Saturday, April 29, 2006

BKG

The first strong computer opponent was BKG 9.8. It was programmed by Hans Berliner in the late 1970s on a PDP-10 as an experiment in evaluating board positions. Early versions of BKG played badly even against poor players, but Berliner noticed that the critical mistakes the program made were always at phase changes. He applied basic principles of fuzzy logic to smooth out the transition between phase changes, and by July 1979, BKG 9.8 was ready to play against then current world champion Luigi Villa. It won the match, 7-1, becoming the first computer program to defeat a world champion in any game, although this was mostly a matter of luck, as the computer happened to get better dice rolls than its opponent in that match.

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bkgm strategy

OK my math is all screwed up in the OP, but it still seemslike Black's equity here should be a little over 50% of thecube value. Black's EV seems like it should be 19/36 * 32.That's 16.89 points, which seems like a better settlementvalue than "2."I don't know what I was thinking before with +64. My onlyexcuse is that it was like 5am.

Wednesday, April 26, 2006

How rollouts work II

It will come as no surprise that a rollout with a limited number of trialsfollows exactly the same procedure. It's sufficient to say that theproportion of wins/gammons etc. that come up when Jellyfish plays againstitself (say) 1296 times, aren't likely to vary all that much from theproportion we would get if we measured the proportion of results in everygame we could possibly get of Jellyfish playing against itself. (Ofcourse, there may still be some doubt whether the results of JF vs. JF arerepresentative of the results of a perfect player vs. a perfect player, orof you vs. Joe Average, but that's another story.)

How rollouts work I

The million dollar question is simple enough: out of all the games thatcould result from playing this position, how many do we win (and how manyof our wins and losses are gammons, and how many are backgammons)? Themodel is exactly the same as if we had an urn with a googol balls in it(it's a big urn), and many of the balls have "win" written on them, andsome say "gammon loss", and if we look hard enough there are a few thatread "backgammon win", and so on. (Balls and urns are to probabilitytheorists what teapots and chequerboards are to computer graphicsresearchers, or "squeamish ossifrage" is to cryptographers -- they seem tocome with the territory.) Instead of having the patience to count thegoogol balls, we just give the urn a really good shake and then pull 100balls out without looking, and say for instance "Well, I got 53 wins, 31losses, 9 gammon wins, 6 gammon losses, and a backgammon win -- looks likemy equity's roughly +0.26." and go home. If we were a bit more thorough(but there's still a long way between my "thorough" and yours!), we couldgo a bit further and figure out that by cheating and measuring the sampleproportions instead of the population proportions, we introduced a standarderror of 0.06 into our result. (Of course, the trick is to select a samplesize that's big enough that you reduce the standard error to a tolerablelevel, but small enough that the answer arrives before you get bored.)

How rollouts work

Whoa... being thorough is one thing, but performing over a googolevaluations to roll out a single position is quite another! Fortunately wedon't have to evaluate every position that could potentially result fromeach play to come up with an answer we can have some reasonable confidencein; by taking a shortcut here and there (and adding a dose of samplingtheory) we can get away with much less work than that.

Replacing backgammon dice

It is a matter of local rules, but usually you have the right to ask forthe dice to be changed at the end of any game (but not within a game,barring exceptional circumstances). If precision dice are not beingused, you are entitled to ask for some - which is perfectly acceptable,and indeed it is very unusual to find tournament players other than theoccasional novice who don't have any. If precision dice are being used,it is more tricky. If it's just that you're having an unlucky stretch,and that changing them will help, you should get a grip on yourselfbecause you may well be starting to steam. If you suspect that theprecision dice are rigged, you need a *very* good reason for yoursuspicions to avoid upsetting your opponent in the event you are wrong.

Touch-Move

I agree that it is better to avoid shuffling checkers, and I apologize if Itake a move back.!

Touch-move rule in backgammon?

Hi all bg lovers.
In order to make backgammon more fair and attractive for top players I
will like to come with a suggestion.
In great tourneys it's common to use the clock when it's down to 16
opponents left. To expand, the way to favour the best players, I
would like backgammon to use the rule of chess. If you touch your
checker, you have to move it that is. This in a combo with the clock
would be refreshing and good.
I reckon that when they established the rules in chess there were some
noise and controversial discussions. Now they are used to it and only
small children play without a clock and even they use "the touching
rule" in serious chess tournaments.

