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Backgammon Variants

This page is taken from information in the FAQ which used to be edited by Mark Damish. It in turn was compiled from newsgroup postings.

What other backgammon games can be played on the board?


Acey-deucy

From: Peter Nickless

In this game all the men start off the board. They enter and move around the board in the same way as men sent home in regular backgammon games. In other words, the white men enter in black's home board and move around through black's outer board and white's outer board until all are gathered in white's home board; then white can start to bear them off. Black enters his men in the white home board and moves around in the same manner.

Rules of this game are the same as for backgammon, except that you can move any man you want to at any time, whether or not you have men to bring in. In addition, the roll of 1-2 -- acey-deucy -- is an especially valuable roll. You begin by playing your ace-deuce. Then you play any number four times (in other words, you pick any double you wish). Then you get an extra roll, and if this extra roll is also 1-2 you get the same extras with it.

Early game strategy in acey-deucy is to try to establish advanced points as quickly as you can, and if possible also establish adjacent points as base for a prime. If both sides develop primes right smack up against one another, the advantage lies with the prime that is farther advanced. Even if the man with the farther-advanced prime has to break his first, he will probably win the game; if he can hold his prime longer, he almost surely will win.

Credit: The Backgammon Book, Oswald Jacoby/John Crawford

[Acey-deucy is a fun game, with a much greater element of luck or chance than regular backgammon game. 1-2 rolls are deadly. You are never out-of-it right to the end. The pace is fast and furious (at least compared to regular backgammon -- which, incidentally, I still prefer, but Acey-deucy makes a nice change of pace once in a while). One key point of strategy -- block your opponent from a play of 1 or 2 if you can. This opportunity only occasionally presents itself, but watch for it. If you can't play your lowly 1-2, you lose the bonus double and extra roll. ...Mark Damish]


One Point Matches

This variant is played the same as 'regular' backgammon with two exceptions; the cube is not used, and gammons/backgammon don't exist. This often leads to very strategicaly played games, where a back-game is more of an option than in the regular version since staying back forever never leads to losing more than one point. Since all games are played to to completion, `slime vigorish' to turn a game around suddenly occurs more frequently since you cannot cube your opponent out.

Why play 'one point matches'? Well, similar games occur all of the time in tournament play. Double match point, and crawford to an even score are examples.

One point matches have been labled the 'Crack' of backgammon games at the New England Backgammon Club, and the opium of the game by others.


Hyper-Backgammon

From: Michael Urban Date: 14 Oct 1993

Each side starts with 3 checkers on their respective 24, 23, and 22 points. The cube is in play. Jacoby rule in effect. Matches will start at 7 points and work their way up in later rounds. All other normal backgammon rules apply.


Nackgammon

From: Rolf Kleef Date: 15 Oct 1993

Nackgammon: The same as backgammon, but with a different starting position: instead of five men on both your midpoint and 6-point, you just put four there. The remaining two men end up at the 23-point.

This was invented by Nack Ballard (hence the name), to force his bg students to practice positional play. Games tend to be much longer, since you can't easily start a race with a 65 or 66 opening-phase roll.


Tapa

From: vladimir@cs.ualberta.ca Date: 24 Jan 1995

The word "tapa" means "bottle cap" and it's an apt name because one seeks to block out the opponent's pieces.

In this variant, the move direction and game objective are the same as in backgammon game. There is one important difference: 
Blots (single men) are not taken out when hit. Rather, the opponent's man rests on top of the blot and thus forms a point. Points can also be formed in the usual way, by placing two or more of your men at the same slot.

If you leave a blot at your home slot (1 or 24) and it gets covered, you certainly lose a backgammon (unless your opponent has done the same, in which case it's a tie).

A long doublet (5 and 5 or 6 and 6) in the initial stage of the game can be very useful because usually the opponent would have some blots in their home quadrant and you may cover them. The closer this happens to their home slot, the better, because the later you will free the blot when you are bearing off.

Tapa is very much a game of strategy. Even if you get caught very close to your home row, you may be able to force the opponent to free it by blocking enough of his men, so that he doesn't have any other move. During most of the game it better to move SLOWER rather than faster. Primes are not necessarily useful, eg when the opponent has enough space for short moves behind the prime.

If nobody gets caught in the early stage, the two players try to advance their men in "almost primed" formations. Then the passing-through of the two armies can be a rather dramatic clash.

