Michel SEMERTZIDIS, Ph.d.,    Financial Web Site


TAVLI

Hit Some Blots
STRATEGY
THE SEVEN PILARS
36 COMBINATIONS
PROBABILITY OF HITTING A BLOT
PROBABILITIES OF ENTERING FROM BAR
ODDS FOR AND AGAINST BEARING YOUR LAST MAN OR LAST TWO MEN OFF IN ONE OR TWO ROLLS
NUMBER OF WAYS TO MAKE A POINT
OUVERTURES
BLITZ
GENERAL
SAFE vs BOLD PLAY
BACK GAME (MASO)
GAMMON CONSIDERATIONS
TA : TIMING ADVANTAGE or PRIME vs PRIME
PIP COUNT
MAZEMA
DOUBLES
PSYCHOLOGY OF DOUBLING
SETTLEMENTS
CHOUETTE
MATCH PLAY
SNOWIE
BACKGAMMON RULES OF THUMB


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Walter Trice: Let's Hit Some Blots
Backgammon strategy in a nutshell: hit blots, make points, win the race. It seems too simple, but most players could improve their game by focusing on this formula. Almost all players below the expert level could get better results simply by hitting blots and making points more often instead of just moving the checkers around to spots where they look superficially safer.
If you don't believe me, try using a neural network program such as GNU or Snowie to analyze your matches. Set your error threshold at a level that turns up two or three errors in a typical game. Start by working on the "hit blots" part, which happens to be the most important. Collect your checker play errors where either you hit a blot but should not have, or you failed to hit a blot but should have.
Save the two different types of errors in separate folders.
In all likelihood you will find that the "failure to hit" group outnumbers the "improper hit" collection. Later on you may want to refine your classification of hit/don't problems, since they do vary greatly in their characteristics in different phases of the game and in different types of positions.
I did a bit of field research over the past couple of weeks to collect positions for this article, playing matches on various internet servers against a variety of players. Generally my opponents were weaker than me, but many were well above average for their environment, ranging up to the level of strong intermediates in the live tournament scene.
I had no difficulty finding errors in hit-or-don't situations, and the great majority were failures to hit. The most common type of error was the missed loose home board hit in the opening.


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STRATEGY

SUN TZU : WHENEVER POSSIBLE DO THE UNEXPECTED AND GIVE NO WARNING.

When things are going your way -when you're in the pattern of succes- it makes sense to put more on the line and slightly increase your risk.
And when you are strong, YOU decide when to stop; don't be forced into early retirement. But when things are against you, stop and regroup.
Never do anything out of fear, if you can avoid it. Fear clouds your thinking and places your focus on the negative outcome.
If you need to win then will you lose because you will be focused on what is at stake and not on the objective.

DISPERSE TO CONCENTRATE : The concentration of strength against weakness. To be able to concentrate one must be able to disperse the opponent's strength, which can only be brought about by a dispersion of one's strengths. YOUR DIPSERSION, HIS DIPSERSION, YOUR CONCENTRATION.
DISLOCATE AND EXPLOIT : Don't attack when and where they most expect; attack when and where the least expect.
ERRONEOUS SIGNALS : Signaling is deployed as a feint to focus the other side's ressources at a point where no attack is planned.


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THE SEVEN PILARS
1. Make the move your opponent does not want you to make - "pressure playing".
2. Always take the 3-1 odds when you have better than 25% chanc to win.
3. It is better to kill than to be assasinated.
4. Duplication better to give than to get.
5. Timing Advantage (TA). Dictator of the Game Plan (GP).
6. Count the odds.
7. Courage.



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36 COMBINATIONS, 21 THROWS (EACH DOUBLE 1/36, EACH NON DOUBLE 2/36): AVERAGE THROW 8.17 Standard Deviation (variation from the mean) = 4.3 approx. 4 because of the waste of 6's and the efficiency of 1,2' is more accurate to consider 4.
66 55 44 33 22 11....6*1
65 54 43 32 21.......5*2
64 53 42 31..........4*2
63 52 41.............3*2
62 51................2*2
61...................1*2

THE MAGIC MATRIX

- 00 00 00 00 00 00 7
- 11 12 13 14 15 16 8
2 21 22 23 24 25 26 9
3 31 32 33 34 35 36 10
4 41 42 43 44 45 46 11
5 51 52 53 54 55 56 12
6 61 62 63 64 65 66
The longest diagonal has 6 entries and represents the number 7.


