The player who can’t count the position fast and accurately concedes a significant advantage to the player who can. There are many players at advanced level and even some experts who can’t do it easily, but all that one can say is that they would be even better players if they could. They are like skilled cabinet makers who can’t put up a shelf in the kitchen!
On the other hand, pip counting is a skill that even a beginner can acquire with a little application and once learned, it will win you points steadily for the rest of your life. However, this is one area where I don’t feel that I can add anything useful to what has already been written on the subject, so here is the link to what I consider to be the definitive article on counting, written by the American master player Jack Kissane. I really have nothing to add to this superlative piece.
There are many systems designed to reduce the work required in the calculation, although all of them in my view require considerable mental agility. One of the most interesting is Sho Sengoku’s “Five Count” system. Take a look at it and see if it is helpful for you.
Pip counting isn’t learned in a moment. You do have to practice it every day, like learning to play scales on the piano. Do it with pencil and paper at first if retaining several numbers in your head at one time is hard for you, but practice makes perfect. Do it until it is easy. You will never regret it.
Let’s move on to propositions. A proposition is an offer to play a position for money and they come in all shapes and sizes. They can be a very useful learning aid and if you are skilful and lucky, they can also earn you a lot of money! If you attend a live tournament, particularly if you are a beginner, a nice gentleman will lay out the checkers on a board and offer you the opportunity to risk a little spending cash on his prop. All of these require a great deal of skill and should be avoided! The position below is a typical example.
This is one of Walter Trice’s “Saturday Night Specials”, a seemingly innocuous little problem much imitated by lesser mortals over the years. The gentleman offering the proposition will invite you to play either side of this, rolling to see who goes first with the cube in the middle for small stakes. He doesn’t mind if the stakes are small, because each game will last about 1 minute! If he allows you to play either side, where is his edge? Doesn’t this mean that the positions are equal? Actually, Red is minutely better (by 0.3 pips!), but to all intents and purposes, they are equal. His edge lies in the fact that he will know how to use the cube in this position and it is likely that you won’t.
What he knows how to do, is to compare Red’s side, with five checkers already off and 50 pips to go, with White’s side, no checkers off, but certain to be off in 8 rolls and probably less. White’s pip count in this position is 30, but it is useless for comparing it to Red’s position, because unless she rolls all ones twos and threes from here on, she will waste a lot of pips every time she rolls a larger number. Red is in a pip race, while White is in a roll race and Walter is the man who discovered how to compare the two.
He calls his wonderful invention the Effective Pip Count (EPC) and it works like this. The EPC of a roll position can be expressed by the formula 7n+1, where n is the maximum number of rolls that are needed to bear off all the checkers. White is in an 8 roll position here, so (7 x 8) + 1 = 57. What we have effectively done is to adjust White’s pip count to allow for wastage when she rolls high numbers and has to use them to bear off checkers from low points.
In order to compare it to Red’s pip count we have to adjust that for wastage too. It may appear at first sight that Red won’t have any wastage, because he will take off checkers with sixes, fives and fours and move checkers to fill the lower points with threes, twos and ones. At first that will be true, but in fact later on he will have some wastage. There is no formula for this, but this position has wastage of about 7 pips, a fairly typical figure for this configuration. Adding 7 to Red’s raw pip count gives him an EPC of 57, equal to White. If you have downloaded GNUBG and are using it to help your game, then you will find the EPC displayed in bear offs, so you can compare that to actual pip counts and begin to get a feel for wastage.
So, now that we have our wonderful EPCs, how do we use them to figure out the correct cube action for this type of position? Unfortunately we can’t compare them in the same way as normal pip counts, but the cube action isn’t too difficult to compute. Start with the number of rolls needed by the player on roll and subtract three. The resulting number is the maximum deficit in EPC where the trailer still has a take. In the position on the board, White is in an 8 roll position. Subtract 3 from 8 to get 5 and if Red is 5 EPC pips behind, he can still take. If he is four pips behind, White can redouble and if he is three pips behind, White has an initial double but not a redouble.
When Red is on roll, it isn’t immediately clear how many rolls he does need to get off, but all we have to do is convert his EPC to a roll equivalent. He has an EPC of 57 and using the 7n+1 = EPC formula backwards (EPC-1)/7 = n, then (57-1)/7 = 8 and just as above, White will be able to take with a deficit of 5, while Red will have a redouble with a lead of 4 and an initial double with a lead of 3. Red’s wastage will remain about the same for several more rolls, typically 6.5 to 7, so you should be able to use the EPC to guide your cube action throughout the bearoff. Sounds complicated doesn’t it? It is at first, but I guarantee that if you sit down with your practice buddy and play this prop out a hundred times, checking the EPC constantly, then it will become second nature to you. You may even become a hustler yourself!