Tapa is quite popular in Bulgaria. In fact people play three games --BG, Gul Bara, and Tapa-- in a row. The cube isn't used and there are no backgammons (although there are gammons, called "mars"). I think these games (or at least the names) have come to Bulgaria from Turkey. Some people (esp. the older ones) use Turkish names for the rolls, eg "shesh-besh" is "6 and 5". I'd say backgammon is the favorite recreation of Bulgarian pensioners.


Narde

From: Vincent Zweije

In Kazachstan, and probably Russia too, people play a game called "Narde" on a backgammon board. It is also played with 15 checkers each, in the following starting position (point numbering is taken from the backgammon game).

Do to language problems I never got a formal introduction to the game. I'll have to write down the rules out of my head. It is played like backgammon, with the following exceptions:

1: Both players move in the same direction. X moves from 12 down to 1, then to 24 and down to 13, and finally off; O moves from 24 down to 13, then to 12 and down to 1, and finally off. 2: A point is already made with one checker on it. There is no hitting in the game. 3: Doublets are not special. If you roll 3-3, you get to move a checker three pips twice. Possibly the same checker.

Bearing off is like backgammon. Moving is mandatory when possible. I don't know whether, like in backgammon, you have to move the higher of the dice if you have to choose. It never happened during actual play.

This version is almost fully one of chance. The main thing is to take care not to get blocked by a six-point prime (already made with six checkers in a row!).


Gul Bara

From: vladimir@cs.ualberta.ca Date: 24 Jan 1995

Gul Bara is similar to Narde, but double rolls are very powerful, eg if you roll 1 and 1 then you get to move 4 ones, 4 twos, 4 threes, ..., 4 sixes.


Feuga

From: Igor Sheyn Date: 4 May 1995

OK, here's the attempt to put down a complete set of rule for the game called feuga in Greek.

Equipment: Backgammon board, 15 checkers for each player, 2 pairs of dice (we play it with 1 pair, but let's keep it to bg as close to possible).

Initial checkers setup: Each player has all of his checker on the same point.

Direction: Both players move counter clock-wise. Using numeration above, O moves from 1 to 19-24 quater, which is his home. X moves from 13 to 24 and then continues 1 to 7-12 quater, which is his home.

Goal: Bring your men home and bear them off as in backgammon.

Main difference from backgammon: Hitting is not a part of a game, hence the point is considered made when there's only 1 checker on it (no blots and slotting in this game).

Various aspects: the initial point for each player (13 for X, 1 for O in the setup above) is called "head". A player is allowed to move only 1 checker from his head per roll. If he can't obey this rule on any given roll, he can't play his roll fully. Exception: if your 1st roll of the game is 6-6 or 4-4, you're allowed to play 2 checkers off your head, 1/7(2) with 6-6 and 1/9(2) with 4-4.

Priming: there's one restriction on building a 6prime. You can build a 6prime only provided there's at least one opposing checker ahead of your prime. E.g., if you want to build your prime from 1 to 6 as O, X has to have at least 1 checker anywhere from 7 to 12. This rule is to prevent trivial strategy of building 6prime right in the beginning and then just rolling it home.

Gammon: Gammon is counted in same way as in BG. Backgammons do not count (as far as I know).

Cube: No cube is used (this can be easily fixed though).

Diceless Backgammon

From: Igor Date: 27 Mar 1992

In fact, there's a version of backgammon game, which is much more popular than regular bg in USSR, especially in Azerbajdzhan and Uzbekistan. 
Main features are following:

And, as far as I know, there are tournaments, where people play this version without dices, i.e. calling their rolls. Consequently, there exist time control in this tournaments.

multiplier 85 / (T + 6), I use (24 / T + 3). Neil Kazaross has invented another system, which he calls Neil's Numbers, which relies on learning the following short table of numbers instead of calculating a multiplier. The table is

T    3  4  5  6  7  8  9  10  11  12  13  14  15  multiplier   10  9  8  7     6          5               4  
One should interpolate where no number is given. For example, at 3-away, 8-away, the difference is 5 and the multiplier is 6, so we get the equity (5 x 6) + 50 = 80 again. At 3-away, 7-away, the multiplier is half way between 6 and 7, so we take 6.5 and get the equity 
(4 x 6.5) + 50 = 76 again.