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PROBABILITY OF HITTING A BLOT
SINGLE SHOT 11/36
DOUBLE SHOT 20/36
TRIPLE SHOT 27/36

RULE OF ELEVEN : 11 PIPS IS THE OPTIMUM DISTANCE FOR X TO KEEP HIS BLOT (AND POTENTIAL HITTER) FROM O's BLOT.

Number (distance)
(we don't take here in consideration any points between you and the blot)
6 (17/36)
5, 4 (15/36)
3 (14/36)
2 (12/36)
1 (11/36)
8, 7 (6/36)
9 (5/36)
10, 12 (3/36)
11 (2/36)
15, 16, 18, 20, 24 (1/36)

Number (distance)
(we don't take here in consideration any points between you and the blot)
1 11/36 (12,21,13,31,14,41,15,51,16,61,+11)
2 12/36 (+11)
3 14/36 (+11,12,21)
4 15/36 (+11,22,13,31)
5 15/36 (+14,41,23,32)
6 17/36 (+22,33,15,51,24,42)
7 6/36
8 6/36
9 5/36
10 3/36
11 2/36
12 3/36
13, 14 0/36
15 1/36
16 1/36
17 0/36
18 1/36
19 0/36
20 1/36
21, 22, 23 0/36
24 1/36
When you are exposed to two numbers the chance that you will be hit is determined by adding the two individual ways and subtracting any duplication.


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PROBABILITIES OF ENTERING FROM BAR
points open.....ways to come in....chances of come in
...5.................35.................97% (35/1)
...4.................32.................89% (32/4)
...3.................27.................75% (27/9)
...2.................20.................56% (20/16) <-------
...1.................11.................31% (11/25)

PROBABILITIES OF ENTERING FROM BAR
points open........IN NO MORE THAN :
..............1.......2.......3........4......5
............roll....rolls...rolls...rolls...rolls
....3.......0.750....0.937....0.984....0.996....0.999
....2.......0.556....0.802....0.912....0.961....0.983
....1.......0.306....0.518....0.665....0.767....0.838

PROBABILITIES OF COMING IN FROM BAR WITH TWO MEN OUT
points open....both men.....one man.......neither
....5...........25/36...........10/36...........1/36
....4...........16/36...........16/36...........4/36
....3...........9/36...........18/36...........9/36
....2...........4/36...........16/36...........16/36
....1...........1/36...........10/36...........25/36
(in order to calculate the column 2 (both man) note that when you have to bring in two men the number of succesful rolls is the square of the number of open points (1^2, 2^2, 3^2, 4^2, 5^2)



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ODDS FOR AND AGAINST BEARING YOUR LAST MAN OR LAST TWO MEN OFF IN ONE OR TWO ROLLS (61,43,33 BADS IN ORDER)
Men's..........number of.....odds in favour....your probability
location......ways to bear...or against........of bearing all
..................all first time.......................in two rolls
66..................4.......8/1 against...........78%
65..................6.......5/1 against...........88%
55..................6.......5/1 against...........92%
64..................8.......7/2 against...........93%
54..................10......13/5 against..........96%
63..................10......13/5 against..........97%
44..................11......25/11 against.........98%
62..................13......23/13 against.........99%
53..................14......11/7 against..........99%
61..................15......7/5 against...........99+%
43..................17......19/17 against.........99+%
33..................17......19/17 against.........99+%
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
52..................19......19/17 in favour......100% certain
51..................23......23/13 in favour......100% certain
42..................23......23/13 in favour......100% certain
32..................25......25/11 in favour......100% certain
22..................26......13/5 in favour.......100% certain
6...................27......3/1 in favour........100% certain
41..................29......29/7 in favour.......100% certain
5...................31......31/5 in favour.......100% certain
31..................34......17/1 in favour.......100% certain
4...................34......17/1 in favour.......100% certain
21..................36......certain to bear off..100% certain
3...................36......certain to bear off..100% certain
11..................36......certain to bear off..100% certain
2...................36......certain to bear off..100% certain

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NUMBER OF WAYS TO MAKE A POINT
Number of builders...with doubles...without doubles
............1............1............0
............2............4............2
............3............9............6
............4...........16...........12
............5...........25...........20
............6...........36...........30


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OUVERTURES
21 6/5, 13/11 ou 13/10 ou 24/23, 13/11
62 24/18, 13/11 ou 13/5 (old)
in general, a loose six in the opening should be played to the opposing bar-point rather to your own bar-point. The downside is less, while the upside is greater.
jamais spliter les 24 à 24 et 22 parce qu'il peut les frapper les deux avec 55
33 8/5(2), 6/3(2) ou 8/5(2), 24/21(2) ou 13/7(2)
22 13/11(2), 6/4(2) ou 24/20(2)
44 faire mon 4 et son 5
32,43,53,54 descendre 2 hommes
64, 63 comme 65 (si adversaire mauvais descendre 2 hommes)
41 13/9, 6/5 ou 13/9, 24/23 ou 13/8
51 13/8, 6/5 ou 13/8, 24/23

SPLIT your back men from 25 to 24

The four back men are the concern at the early game extricate your back men and block his two back men



REPLIES TO THE OPENINGS MOVES
If he has made a point in his inner board, don't move back men to his bar point.

