Michel SEMERTZIDIS, Ph.d., Financial Web Site
CALCUL......7,8,9 SHOT....DIRECT SINGLE SHOT.........52,33,43 bearing
then multiply the cube with this fraction (or the cube*2 if the opponent loses a double if he does not throw the winning shot)
HINTS FOR CHOUETTE PLAYERS
1. Don't chicken out just because you are in the box.
2. If Timing Advantage is about to slip away for good you should negotiate by settlements, especially if you are in the box. Don't get stuck in a corner where the whole evening's result is going to ride on the outcome of one or twho rolls.
3. Try not to be too greedy. Use prudent money management. Never shoot the whole works on one colossal roll unless you are prepared to quite the game for several monthsor more if the risk doesn't comme off.
4. Put pressure on the box. So if you judge the man in the box to be conservative by nature, PUT ON PRESSURE BY DOUBLING HIM IN POSITIONS WHERE HE IS IN REAL DANGER OF LOSING A GAMMON.
CRAWFORD RULE : If you are on the score just one point short of what you need to win the X-point match the Crawford rule says there can be no doubling in next game. Ex : 4-1 in a 5-point match. in the next game no doubling allowed. But then in the follwing one doubling is allowed.
CRAWFORD SITUATION : If you are doubled when you are at en even number on the score and your opponent reaches the CRAWFORD SITUATION it's best for you. Ex: 17 points match and you are ahead 14-12 with the cube on 2 on the opponent side. If he doubles : a) you take and lose ---> new score 14-16. b) you drop ---> new score 14-14. In both cases you have to win two games in a row in in order to win the match.
MATCH EQUITIES - JANOWSKI FORMULA:
D=difference between the two players scores
T=number of points the trailer player needs to win the match
Match winning probability of the leading player is 50+(D*85/(T+6)). Or if the Crawford game is being played this change to 55+(D*55/(T+2)).
>MATCH EQUITIES - UNDERWOOD FORMULA:
W=the match length
Match winning probability of the leading player is 50+ the first (L-T) numbers from the following sequence : 9 8 6 5 4 3 2 2 2 2 2 2 . If W-L>4 the substract ((W-L)+(W-T))/4 from the number previpously calculated.
Explanation of Snowie's HTML output
Checker play frames
# Ply Move Equity
* 4 2 13/9 0.091 (-0.024)
0.6% 15.7% 53.1% 46.9% 12.8% 0.5%
The first line shows the following information:
* 4 rank of the given move (* before the rank indicates that it is the played move)
2 ply of the evaluation
13/9 move string
0.091 cubeful equity of the move
(-0.024) difference of equity with best move
The second line (hidden if the Detail Mode has not been checked) displays the complete cubeless evaluation of the move:
0.6% 15.7% 53.1% 46.9% 12.8% 0.5%
Player's wins Player's losses
If you check the Evaluation Parameters, you get additional information about how the evaluation was computed.
Cube action frames
Example: Cube action equity
3-Ply Money equity: 0.469
0.6% 19.4% 66.9% 33.1% 6.7% 0.2%
1. No double 0.711
2. Double, take 0.696 (-0.015)
3. Double, pass 1.000 (+0.289)
Proper cube action: No double 5%
The first two lines display the cubeless evaluation of the position. The evaluation can be of type 1-Ply, 2-Ply, 3-Ply, Mini-Rollout, Rollout or Database. Below the cubeless money equity of the position, the detailed probabilities are also displayed. They are in the same order as the detailed line for the checker play.
The next section displays the cubeful equities of the possible cube actions. From the point of view of the player in action there are two possible actions: Double or No Double. If the player in action decides to double, then there are two options for his opponent: either take or pass the offered cube. Therefore, there are three possible actions that can be played: No double, Double, take or Double, pass. The first line corresponds to the correct action for both sides. The second line displays the line which corresponds to the wrong double/no double action but with the correct response of the opponent. Finally, the last line corresponds to the equity you would have if your opponent would do the wrong take/pass decision to an offered double.
In the example above the cubeful equity of not doubling is 0.711 pts/game. Now, if you offer a double and your opponent correctly takes the cube you will only earn 0.696 pts/game on average and finally if you double and your opponent passes you will earn 1 pt. Of course your best equity is the 1 pt you would win if you double and your opponent passes but since you have no control on what your opponent will do, the best action here is not to double so that you secure an equity of 0.711 which is better than the equity of 0.696 you have if you double.
As we have seen, the best equity you can earn here is the 1 pt if your opponent passes. Suppose you have the suspicion that your opponent might pass but you are not sure. Is Snowie able to tell whether you should whip it anyway to profit from his occasional incorrect passes? Yes, Snowie is able to tell you that. Snowie gives you a borderline frequency at which your opponent is supposed to pass to make the theoretically incorrect double practically correct. In our example Snowie says that this frequency is 5%. Therefore, the double becomes correct if you think there is a 5% chance that your opponent passes the cube!