Tuesday, April 25, 2006

How to tell when somebody's cheating

There are several ways to cheat, but in reality none of them involve the
dice, no matter how much whining and complaining you might hear. The only
way you can be cheated "directly", that I know of, is if someone is using
snowie or jellyfish to determine their moves. That can be detected by
analyzing the match yourself and seeing if the opponent is playing at too
high a level. The rest of the cheating involves obtaining ratings points
by other various nefarious means, and if you played one of those morons,
they could not cheat you by somehow winning your match unfairly.

2003

1.
NACK BALLARD (1)*
USA
2.
Jerry Grandell (2)
Sweden
3.
Dirk Schiemann (4)
Germany
4.
Johannes Levermann (3)
Germany
5.
Paul "X-22" Magriel (6)
USA
6.
David Wells (23)
USA
7.
Neil Kazaross (7)
USA
8.
"Falafel" Natanzon (17)
Israel
9.
Mads Andersen (16)
Denmark
10.
Jörgen Granstedt (5)
Sweden
11.
Kit Woolsey (10)
USA
12.
Jake Jacobs (9)
USA
13.
Steve Sax (20)
USA
14.
François Tardieu (21)
France
15.
Bill Robertie (14)
USA
16.
Mike Senkiewicz (8)
USA
17.
Peter Jes Thomsen (13)
Denmark
18.
Michael Meyburg (11)
Germany
19.
Mike Svobodny (12)
USA
20.
Paul Weaver (19)
USA
21.
Malcolm Davis (31)
USA
22.
Howard Ring (18)
USA
23.
Gus Jacobsen Hansen (22)
Denmark
24.
Lars Bønding (176)
Denmark
25.
Brian Elgaard (68)
Denmark
26.
Kent Goulding (15)
USA
27.
Hugh Sconyers (32)
USA
28.
Morten Holm (40)
Denmark
29.
Mike Corbett (34)
USA
30.
Ralf Jonas (33)
Germany
31.
Frank Talbot (37)
USA
32.
Leo Fernandez (25)
Argentina

2005

RANK
2005 GIANTS of BACKGAMMON
COUNTRY
1.
NACK BALLARD (1)*
USA
2.
Neil Kazaross (7)
USA
3.
François Tardieu (14)
France
4.
"Falafel" Natanzon (8)
Israel
5.
Kit Woolsey (11)
USA
6.
Steve Sax (13)
USA
7.
Lars Bønding (24)
Denmark
8.
Dirk Schiemann (3)
Germany
9.
Jerry Grandell (2)
Sweden
10.
Paul "X-22" Magriel (5)
USA
11.
Johannes Levermann (4)
Germany
12.
Peter Jes Thomsen (17)
Denmark
13.
Jörgen Granstedt (10)
Sweden
14.
Jake Jacobs (12)
USA
15.
Bob Wachtel (55)
USA
16.
Paul Weaver (20)
USA
17.
Malcolm Davis (21)
USA
18.
John O'Hagan (72)
USA
19.
Mike Senkiewicz (16)
USA
20.
Bill Robertie (15)
USA
21.
Frank Talbot (31)
USA
22.
Mads Andersen (9)
Denmark
23.
Walter Trice (54)
USA
24.
Mike Svobodny (19)
USA
25.
David Wells (6)
USA
26.
Gus Jacobsen Hansen (23)
Denmark
27.
Morten Holm (28)
Denmark
28.
Masayuki Mochizuki (71)
Japan
29.
Ed O'Laughlin (56)
USA
30.
Mike Corbett (29)
USA
31.
Lars Trabolt (34)
Denmark
32.
Michael Meyburg (18)
Germany

Who are the top bkgm players in the world?

98 ballots were submitted in 2005, of which 45% came from foreign voters. The ballots nominated 273 different players for the Giants of Backgammon. Here are the 32 top-ranked players in the world:

When you are the Captain.