If he has split his back men don't expose a man in your outer board.

If he has put a blot where you can hit it, in general you have to hit it.

Reply to (63 24/18, 13/10)
52 13/8, 6/2 (if you have to expose a blot to a direct shot expose one where it will help you most)
51 8/7*, 6/1*
41 8/7*, 24/20

Reply to 31
43 or 32 move two men from 13


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BLITZ
55 is the most common blitzing double.
Blitzes are characterized by quick double, big swings of fortune, and plenty of gammons.
Evaluate a blitz:
- How many home boards points does the attacker have? Doubling with just a 2-point board is unusual. 3-point boards often yield strong doubles but clear takes. 4-point boards are the sign of a likely pass.
- How many checkers on the bar? One checker is typical. Two checkers on the bar usually means a pass.
- How many vulnerable blots does the defender have? One is tolerable. More than that usually points to a pass.
- How many builders does the attacker have? More is better.
- Does the defender have points made in his home board? Even one extra home board point enhances the defender's chances enormously.


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GENERAL
THINKING WHEN PLAYING: PLAN, CUBE, DOUBLETS, CANDIDATE PLAYS
0.0) PATIENCE
0) HAVE A PLAN
1) CUBE : before every roll CUBE DECISION
2) DOUBLET : if I have thrown a doublet, probably A LARGE NUMBER OF CANDIDATES PLAYS.
3.a) CANDIDATES : I try to IDENTIFY ALL THE CANDIDATES PLAYS.
3.b) COUNT THE WAYS

TOP PRIORITIES POINTS : 5, 4, 7. (Chez l'adversaire le 7 point au début: pendant qu'il se bat pour le point 7 il ne fait pas des point dans son board, et de toutes façons tu peux rester jusqu'à la fin du jeu et tu tiens son midpoint (13).
Dont make the oponents 2 point.
Block the opponents points 6 points in front of him (this is another reason why is wrong to make your opponent 2 point.
When you have to expose a blot to a direct shot expose it where will do the most good if it isnt hit.

Mieux vaut taper que construire. - Mieux vaut un avantage permanent qu'un avantage temporaire.
In most positions hitting two checkers is very powerfull game. Don't miss it. (sauf si tu ne veux pas l'aider à son backgame ou si tu as vraiment mieux à faire.
Inversement, éviter de se faire taper deux soldats.

If both you and your opponent want to make the same point, don't slot it, wait to make it naturally.

Si l'adversaire met un soldat à son point 5 il faut absolument le taper.

If your opponent piled up, don't be hurry to run. Stay back and wait for a shot which will invariably materialize. In the interior get a good inner defense ready.

Pour avancer un PRIME, il faut avoir un soldat sur le prime, que tu dois envoyer juste devant le prime et le couvrir par la suite.
Another important technique to use in building a prime is to made it in reverse. We usually want to lengthen a prime by adding additional points to the front, but in some cases it is much easier and quicker to add on points in back.

Don't slot when your opponent has two men on the bar (even for the sixth point) wait until he reenters with one man and then hit him even with a blot if necessary.

BLOCKING: You block a point of your opponent making a point 5 or 6 pips in front of him. When the opponent has only one man back the rule loses much of his force.

HOLDING YOUR MIDPOINT. : As long as you have men back in your opponents inner board you should not give the midpoint (unless you have established some other outfield point). A good stratagem is to lure your opponent off his midpoint, after wich you take control of the outfield and you strangle him.

DO NOT SLOT IN YOUR INNER BOARD WHEN YOUR BACK MEN ARE SPLIT OR EXPOSED, et le contraire. Si il slot, le taper quelque soit pour ne pas le laisser faire les points qu'il a sloté.

When both have the 5 point, the first who gives up his anchor is usually exposed and vulnerable and thus at a distinct disadvantage.