Notes:

  1. None of these formulae works when L = 1, i.e. in the Crawford game. You'll just have to learn those.
  2. Stick to one formula or another within one calculation: don't mix them up.
  3. All the formulae underestimate slightly when L = 2, and T is between 5 and 9 inclusive. You might like to add 2% to these equities with any of the formulae if you're worried.
  4. When T is 13 or more, none of the formulae is great but mine is bad. Also the arithmetic in mine isn't any easier by then. If you're playing long matches, you might find Janowski's formula or Neil's numbers better at the beginning of the match (or when one of you is still at the beginning!).
  5. My formula does worse than Janowski's and Neil's when T = 11 and L = 2, 3; also when T = 12 and L = 2, 3, 4. All these equities are in the 90-95% range anyway.

I (of course!) think my formula is best when T is at most 12. It is accurate to within 1%, except as noted above, and, I claim, is much easier to calculate than Janowski's formula in all those cases, and doesn't require learning Neil's numbers. But you should choose the one that you find most useful.

Using the match equity to influence doubling decisions

The problem of making doubling decisions in matches is a complicated one, even if we know the match equities and the probability of winning this game. For simplicity, therefore, let us consider situations in which the game effectively ends after this roll. Typically these are situations in which the player doubling can either hit a shot or finish bearing off this roll, thus winning the game, or miss and lose the game (by the opponent finishing bearing off immediately, or by being redoubled and having to concede); or situations in which the cube is dead because the player taking the double will then have enough points to win the match on winning the game, and thus will not redouble.

For such special situations, the correct doubling strategy can be worked out exactly. For example, suppose I am losing 13-11 in a 15 point match. I have two pieces left on my one point. My opponent has one piece left on his two point and one on his three point. He doubles to 2. What should I do?

These calculations are most easily worked out by using the following formula for my take point(the probability of winning above which I can take the cube). If I drop the cube, I will have a certain match equity. From this base, the amount I gain by taking and winning will be called mygain . The amount I lose by taking and losing will be called my risk . Then my takepoint is

risk  ----------- .  risk + gain  

In a money game, I would be risking 1 point (the difference between -1 and -2) to gain 3 (the difference between -1 and +2), so my take point would be at 25%. In the above example, I carry out a similar calculation as follows. If I drop, the score would be 14-11, and my equity, consulting the equity table, would be 17%; if I take and win the score would 13-13, so my equity would be 50%; if I take and lose, I would lose the match, and my equity would be zero. So I am risking 17% to gain 33%, and my take point is therefore

17  -------   =   34% .  17 + 33  
Now a quick count reveals that my opponent bears off if and only if he doesn't roll a 1, so I win 11 out of every 36 games, or 31% of the time. So I should take the cube in a money game, but drop at the match score indicated.

Where does the above formula come from? Suppose my equity is A if I drop, B if I take and win, and C if I lose. Suppose furthermore that I have a probability p of winning. If I take my equity is then

p B + (1 - p) C .  
So I should take if and only if
p B + (1 - p) C  >  A  if and only if   p (B - A + A - C)  >  (A - C)  A - C              risk  if and only if   p  >  -----------------  =  -----------  (B - A) + (A - C)     gain + risk  

Other calculations we can do precisely are when it is not the last roll of the game, but the person being doubled can, because of the match score, immediately redouble. For example, suppose I am winning 11-7 in a 15 point match. I hold the cube at 2. When should I double?

If my opponent takes, he can immediately redouble so we would be playing for the match, that is for an equity of 0% or 100%. If I don't double and win, the score is 13-7, with an equity of 88%. If I don't double and lose, the score is 11-9, with an equity of 64%. This time I am risking 64% (the difference between the two losing equities) to gain 12% (the difference between the two winning equities), so my doubling point is

64  -------   =   84% .  64 + 12  
(We can do a calculation similar to the above one to show that this is the correct doubling point). Similarly, if my opponent drops he has an equity (at 13-7 down) of 12%. So he will take if his probability of winning this game (with the cube dead) is greater than 12%.

In general we have to take into account the probability of gammons, and of redoubles, and how many and how big our market losers are, and it is not clear how to do this. For example, in the final example above, I would probably want to try and play for a gammon if there was still a reasonable chance of that, and only double if that became unlikely