Turn on Board Notation so that you can understand the comments your team is making.If you want advice on a move, type the move in the chat box at the bottom of the screen before moving. You do not have to ask for advice, or to follow it. But it will be very frustrating to your teammates if you don’t ask their advice and then make foolish moves. It is generally considered good practice that, if you are a relatively weak player, to ask advice from the strong players, and if you are the strongest player on the team to just move. The bottom line is that your teammates will forgive you anything if you win, but if you lose and they think you did so foolishly, you won’t become very popular! Remember too that everyone else wants to be involved in the game. If you just keep moving without ever asking for advice, even on close plays, you’re taking your teammates out of the game.When you are in a position where anyone on the the team might even be thinking of doubling, wait just a couple seconds before rolling. Give them the chance to say “double.” If anyone doubles, make sure to wait until the box has decided on all the cubes. But also, don’t wait forever to roll. If there has been any cube action, give the monitor a minute to record the results. Remember, he’s got a lot of paperwork to keep track of!Never use the “double” button on the board. If you want to double, say “double.” It will be very frustrating if the box reflexively drops and the game ends.A special situation arises if you drop but someone else on the team takes. Now, you are no longer allowed to participate in the game. In a real-life chouette, you would leave your seat and the person next in line to be Captain would take your place. But of course we can’t do that on the zone. So if that happens, stay in your seat but you must now ask for advice on every move, and let the new Captain (the monitor will tell you who that is) make the final decision. This is a bit cumbersome and annoying, but I have found it happens very rarely. When you are the Box. If you are doubled by one or more players, wait until everyone has had a chance to double. You might ask “anyone else?” You do not have to decide to take or drop until everyone has doubled who wants to. If you’re going to drop, then of course everyone will suddenly want to double!If you double, wait for everyone to decide to take or drop before rolling, and give the monitor time to record the results.When you are on the Team. PAY ATTENTION. It’s easy to lose interest in the game if you’re not an active participant, but you are very much a part of the game. One of the most frustrating things is when the box says “Double all” and one or two players on the team don’t respond and you’re wating. When I am the monitor, I often will just decide for players based on the consensus decision. Turn on Board Notation. That way, if you want to make a suggestion for a move, you can say “W12-B6” – rather than – “take one off that big stack on the left and move it 7.” It will be a lot easier for everyone.Know the position of your cube. If you have doubled and the box has taken, don’t say “double.” You can’t double, and it will only slow the game down if the monitor has to tell you that you have already given your cube. (Of course, if you doubled to 2 and the box has redoubled to 4, you can now double to 8!) Likewise, if you doubled and the box dropped, you’ve already won this game. You’re out, you can’t win the same game twice!For Everyone. Take the game seriously. I know one player who always doubles at the first opportunity, takes every double, and immediately redoubles. That kind of takes away from the game, because this is supposed to be fun, but it’s supposed to be a test of skill. Pretend you’re playing for $10 a point! If that were the case, you’d play your best, you’d certainly pay attention even when you’re on the team. And if you were Captain and had money on the line, you’d try to get the better players to help you win. If you pretend you’re playing for real money, you’ll find you have more fun!Be patient. A real-life chouette goes almost as fast as a regular game, and when it slows down it's because people are discussing (or arguing!) over checker plays, which is part of the fun. Online, because the software doesn’t support chouettes, it can slow down a little. Try to be a little patient and keep focused on the game.If you have to leave, leave. There’s no requirement that you stay in a chouette for any particular period of time. If you’re losing interest, then just say that you’re leaving and leave. It’s best if you stay to the end of the current game, though. There is no universal set of rules for a chouette. I have adopted the following rules for chouettes that I run. I’ve done this because I think they work best, and because while there are some rules used in every real-life chouette, some of them are not familiar to most players on the zone and I don’t want to complicate things. Jacoby Rule, beavers but no raccoons. If you don’t know what these are, don’t worry about them. Players on the team can consult only after their cube has been turned. This means that the Captain is free to play the opening in peace, while getting help once the game has advanced. If any player drops, the Captain may buy his cube. What that means is that the player who drops pays the Captain the undoubled value of the cube, rather than the box. The Captain is now playing with two (or three or four or five) cubes against the box. If all players but one drop, that player must either drop or he must buy all the other cubes. This prevents one player from holding up the game. However, in this case it works a little differently. The box still gets the point from all the cubes. However, each player on the team pays the remaining player one additional point, and they now join the box. So for example, suppose there are four players on the team, A, B, C, and D, and all but B drop. A, C, and D each pay the box one point and pay B one point. B is now playing with a 2-cube against the box and against A, C, and D. If the box wins the game, he will win 5 points (the three he got from A, C, and D, and two from B), B will lose 5 points (he lost 4 2-cubes, but was paid three points) and A, C, and D break even (they paid the box one point and paid B one point, but they won 2 points against B). If B wins, he will win 11 points (the 4 2-cubes plus the 3 points he was paid), the Captain will win 1 point (he loses 2 points to B and won one point from each of A, C, and D) and A, C, and D will each lose 4 points (the point they lose to the box, the point they paid B, plus the 2-cube they lost in the game). I know this sounds complicated, but it makes sense. If you are doubled and drop, you are saying that you would rather pay one point to get out of the game than play on with a 2-cube. So if someone said “I think it’s better to play on with a 2-cube than drop” you should be willing to say “OK, I will pay you one point to take that inferior side of the board and play it with a 2-cube.” This way, if one player wants to play on, everyone is still involved in the game. Settlements are allowed. Let me give a very simple example. Suppose you are in a last-roll position. The cube is at 4, and you have one checker on your 5-point and one on your one-point; your opponent has one checker on his one-point. You have 23 rolls that win the game and 13 that lose. On average in 36 games you will win 92 points and lose 52, for a net average of (92-52) / 36, or about 1.1 points. You might say “I’ll take one point.” Anyone who wants can now pay you one point and the game ends for them. Settlements can be proposed by either side at any time. But please don’t be ridiculous. Let’s say you are closed out with three checkers on the bar and no checkers off. The expert “rule of thumb” is that you have about a 75% chance of being gammoned in this situation, and while you will win a few games, you will also lose a few backgammons. If the cube is at 2, don’t keep saying “I’ll offer two.” And don’t argue over a proposed settlement. If someone offered me 2 points in that situation, I might say “I’ll take three” (even though I know the position is worth more like 3 ½). Just don’t hold up the game haggling. If you’re going to offer a settlement, make it a fair one. Don’t insult your opponent by offering a ridiculous one. OK – now that you’re an expert – join a chouette, pay attention, and most of all - have fun!