NUMBERS : We favor large numbers because help us in races, allow us to escape. But small numbers keep us from crashing and enable us to smooth out our distribution. The problem with large numbers is that usually may be taken in few ways. Often they compel forced moves. In most positions small numbers are friendly. So when we look aheadwe pay special attention to hostile 6's and 5's in planning ahead.Thats why we use a spare ace to fill a hole on our 5-point rather than on our 1-point.
Of all shakes the double-5's is the most perverse. You should always be on the lookout for oportunities to get double-5's to work for you rather than against you.


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SAFE vs BOLD PLAY
When you have more men back than your opponent, you try to force an exchange of hits (you slot the 5,4,7).
If your inner board is stronger Play Bold.
If you are behind in the race Play Bold.
Do you have an anchor? Play bold.
Has he a strong inner board? Play safe.
Has he blots in his inner board? Play bold.


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BACK GAME (MASO)
AVOID IT (risk double or triple). The back game is an all out gamble. You might lose a double but your opponent no.
NEVER DOUBLE a potential back game
In defending a back game you must try not to help your opponent by hitting his open men. More importantly and if his timing is right you must allow yourself to be hit, especially when he has no blot in his board. If he has got 3 men in your inner board already, under no circumstances give him a 4th.

1) Once you are in a full back game leave blots galore. 2) Timing. 3) Do not hit to early (you need at least 3.4 points in your board).

Ne jamais faire plus que 3 points chez l'adversaire pour lui permettre de jouer.
Holding 3 points in the adversary is super.

If you have more than two men on the one point, the extra men are liabilities.

If you are on the adversary one point with one man and he has only 2 men don't wait. If he has 3 men wait.

Otan eisai mplokarismenos sto board tou antipalou kai den theleis na xalaseis to prime sou, paikse ta mikra (asous kai dyo) apo to 7 et/ou 6 point sou gia na mhn exeis 6 et/ou 5 gia na paikseis sthn sunexeia, kai ta loipa.

The key to winning back games (as opposed to just hitting an opposing blot during the bear-off) is to keep your own 1 point open for the enemy blot to enter. Otherwise if for example your board consists of your 1, 2, 3, and 4 points, the opponent will be able to enter on your 5 or 6 points, and a desperate struggle will follow, with you trying to hit again and again while he tries to escape.

In a back game, hit your shot first, then think of doubling. You still have to contain the checker you hit.

SNOWIE SIMULATIONS (KALA BACKGAME: OTIDHPOTE ME 2 KAI 3 EXTOS TOU 12) (KAKA OTIDHPOTE ME 1 EXTOS 31)
BACKGAME..........POINT.....CUBE ACTION
..................LOST......OPPONENT.../....BACKGAMER
...34.............0.56..........No double / Take...(often save a gammon if you lose)
...32.............0.58..........No double / Take...(outstanding chance to win)
...31.............0.80..........No double / Take...(outstanding chance to win)
...42.............0.71..........No double / Take
...52.............0.80..........No double / Take <-------------
...53.............0.86..........Double / Take
...54.............0.88..........Double / Take
...41.............0.94..........Double / Take <-------------
...21.............1.03..........Double / Pass (difficulties to recirculate and he cant play the 6 and 5)
...51.............1.24..........Double / Pass
We can see that the best back games have an anchor in the 3 point and the worst in the 1 point (no six for the opponent, and no timing for the backgamer)


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GAMMON CONSIDERATIONS
Your opponent is CLOSED OUT: 3 men out with your inner prime done, you are very strong favorite to gammon him; more than 3 on the bar are superfluous and potentially dangerous.
With 2 men closed out and with no other men in the outfield he is a slight favorite to save the gammon (40% to be gammoned).
With 1 man closed out you definitely try to hit a second man, since there is virtually no chance to gammon him with no other men in the outfield.

The following table is the gammon (G), backgammon (BG) and plain game losses (L) for from 1 to 5 CHECKERS CLOSED OUT.
Men on bar..G.......BG......L
....1.......4%......0%......2.3%
....2.......43%.....1%......5.2%
....3.......71%.....8%......5.7%
....4.......65%.....22%......6.1%
....5.......43%.....42%......6.7%

When your opponent has exactly 2 men ON A POINT IN YOUR INNER BOARD and the rest of his men are in his inner board you open your prime and he has no choice but to come out. Then you attack the one man with your builders. Or you have a man far enough back. So you will have the opportunity to pick up the released man. This play must not be attempted until your opponent has broken his inner board and holds 4 points at the most, preferably 3 points.

The following table is a table of gammon (G), backgammon (BG) and plain game losses (L) for from 1 to 5 CHECKERS ON THE 1 POINT.
Men on the 1 point....G.....BG......L
........1.............3%....0%......5%
........2............15%....1%.....11%
........3............32%....3%.....14%
........4............47%....8%.....16%
........5............55%...12%.....14%

Hitting additional men: You must not close him out too soon. Instead of closing him out, allow him to come in behind a prime, so he will have to take his moves in his home board.


