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Roland's Unofficial BG Glossary including
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Strategy / Money games / Chouettes / Propositions / Ver.26-Jan-0
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Contents : Stuff for Novice players / Beginners / Intermediate / Advanced / Expert / World-Class

Boring Stuff about Dice Numbers for Novice Players :

What are my chances of rolling a double ? Short answer 6/36 = 1/6th of the time or 16.7 %. There are 36 different ways you can roll 2 dice (I promise & if you don't believe me just go away and read a beginner's backgammon book). There are two ways out of 36 you can roll a (56) (a 5 on the green die, and a 6 on the red die, or a 6 on the green and a 5 on the red), however there's only one way to roll a double 6 (a 6 on the green die and a 6 on the red die). ("Shikes, they both have to be 6!!") Therefore the combination number (56) comes up twice as often as the double 6. Ok, just for the non-believers ; the 36 combinations of throws with 2 dice are :

12

21

31

41

51

61

13

23

32

42

52

62

14

24

34

43

53

63

15

25

35

45

54

64

16

26

36

46

56

65

11

22

33

44

55

66

Above : The 36 dice rolls : Don't forget all the bold combinations appear twice (ie. you get (23) which is the same roll as (32). It doesn't matter which comes out the cup first ! As long as they come out roughly together!). Steve Morris has made a nice (really nice.. I mean it's worth spending some time looking at it carefully) diagram of the 36 possible throws :

The 36 Dice throws (Courtesy of Steve Morris)

Which blots are hardest to hit ? A nice concept to grasp is if you need to leave a blot, or a single checker, how far away from your enemy should you leave it ? The short answer is direct blots suffer the most chances of being hit from 1 to 6 points away (6 points away being the worst). Indirect shots (7 or more) are much harder to hit ; the further away you are the harder it is to be hit or to hit. If you are 13 or 14 points away, you cannot be hit, but you can be hit with a double 5 when 15 points away, (as long as the 5th and 10th points are not blocked!). Assuming all the following dice rolls can be played, and no points are blocking certain combinations, then the chances of hitting x number of points away are as follows ;

No. of pips away how many hits ? as a percentage ? Which rolls hit ?
       
1 11/36 30.6 % (12,13,14,15,16)+11
2 12/36 33.3 % (21,23,24,25,26)+11+22
3 14/36 38.9 % (31,32,34,35,36,12)+11+33
4 15/36 41.7 % (41,42,43,45,46,31)+11+22+44
5 15/36 41.7 % (51,52,53,54,56,32,41)+55
6 17/36 47.2 % (61,62,63,64,65,42,51)+22+33+66
7 6/36 16.7 % (34,52,61)
8 6/36 16.7 % (53,62)+22+44
9 5/36 13.9 % (45,63)+33
10 3/36 8.3 % (64)+55
11 2/36 5.6 % (65)
12 3/36 8.3 % +33+44+66
15 1/36 2.8 % +55
16 1/36 2.8 % +44
18 1/36 2.8 % +66
20 1/36 2.8 % +55
24 1/36 2.8 % +66

Above : Note the rolls which hit (bold numbers in brackets) count as 2 rolls ; because 12 can be rolled in 2 different ways (12 or 21). No, I'm not being funny, that's 2 chances out of 36 to roll that combination number. There is only one chance in 36 of rolling a specific double, like double 4. But, careful, it does happen ! From this table, you may well realise that the worst place to leave a blot is 6 away from your opponent. Now in practice, if he's behind a 5 prime, and needs exactly a 6 to hit then he has 11 good numbers instead of 17. If you have blocked his double 3s but all else hits you, then he has 16 instead of 17 good rolls. Below, here's the same information displayed on a bar (where you might end up) chart, courtesy of Steve Morris :

Steve's Bar chart "Chances of hitting a shot"

Above and below : Chances of hitting a shot (below includes exact percentages)

chances of hitting

Below : The chances of rolling a double or a specific "fly" shot

chances of rolling a double

What are my chances of hitting a double or triple shot ? They're good and get better the more direct shots you get. If you have 6 different direct shots, or your opponent has an empty home board I'll guarantee you'll hit or re-enter every time ! This table is also good for estimating your chances of entering from the bar when there are 2 gaps, 3 gaps or more :

Number of shots What kind of situation ? Good rolls ? as a percentage ?
       