How To Play A Chouette


How To Play A Chouette


A chouette is a fun, social, multi-player form of backgammon. It can be a tremendous amount of fun, with lots of cube turns, players taking different points of view, getting to rotate and play as a teammate of another player one game and against him the next.
However, if it’s not done right, especially online, it can get boring quickly. This page will give you an outline of what a chouette is and how to play. I strongly suggest that you print this out and keep it to refer to while playing.
You might want to review that. But let me give a very brief description.
One player – the “box” – plays against a team. One member of the team is the “Captain.” This all takes place on one board. The Captain has final say over all checker plays, although he can ask his teammates for help in some situations. However, each player has his own doubling cube. He can double regardless of what his teammates do, and he can take or drop if doubled on his own.
A chouette is played just like a money game. There is no “match score” – you play one game, win or lose points, then go on to the next game. Positions change every game. In general, if the box wins, he stays as the box; if the Captain wins he becomes the box. Whether the Captain wins or loses, the next player in line becomes the Captain.
The scoring is just points won or lost. Each player has a running score, of plus or minus a certain number of points, or even. If you were playing for money, you would multiply this by the stakes, and that’s how many dollars ahead or behind you would be. Naturally, the sum of all the scores is always zero.
Online chouettes can be somewhat awkward to run. There is no special software on the Zone for chouettes. What is required is someone to run the chouette who understands a chouette, whom I call a monitor. The monitor keeps track of the position of all cubes, and tallies the running score. When a chouette gets large, it gets to be a lot of work.
I have listed below everyone’s responsibilities. I know from experience that if everyone doesn’t follow these, it can really ruin things for everyone. Please print them out and read them, and then have them handy to refer to.
A chouette can be an awful lot of fun. For the team, there is the opportunity to gang up on one helpless victim (the box), to consult on checker plays, to show how much smarter you are than the others by, say, dropping a double and losing one point when everyone else goes on to lose a doubled gammon – or by taking and winning two points when most of your teammates dropped and lost one. There is the excitement of being the box and winning or losing 5 or 10 or 20 points at a time – I once saw, I think, the box win 80 points in a single game in an online chouette (two cubes at 16, two at 8, and he won a gammon).