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TA : TIMING ADVANTAGE or PRIME vs PRIME
Kill the 6 and the 5. Otan eisai ligo prin apo to telos kai den exeis Timing Advantage paikse apo to 7,8,9 me 1 h me mikra zaria mesa sto board sou (h sto 7 h 8 an exei o antipalos mesa sto board sou points sto 1 h 2) gian mhn mporeis na paikseis meta ta 6 kai ta 5. That's why we brake our points in order (starting by the 6, 5, 4 ...).
MAIM (mituler, defigurer). If you can't kill your numbers, try to maim them. Maiming is half-killing it, disabling yourself from playing the number except when it occurs in certain favorable combinations. For example if you are blocked six pips away. For example you can kill you last six because you have an almost prime and you have a point outside in the 18 blocked six pips away in the 12 and 1 and 2 pips away in the 17 and 16. Then you cant play any six unless you have the the necessary 36, 46 or 56.


It's easier to go out from a semi prime of AAYAAAVY if you rest far (from Y to Y you nead a 5 or 41 : 13/36) but if you advance you need a 4 (11/36).
(A: adv, Y:you, V:vide)

OUTSIDE PRIMES : on every roll the blocked oponent will probably not be able to play some of his numbers.


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PIP COUNT
First I total all the pips of my lone men. Then I total the points with 2 men and mutliply by 2, and so on.

Faire la moyen du block en distance du 0 et multiplier par le nombre de pions.

5 prime = mid point X 10

2 opposites = 25

5 blots and 5 blots with 1 gap = gap X 10

All checkers in your opponent home board are counted as 20 plus the pips required to get to the 20 point.

Pour compter à la louche nous pouvons multiplier par 1 les soldats dans notre inner board par 2 à notre outer board par 3 à son outer board et par 4 à son board


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MAZEMA
Coming Home After the Close-Out
KLEINMAN COUNT is desired to prevent leaving shots on forced moves with large doublets, especially double-6's. Your Kleinman Count is the sum of the number of crossovers you need to bring all your men home and the number of men you have on the most retarded points in each quadrant: 6-point, 12-point, 18-point and 24-point. A Kleinman Count of 5 represents an immediate danger of leaving a shot with double-6's.A Kleinman Count of 7 represents an immediate danger to having to choose between coming down to a Kleinman Count of 5 and moving a man deep inside your home board. It is generally desirable to keep you Kleinman Count on the even numbers, 8, 6, 4 - until all your men are home.
Flexibility : 1: you should keep your two last men fairly close to each other, rather than spread apart. This retain your option, on most of youtr rolls, of taking either number with either man or of taking both numbers with the sam man.
Flexibility : 2: you should avoid the extreme points of a quadrant (e.g., the 18- and 13-points in your opponent's outer board. At these extreme points, you often have no choice whether to cross a quadrant in playing your numbers.

Checkers on 6 is good. Put many.

Gaps at 1,2,3 OK. Gaps 4,5 BAD
It is better to waste a few pips when bearing in, in order to make sure that the 4 and the 5 point have enough spare checkers.
Faire comme suit: 753
7 blots sto 6
5 blots sto 5
3 blots sto 4
When bearing in your inner board avoid going in "deep", in other words 1, 2 or 3.

When bearing in, with or without opposition, try to maximize the number of crossovers (move a checker from one quadrant to another), and do it as possible with 1 or 2 and not with 5 and 6.
When bearing DO NOT ADVANCE CHECKERS DEEPLY INTO ANY QUADRANTS.

A l'avant dernier coup avant d'entrer les 2 derniers pions, prévoir le coup de 66 ou 55 de la prochain fois.

"Rule of even": you should always try to have an even number of pieces on your last two occupied positions.
An einai xtyphmenos eksw, prepei na exeis even kai kalytera dyo sta dyo teleutaia points kai idiaitera sto teleutaio point.
An o antipalos exei point sto 1, empilez sta dyo teleutaia (6,5, h 4) 3 soldats. et reflechis a chaque fois pour un 65 ou 54 au next roll.

An exeis 2 pionia se kathe ena sto board sou kai o antipalos einai eksw (h exei dyo pionia sto 2) kai exeis p.x. 41 na paikseis, mhn paikseis apo to 6 alla apo to 4 pairnontas to 4 kai spazwntas to 1 (etsi sto epomeno roll afhneis blot mono me 62. An eixes paiksei apo to 6 sto epomeno roll afhneis blot me 66, 55, 44, 65, 64, 54, 53, 63. An exeis na paikseis 51 perneis to 5 kai spas to 1 apo to 5.