BACKGAMMON RULES OF THUMB, by Phil Simborg
Over the board we often have tough decisions to make. If we truly took the time to reason through all of the variables and consider all of the ramifications of every play, it would not only take hours to make a decision, we would probably end up being very confused.
Top players don't have a lot of really tough decisions to make during a typical game. And that's because they have thousands of reference positions in their heads that generally tell them the basic strategy and decision for given situations, but also because they are constantly applying Rules of Thumb that they have adopted over the years. These Rules of Thumb help them quickly rule out most of the bad plays and decisions and generally direct them to the right decision.
I have been giving lessons to beginner and intermediate players for about 20 years, and I am still taking lessons, myself, and getting coaching from some of the best players in the world. I have found that there are certain Rules of Thumb that keep coming up over and over again, and for your benefit, I thought I would simply list them for you.
If you already know all of these rules of thumb, great…just remember to use them. And if there are some you don't know, at least now you know something you don't know and you can get some help from an expert or a good backgammon book and learn about it.
One of the first things a beginner learns is that the game is all about the race. So they learn, in effect, a rule of thumb that they should be aware of or know the pip count and adjust their play and cube decisions accordingly. They also learn that there are opening moves that have been proven to be best, so as a rule of thumb they will make points with 3-1, 4-2, 5-3, and 6-1, and there are rules of thumb about all other opening rolls.
Of course these rules do not apply in every situation, and if applied at the wrong time they could lead you to the wrong play or cube decision, but overall, I guarantee you that knowledge of these rules will greatly help and simplify your decision-making process.
Checker Play Rules of Thumb:
Always consider: can I hit, can I make a point, can I safety checkers
If I have to leave blots, can I use duplication to reduce risks
Can I hit and make a point
Can I hit two checkers
Can I make a 6-prime, and if not, can I make a 5 or 4 prime
Most of the time, in the early game, if you can make your 5 point, it's the right play
Try not to stack a lot of checkers on the same point
Try not to put checkers out of play
Try to leave indirect shots instead of direct shots
Offense/offense, defense/defense (when you are in an offensive position, tend to make the more offensive play, and when you are in a defensive position, tend to make the more defensive play)
If you fear being doubled, which play is least likely to get you the cube
If your opponent is on your 4 point or higher, the game is predominantly a race; if he is on lower points, the race is less of a factor
In the early game, if he has 2 checkers on his 8 point, be more inclined to split your back checkers
If you have more inner board points than your opponent, be more inclined to get into a hitting game, and conversely, if you have fewer points, be less inclined.
If you are up in the race, be more inclined to play safe and to run. If you are behind in the race, look for blocking and hitting opportunities
Generally, it is good to slot the back of the prime. Try to make your points in order and make points together.
Generally, if your opponent is at the edge of your prime, that's an invitation to hit him.
At Double-Match-Point, be more willing to take a big risk if the odds are in your favor and success means winning the match.
If you are at a score where saving gammons is important, making an advanced anchor is a priority. Staying away from back games is also a priority.
If you are at a score where winning gammons is important, attempting to blitz and hit is a priority even if it risks your getting into a back game. Try to keep your opponent from making an advanced anchor.
Any time you are not sure which move to make, put yourself in your opponent's shoes and ask yourself which move you would hope your opponent would not make.
When considering alternative moves, think about what gets you not only the most wins and losses, but also the most gammons and backgammons.
When considering moves, think about how your move might affect his or your cube decision on the next few rolls.
Cube Decision Rules of Thumb:
Think about your cube strategy, match equity, and take points, given the score, before each game begins.
Think about whether or not you should be doubling before every roll.
Major things to consider about doubling are race, opportunity, and threats. Assess all three in your decision-making process.
If you are thinking about doubling, apply Woolsey's Law: Put yourself in your opponent's shoes and ask yourself if you are sure if it's a take or sure if it's a drop, and if you're not sure, then for sure it's a double.
If you are thinking about doubling, apply Simborg's Law: Put yourself in your opponent's shoes and ask yourself which decision causes the most pain. Would you love to see the cube or hate to see it? (The goal, in Backgammon, is to cause as much pain as possible to your opponent.)
If you're not sure about giving the cube, ask yourself how you would feel if he takes it, and how you would feel if he drops it. That should give you some direction on whether or not to give it.
When you are thinking of doubling, always ask yourself if you are "too good" to double.
When you're not quite sure whether to give the cube or not, give it. You might be making a mistake not to cube, and you might be making a mistake to cube, but you only give your opponent a chance to make a mistake if you do cube.
At 2-away/2-away double as soon as you are up even slightly. If you're not sure, double anyway.
At 2-away/2-away take any cube if you think you can win 1/3 of the games or more. (Gammons and backgammons don't matter.)
If it's post-Crawford and you are losing, give the cube on the first roll every time.
If it's post-Crawford and you are winning, if your opponent is an even number away from winning the match, you might have a "free drop."
Don't forget that you are playing a human being, and take into account what you know, or think you know about that person's tendencies relative to taking and dropping cubes.