Please review very carefully your responsibilities:

NEW YORK

MIDTOWN BACKGAMMON & CHESS CLUBContact: Beverly Flowers. 212/575-2003Venue: Clubroom; 265 W. 37th Street (Suite 303); New York, New YorkMeeting: Daily at 12:00 PM. Tournaments Sunday at 2:30 PM
TIMES SQUARE BACKGAMMON & CHESSContact: Victor Ashkenazi. 973/204-6932Venue: Bryant Park; 5th Avenue & 42nd Street; New York, New YorkMeeting: Daily except Sunday at 12 noon April through December

TEXAS

DALLAS BACKGAMMON LEAGUEContact: Tom Wheeler. 972/484-3038Venue: IHOP, 3910 Belt Line Road, Addison, TexasMeeting: Wednesday at 8:00 PM

WASHINGTON

PUGET SOUND BACKGAMMON CLUBContact: Ruth Robbins. 425/226-3120Venue: Wizards Restaurant/Casino; 15739 Ambaum Boulevard SW; Burien, WashingtonMeeting: Tuesday at 7:30 PM

HAWAII


ALOHA STATE BACKGAMMON CLUBContact: George Quillin. 808/922-2674Venue: Elks Club; 2999 Kalakaua Avenue; Honolulu, HawaiiMeeting: Friday at 7:30 PM

USA Backgammon Clubs

GAMMON ASSOCIATESContact: Patrick Gibson. 818/901-0464Venue: Acapulco Cantina; 3113 W. Olive Street; Burbank, CaliforniaMeeting: Tuesday at 6:00 PM
Venue: A.R. Private Club; 8471 Beverly Blvd., Suite 201; Los Angeles, CaliforniaMeeting: Sunday at 2:00 PM
SACRAMENTO BACKGAMMON CLUBContact: Doug Wilson. 530/756-4872Venue: Player's Sports Pub & Grill; 4060 Sunrise Blvd.; Fair Oaks, CaliforniaMeeting: 2nd and 4th Tuesday monthly at 6:30 PM
BACKGAMMON CLUB OF SAN DIEGOContact: Tom Fahland. 858/472-1516Venue: Coast Cafe in the Embassy Suites Hotel; 4550 La Jolla Village Drive; La Jolla, CaliforniaMeeting: Tuesday at 6:00 PM
BACKGAMMON BY THE BAYContact: Beth Skillman. 831/688-9722Venue: Peking Express Restaurant; 2068 Center Street.; Berkeley, CaliforniaMeeting: 2nd Saturday monthly at 12:00 PM
Venue: Britannia Arms Pub & Restaurant; 1087 De Anza Boulevard; Cupertino, CaliforniaMeeting: 4th Saturday monthly at 1:00 PM
RESTAURANT ROY BACKGAMMONContact: Roy Gandy. 805/966-5636Venue: Restaurant Roy; 7 West Carrilo Street; Santa Barbara, CaliforniaMeeting: First Monday monthly at 7:00 PM

Presentation

To make it easy to follow the games, we have included a diagram before each play showing the position of the board and the roll of the dice. A good learning exercise is to examine each position and decide what you would do if you were playing. Then check to see how your choice compares with that of the players and commentators.

Each play is given as a series of moves separated by commas. A move consists of a starting point, a slash (/), and a finishing point. For example, 8/5 indicates that a checker moves from the eight point to the five point. An asterisk (*) indicates that a checker has been hit. A number in parentheses indicates that that number of checkers move together. Points are numbered from the point of view of the player whose turn it is. The farthest-away point is number 24 and checkers always move from higher points to lower points.

Introduction

In February of 1994, Kit Woolsey and Jeremy Bagai thought it would be a good idea to annotate a match for FIBS players so they could see the thinking processes of the more experienced players. They played a fairly interesting match, logged it, and then annotated it independently. You will see the reasons for their plays and cube decisions, as well their second thoughts upon later analysis which often came to a different conclusion than the original choices.

In addition, Gerry Tesauro volunteered TD-Gammon's valuable help. TD analyzed the whole match and listed its top three choices for each play along with its estimated equities. These equities are always assuming a 1-cube and they do not take into account cube ownership. For example, on a pass/take decision, an equity of -.50 would be a break-even decision, since that would translate to an equity of -.100 on a 2-cube. TD was also nice enough to comment on the game, giving the reasons behind its choices as well as getting in a few snide remarks about the players' mistakes.

Just a word of caution about TD-Gammon's estimates: TD-Gammon's area of expertise is in overall positional judgment decisions, where its vast training experience allows it to accurately weigh the relevant factors. But on certain more technical positions TD-Gammon does not do as well. So you have to be careful about when to accept its recommendations.