Si tu entres les 2 derniers pions et lui il a qu'un roll avant de finir, essaye de remplir toutes les cases et non pas rentrer les deux. Ca suffit de rentrer 1 de 2 mais le mettre au trou.

Otan exei ena soldat sto 1 xtypa ton gia na fygei, extos an einai sigouro oti tha fygei monos tou sto epomeno roll (me ena 6 h 5 px.).

If you have borne several men and then you leave a triple shot the odds are 3/1 in your opponents favor, so you have to take, and to top it if he misses you can redouble.

Si je luis bloque un point à mon board, lui ouvrir la possibilité max pour qu'il le casse pour lui taper le soldat qu'il va rester seul.

61,52 : on peut jouer d'abord le 1 ou le 2 et prendre avec le 5 ou le 6 un plus petit.

Si il a 3 soldats à ramasser et moi plein, je dois lui taper au moins 2 soldats.

RETURN PLAY: If you have a semi-prime 34567 with one man of the adversary in the 1 or the 2 and he has only some mans to borne off and he has shots in his board, you have to hit his man on your board and to expose another man on the 1 or 2, so you will return to hit the other mans of the adversary.

Bear off a checker whenever you can, if you can't, fill in a gap.

ODD AND EVEN TWO-HOLLES. The most horrible holes are 2-holes which occur with your men concentrates on the odd-numbered points (3,5). Donc si tu as 5 au 2, 5 au 4 et 5 au 6 tu n'est que 5 vrai pips de retard par rapport à ton opponent qui a 5 au 1, 5 au 3 et 5 au 5.

The ONE-TWO RULE : A solitary man on a high point is of more use to you than two men on lower points, even if the pips are the same. I man on 6 is much better than 2 man on 3

CLOSEST CLOSER. Otan exeis 2 3 pionia kai spas mikra zaria sto mazema play the number with the piece closest to your own position 1.
EXCEPT:
36 and play 2 (menei 43 kai oxi 61)
56 and play 3 (menei 35 kai oxi 62) .............61, 43, 33 PAS BONS DANS L'ORDRE
46 and play 3 (menei 43 kai oxi 61)
56 and play 4 (menei 52 kai oxi 61)
and EXCEPT: 6X and play 1: you must play from 6.

Take down a prime from the back. Sauf si l'adversaire a deux points dans notre board (1,4), nous cassons le 8 et non pas le 7 pour ne pas donner un double shot. En revanche si nous pouvons entrer 2 pions nous entrons le 7 pour prévoir le coup de la prochaine fois.

Si j'entre chez moi, et il y a un point de l'adversaire et il y a un gap des mes soldats et je peux entrer le +6 ou le +7(par rapport à son point), choisir le +6. Etsi meta an den mporesw na tous perassw kai tous dyo tha xreiazetai ena 7 (indirect shot) gia na me xtyphsei kai oxi ena 6 (direct shot). Einai h monh exception gia na mhn xalasw en prime apo to telos tou.

When you have a closed board and you atempt to win a double you should not pick up to many men. A safe number would be 4.

Sto mazema xwris contact utiliser les 1 pour remplir les gaps et non pas pour avancer les pions de l'extérieur.

Prendre de risques uniquement si on a un paire nombre de soldats (à partir de 10) si ils sont dans les petits.

Si on est avec des points presque partout plus 7 et/ou 8 et il a laissé des soldats tout seuls dans notre board, il faut taper les deux même si je laisse de blots parce qu'il ne pourra pas faire de point.

DIVERSIFIER : Poser les spare le plus loin possible du 1. De même si je dois laisser un blot ça vaut mieux de le laisser au plus haut point pour pouvoir l'enlever / couvrir plus facilement au roll suivant; c'est aussi la duplication pour l'adversaire, parce que les nombres qui te frappent sont aussi les mêmes qui sont bons pour la course de ton adversaire. La même chose pour un gap, il faut le faire au plus haut point possible.

Si tu est vraiment en retard à la fin joue les petits nombres du 6 vers le 5 etc, afin de pouvoir utiliser des 55, 44, 33 si ils viennent.


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DOUBLES
WHEN IN DOUBT TAKE.
WHEN IN DOUBT DO NOT DOUBLE.

Once you have given away the cube you must play aggresively as you no longer have acces to the cube to help you.

