor argues for playing on.
Against Aggressive Andy, it is a close decision. The key question is whether or not Andy will take now. This is the type of position Andy will like to play, but he may think it is just too hopeless. If you are convinced that Andy will pass, take a roll. If things go well continue playing on for the gammon, but if Andy wins the next exchange then turn the cube and Andy will probably make a bad take. However, if you think there is a decent chance that Andy will take now, then by all means send the cube over.
Against Steaming Steve, double. He won't recognize how bad his position really is, and odds are that he will snap up the cube. This sort of position is the type where you can really cash in against Steve.
The above positions give some idea of how one can take advantage of an opponent's tendencies to induce cube errors. Of course a lot of these decisions are quite subjective and you may disagree with me on some of them. The important thing is to get the right train of thinking. Reading the opponent's tendencies can be quite tricky, but with practice the skill comes. Once again, don't overdo this and step way out of line. If you make ridiculously early doubles against Timid Timothy in the futile hope that he will pass or if you wait way too long against Steaming Steve in the hope he will take later, you will find yourself throwing away your intrinsic advantage against these players. Most of the time, double when you think you have a double regardless of who you are playing. However, when you have a close decision as to whether or not to double, taking the opponent factor into account may lead you to the winning decision.