Thanks to Kit Woolsey, Jeremy Bagai, and TD-Gammon (Gerry Tesauro) for making this match available. Mark Damish formatted the original text version of the match

Kit Woolsey vs. Jeremy Bagai backgammon

Introduction
In February of 1994, Kit Woolsey and Jeremy Bagai thought it would be a good idea to annotate a match for FIBS players so they could see the thinking processes of the more experienced players. They played a fairly interesting match, logged it, and then annotated it independently. You will see the reasons for their plays and cube decisions, as well their second thoughts upon later analysis which often came to a different conclusion than the original choices.

In addition, Gerry Tesauro volunteered TD-Gammon's valuable help. TD analyzed the whole match and listed its top three choices for each play along with its estimated equities. These equities are always assuming a 1-cube and they do not take into account cube ownership. For example, on a pass/take decision, an equity of -.50 would be a break-even decision, since that would translate to an equity of -.100 on a 2-cube. TD was also nice enough to comment on the game, giving the reasons behind its choices as well as getting in a few snide remarks about the players' mistakes.

Just a word of caution about TD-Gammon's estimates: TD-Gammon's area of expertise is in overall positional judgment decisions, where its vast training experience allows it to accurately weigh the relevant factors. But on certain more technical positions TD-Gammon does not do as well. So you have to be careful about when to accept its recommendations.

Thanks to Kit Woolsey, Jeremy Bagai, and TD-Gammon (Gerry Tesauro) for making this match available. Mark Damish formatted the original text version of the match

Thursday, April 13, 2006

Backgammon is without a doubt a far more fascinating game than most of the modern players realize. It has been popular game for many years. Backgammon instructions are easy to follow and anyone can play Backgammon.

Backgammon is a game that should be taken very seriously if you plan to play it for money. Although many gamblers presume that backgammon is just any other gambling game backgammon is in fact very much a game of skill.

The main goal of the game backgammon is for each of the players to get all of his or her game pieces onto the home board and then to find a way to get all the pieces off the Backgammon board. The first player to achieve this is the winner of the game.

The movement of the pieces is dictated by the number of spots on each of the two dice rolled. As in chess or checkers only one player can move his pieces at a time and to determine who moves first each player takes one dice and rolls it onto the right side of his board on the playing surface.

The player with the higher number plays both numbers and moves either one checker or two separate checkers the corresponding number of spaces equivalent to the spots on each die. In case of a tie, each player rolls one dice again until there are different numbers for each player.

The players will first roll the dice before every move. The player moves with whatever consists with the roll of the dice. If he rolls a 5 and 2, then he will move seven slots. You can break the moves up between two game pieces. In other words, he can move one five spaces and the other piece two. If the same number would appear on both dice rolled, then the active player would be allowed double what the number is. For example, if he rolls a 5-5, then the roller is allowed four moves of five, instead of two moves of five. The checkers must always be moved forward around the board according to the numbers shown on the dice. The numbers on the two dice constitute separate moves. For example, if a player rolls 4 and 6, he may move one checker four spaces to an open point and another checker six spaces to an open point, or he may move the one checker a total of ten spaces to an open point, but only if one of the intermediate points (either four or six spaces from the starting point) is also open. The bar is not counted as a space.

The checkers are always moved around the board from a player's outer board to his inner or home board.

A checker may be moved only to an open point, one that is not occupied by two or more opposing checkers. A checker may move to a point if it is occupied by only one of the opponent's checkers. In this case the opposing checker is hit and placed on the bar.

The Bear Off is the final stage of the game when you remove your checkers from your home board but you cannot start this process until all 15 of your checkers have made it there. After all your men are in the home board you may bear them off according to the numbers on the dice you throw. You must use your entire roll so if you roll a 5 and have no checkers on the 6pt or 5pt, you must take a checker off of the next highest point with checkers on it. If you roll a 5 and have no checkers on the 5pt but you do have a checker on the 6pt, you must move the checker on your 6pt five spaces to the 1pt. You do not have to bear a checker off if you have another legal move which can be useful when your opponent is on the bar or still owns a point in your board. If your opponent hits a blot while you are bearing off, you must enter that checker and bring it all the way around back to your home board before you can continue to bear off checkers. The first player to bear off all 15 checkers wins the game!