1 win in 4 games (25%) is the breakeven point for taking a double if you can't get gammoned. Because you can redouble, the original 25% rule should be thought of as a 22% rule.

Equité = cube * ( 2 * Prob_de_gagner_simple - 1). Example : Equité = 4(2*0.70-1)=1.6. Ce qui veut dire que vous gagnez en moyenne 1.6 points par partie jouée et 160 points si vous jouez 100 parties.
L'équité est entre -cube et +cube

PRAT : POSITION, RACE, THREATS.
These are the 3 factors to consider whether to offer or accept a double. A clear advantage in 2 areas is enough to offer a double. A significant advantage in all 3 areas is a pass.

KIT WOOLSEY: IF YOU DO NOT KNOW YOURSELF IF THE POSITION IS A TAKE, THEN YOU SHOULD DOUBLE.
1) Is a pass, so you double your equity.
2) Your opponent think it is a pass (different judgement, orhe is pessimistic because he is losing), so you taje your point.
3) It is a corect double and a corect take, so OK.
4) It is an incorrect double, you might have an edge anyway, unless you have completely misevalated the position.

THE GAMMON FACTOR
For every two gammons that you are in danger of losing you need to win one additional game to breakeven.
X doubles Y.
y%=percentage of games won by Y.
x%=gammons won by X.
So X will win (100-x-y)% games. In 100 games player Y has the option to drop 100 points or to take and then the difference between what he wins and loses with the cube on 2 plus tthe points he losses from gammo,s at 4 points per game must equal 100 for him to break even on the take, so:
2*(100-x-y)-2y+4X=100, so y=25+x/2. For every two gammons that you are in danger of losing you need to win one additional game to breakeven).

Double paradox: if you refuse 3 games and you are right twice, you are losing money
(3 drops = -3)
(3 takes -2, -2, +2 = -2)

BEFORE YOU OFFER A FIRST DOUBLE MAKE SUR THAT ALL THE FOLLOWING POINTERS ARE OBSERVED:
1/ Your opponent must have two or three (but not four) men bottled up in your inner table.
2/ You have at least four strong blocking points in semi-prime.
3/ You must be further advanced that him by at least two or three throws.
4/ Your opponent must be sufficiently advanced so as to make a satisfactory back game unattractive to him.

3to2 favorite you can double
2to1 favorite you can redouble because before any double the cube is public property but after the first double the cube becomes your property and can never be taken away from you. You should wait in fact until you are certain your adversary will capitulate

WHENEVER YOU BELIEVE THAT YOUR OPPONENT WILL NOT ACCEPT THE DOUBLE, DOUBLE.

IN LONGER RACES (>25pips) THE LEADER NEEDS A 8% ADVANCE TO DOUBLE OR 10% TO REDOUBLE AND THE TRAILER NEEDS TO BE WITHIN 12%-15% TO TAKE. AT AROUND 25 PIPS FOR BOTH THE LEADER CAN DOUBLE AS HE IS EVEN IN THE RACE AND HE ROLLS FIRST.

IF YOU ARE AGAINST CLOSED BOARD, HIT WHILE BEARING OFF, THE BREAKEVEN IS BETWEEN 8 AND 9 MEN OFF, PRESUMED THAT YOU WILL HAVE A "NO-MISS" BEAR-OFF (no gaps at 1 or 2). HOWEVER YOU HAVE TO ACCEPT A DOUBLE IF YOU HAVE BORNE AT LEAST 6 MEN PROVIDED THAT ALL THE REST OF YOUR MEN ARE POSITIONED AT THE LOWER POINTS. THE SAME, IF YOU HAVE BORNE ALL YOUR MEN BUT TWO AND THEY ARE ON THE BAR.

2 LAST PIECES. THE 5-2 RULE
IL NE FAUT PAS DOUBLER EN CROYANT QU'ON PEUT LES PRENDRE D'UN COUP, SI LES PIECES SONT >= 8 OU 61,43,33.
The 5-2 enigma or OSWALD JACOBY PARADOX. If you have the two last pieces on 5 and 2 (or better) and your adversary 2 easiest pieces on 1 you are favorite 17/19 to bear off both and you have to INITIALY double (NOT REDOUBLE). The adversary has to take obviously. BUT if the oponent doubled previously you have to not double, because if you do not throw one of your immediate 19 winning numbers, the oponent will have a very powerfull redouble.

The optimum distance between your last two men is 2.7 pips. Thus in order, your best distances are 3, 2, 4, 1, 5, 0.