Another proposition as old as time itself was a good earner for the hustlers of the old days. It goes like this. The hustler offers to play the pigeon for $10 a point and if the pigeon shows some common sense and refuses, then the hustler says, “Well, I’ll give you the opening roll every game, in fact I’ll do better than that, you can start with 1-1 every game, but you must let me have the cube on my side”. Now even the pigeon knows that having 1-1 to start is a terrific advantage. Between equal players and with the cube in the middle, this start makes him about 59% to win, including 18 gammons. However, these are not equal players and the cube is not in the middle. Owning the cube, the hustler is probably giving an equal player 1/10th of a point start, but against a pigeon he is a nice favorite and moreover, each game is for $20, not 10! Don’t try this one at home children, but it nicely demonstrates the power of cube ownership.
Propositions almost always depend on the hustler knowing how to play the position and you should generally avoid them, but they do have their place in the learning process too. The proposition chouette is a great way for a small group to learn together. It works like this. Play starts as a normal chouette, but when (as inevitably happens) two or more players have differing views of what the correct play should be, then the position can be played as a prop, either there and then or at the end of the game.
The prop is played for the agreed stake until one side gives up, and then everybody learns something. You can do the same with disputed cube actions too. Usually a take/pass proposition is played by the “passers” paying the “takers” a point to play the position owning a 2 cube. Having to play a take as a proposition discourages solo takers from taking a pass in order to try and steal the box. Another way of doing this is for your chouette to have a rule that solo takers must agree to take “extras”. All the droppers have the option to pay the taker one point to take an extra 2 cube. Adopting some of these rules will mean that everybody will learn something as they play, as well as providing a lot of fast action!
If you play for money, then you will soon need to know about settlements. A settlement is just an offer from one side to pay (or take) a number of points to end the game without rolling any further. Take a look at this position.
Red is on roll needing one of the four largest doubles to turn this game around, an 11% chance of winning. A canny and slightly conservative White player might choose to stop Red from rolling and say, “Don’t roll, I’ll take 3 points here”. If you are Red, is this a good offer? It’s easy to work out. If he rolls, Red will win 4 points 11% of the time and lose 4 points 89% of the time, on average losing 78% of 4 points or 3.12 points per game. Red is slightly better off taking White’s offer. What White is doing is paying 0.12 of a point as insurance against Red rolling a devastating joker. Controlling the large swings of fortune in this way is good money management, although in the long run of course it will cost you some money.
With White on roll in this next position a savvy Red player might well say, “Don’t roll, I’ll take a point”. Indeed White might well offer to pay a point before rolling. Is that a good settlement?
Clearly White will win every time that she hits, because she will just double Red out. Her chances of hitting are of course 11/36 or about 30%. Red’s winning chances are 70% from here because White’s winning chances decline sharply after this roll. She will have to give up her anchor with the next 6 and start breaking her board very soon. Ten of Red’s 70 wins will be gammons so we can work out the value of this position quite easily. White wins 30 @ 2 points totaling 60. Red wins 60 @ 2 and 10 @ 4, totaling 160. Red wins exactly one point a game on average. The settlement is exactly correct!
Settlements are usually offered in very simple positions where the dice will decide the outcome and skill isn’t a factor, particularly if the cube is at a high level. This last position is not uncommon.
Red is a very small favorite, with 19 winning rolls and 17 losers, or about 53%. However, the cube has no value for White so Red must double and of course White must take. Both players are going to be slightly nervous about staking 16 points on a single dice roll, so the most usual settlement here is for Red to take a point. He is worth exactly 1/18 x 16 points or 0.88 points in reality, but most White players will happily pay the extra 0.12 points to reduce the risks involved. Another way of cutting down on the huge swings involved in this sort of position is to roll it 8 times with the cube on 2, but for some reason this is rarely done.
If you are offered a settlement of a very large cube that you consider to be unfair, or if you can’t work out whether it is fair or not, then you may like to offer to play several times with a lower cube value. It’s the most accurate settlement there is. Nobody can be forced to take a settlement of course, so if either player insists on rolling, that’s it.
Well, that’s it for this week. I’ll finish by offering a sound piece of advice for aspiring money players. Don’t play for stakes that are too high for you. Stakes should be large enough to be meaningful, but small enough to be affordable. Think of the figure that would be the most that you would ever want to lose in a session, divide it by 200 and that is a good guide. If $200 is the most that you can afford to lose in a night, then a dollar a point is the stake for you. Winning and losing very large amounts loses friends and they are more valuable than the money!
Until next time, enjoy the Game!