IF BOTH PLAYERS HAVE 5 ROLLS LEFT (OR YOU ARE OFF IN 5) AND YOU HAVE A SLIGHT ADVANTAGE WAIT. YOU MAY CONSIDER DOUBLE WITH 4 ROLLS LEFT AND YOU MUST WITH 3 ROLLS LEFT. YOU MUST ALSO COUNT THE FREE MISSES (par exemple si tu n'as rien à l'ass tu risque d'avoir un miss, et si il est impaire tu as un free miss).

If both you have 4 man in the 1 point and 4 man in the 2 point, you have to double and the oponent has to take (27% to gain).

4 rolls position (both players with 8-man on the 1-point) is a double and a take ( 27% de gain >25% necessaire ). (The wining chances for the second player if he takes goes for 2roll, 3roll, 4roll, ..., 8roll : 0.14, 0.21, 0.27, 0.32, 0.35, 0.37, 0.38).

If both you have 2 man in the 2 point, you have to double and the oponent has to accept (20%) because he can redouble if you throw an 1, and he knows that you will certainly accept.

MIRROR CUBE-OFF : MOST ARE PASSES. THE 52, 42, 32 AND 22 ARE SOUND TAKES.

NE PAS PERDRE SON MARCHE.
Si tu vois qu'au prochain coup il risque de te laisser une frappe, et qu'apres c'est fini, il n'acceptera plus ton double, il faut doubler autrement tu rate l'ocasion.


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PSYCHOLOGY OF DOUBLING (CATCH : utiliser sa force pour le pousser dans son mouvement)
***NEVER COMPLAIN ABOUT THE DICE, EITHER YOUR BAD DICE OR YOUR OPPONENT GODD DICE. THIS WILL IRRITATE YOU AND MAKE YOU THINKING MORE NEGATIVE AND WILL ADD TO THE CONFIDENCE OF YOUR OPPONENT.***
Is he a quick doubler? (he always wants you to accept)
Hesitate before take you can even refuse an unsound double; he may start to double more prematurely.

Is he a slow doubler? (he hopes that you will refuse his double)
If you refuse, hesitate, do so slowly.
If you accept do so quickly and cheerfully. He will tend to be slower with his futures doubles

Is he inclined to accept sound doubles. Be more sound. They will still be accepted.

How the score affects:
Losers tend to double unsoundly and to take when they should refuse.
Winners are quick to refuse doubles and slow to turn the cube (the don't want to let the action speed up).
Evens search action, so double easily and take easily.

If a WILDCUBE (EARLY DOUBLER) is big winner, he tones down his cube actions and he becomes normal; so you should not join his chouette. Wait for the time he is big loser, he will become even more EARLY DOUBLER.
Conversely, if a TIGHTCUBE (LATE DOUBLER) is big loser, he sheds his conservatism and his cube actions becomes normal. You want be able to steal any points with early doubles or enjoy the "fre shakes" you ordinarily experience when he can double you out. Avoid his chouette. Wait to play with the "TIGHTCUBE" when he is a big winner. HE will become even more LATEDOUBLER.

Beavering
If beavers are played it is right to beaver at any tiume when the chances are about even or slightly against you (to take into account that the cube will be on your side).
However, there is a strong psychological element in beavering. If yor opponent is quick to double it is good tactics to let him know that you are always prepared to beaver. But if, perhaps because he is losing or is a gambler, he makes obviously bad doubles, it is better just to accept them with a show of dubiety and let him continue in his foolish ways.

When you are playing against someone whose judgment and ability have totally deteriorated because he is a big loser, avoid getting involved I a large game that he might win and thus get off the hook.

End of the day
Prepei na exeis yp opshn sou otan ksereis oti se ligo to paixnidi tha stamathsei oti me to na kaneis double h na dwseis double h beaver prepei na prospathiseis na ephreaseis to score wste na destabiliser ton antipallo sou. P;X an einai -16, mhn ton afhseis na kairdisei me thn mia 16 points…


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SETTLEMENTS
pour simple (m-h)/36*c
pour double (m-h/2)/36*2c ...a verifier...
Examples:


CALCUL......7,8,9 SHOT....DIRECT SINGLE SHOT.........52,33,43 bearing
Favor.............6to30...........or......25/11...........................18/18
Net gain........24/36.........or......14/36..........................0/36
.....=............2/3..............or......7/18=0.4.........................0=CANCEL
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)
(m-h)/36*c


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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.


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MATCH PLAY
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:
T=trailers score
L=leaders score
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.


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SNOWIE
Explanation of Snowie's HTML output

Checker play frames
Example:
# 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%
BG......G......N...........N......G......BG
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!


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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.

 

 

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