1  A single direct shot or single gap in the home board 11/36 30.6 %
2 A double shot, or 2 gaps in a home board 20/36 55.6 %
3 A triple shot or 3 holes / gaps 27/36 75 %
4 A Quadruple shot or your re-entering against opponent's 2 point board 32/36 88.9 %
5 A rare quintuple shot, or chances of not dancing at the start of a game 35/36 97.2 %
6 The chances of re-entering an opponent's empty home board 36/36 100 %

Notes ; When you have a triple shot (75%) you may consider doubling if the hit ruins your opponent's race. When somebody dances (stays on the bar) 2 times in a row against a 2 point board that's unlucky (it's an 11% x 11% = 1.2% chance). I once heard someone danced with 3 double 6s at the start of the game (against a 1 point board), well that kinda sh*te happens once every 50,000 games. A note on the above table ; a double shot is where you need a 3 or a 5 on the dice to hit... (but note that if (12) hits the 3 and (23 or 41) hit the 5 then you have 20+2+4 = 26 yummie shots.) A triple shot is when, for example, your opponent has made his 4 and 5 points, as well as his 6 point, and you need to re-enter from the bar with one checker by throwing a 1, 2 or 3. You will re-enter 75% of the time. Roll it out 20 times, and see if you come in 15 times, and dance 5 times. If your rollouts are off, roll the dice 100 times, and I bet you'll roll a 1, 2 or 3 around 75 times on average. I'm going to try that right now just to boost my confidence ; give me a moment....... there, did it 16/20 times (Yeaha ! I'm going to get those suckers next time they leave me a triple shot! (if I miss then I'll just be the sorry sucker.)). I'll cover 2 blots re-entering next, but as you can see from Steve Morris's chart (below) it's much harder for 2 checkers to re-enter than for one to re-enter :

 Steve's re-entering bar chart

Above and below : Chances of coming on from the Bar (bar chart below has exact percentages)

Coming on from the bar

But I've got 2 on the bar ; so what are my chances of coming in with both ? In the position below it's 25 % for blue, on roll, to bring in both chequers. (And even if you do, it's get blitzed time, dude !). Blue has a 25% chance of staying on the bar with both pieces, (also called dancing). This is because Blue has a 50/50 chance of rolling a 1,3 or 6 with one die, and a 25% chance to do it with both dice (50% x 50%). The 9 rolls that represent this worst nightmare scenario are (13)(16)(36)+11+33+66 = 9 yucky rolls. To come in with both the following 9 rolls (24)(25)(45)+22+44+55 do the job 25% of the time. The remainder of the time (50%) Blue enters with one dice (21)(23)(26)(41)(43)(46)(51)(53)(56) = 18 rolls. The situation is great for Orange who is about to launch a sustained blitzing attack and is too good to double as he has about 60% gammons against blue (and around 80% normal games). Blue should consider taking up the game of poker.

Other board strengths : Below :The chances of 2 checkers re-entering the board from the bar are as follows :

Checkers on Bar 1 open point 2 open points 3 open points 4 open points 5 open points All open points
  5 points made 4 point board 3 point board 2 point board 1 point board No board made
             
1 31 % 55 % 75 % 89 % 97 % 100 %
2 3 % 11 % 25 % 44 % 69 % 100 %

Converting number of shots into % and simpler fractions : Below is a nice table which just expresses things in different ways. Useful for getting a feel for your hitting chances. We've covered the 17/36 shot in a previous table.. but here's the whole picture :

How many shots hit ? As Simple fraction ? As Percentage ?
0/36 0 0%
1/36 1/36 2.8%
2/36 1/18 5.6%
3/36 1/12 8.3%
4/36 1/9 11.1%
5/36   13.9%
6/36 1/6 16.7%
7/36   19.4%
8/36 2/9 22.2%
9/36 1/4 25%
10/36 5/18 27.8%
11/36   30.6%
12/36 1/3 33.3%
13/36   36.1%
14/36 7/18 38.9%
15/36 5/12 41.7%
16/36 4/9 44.4%
17/36   47.2%
18/36 1/2 50%
19/36   52.8%
20/36 5/9 55.6%
21/36 7/12 58.3%
22/36 11/18 61.1%
23/36   63.9%
24/36 2/3 66.7%
25/36   69.4%
26/36 13/18 72.2%
27/36 3/4 75%
28/36 7/9 77.8%
29/36   80.6%
30/36 5/6 83.3%
31/36   86.1%
32/36 8/9 88.9%
33/36 11/12 91.7%
34/36 17/18 94.4%
35/36   97.2%
36/36 1 100%

Some Stuff on the Doubling Cube for Beginners :

Simple Money Game Cubes : Take / Pass decision tips. Simply put, you need 25% winning chance to take a cube in a money game. If I played 4 games, and dropped the cube 4 times, I'd be -4 points (pounds/dollars/euro whatever) in total. If I played 4 games, had no chance, and took the cube when it was offered on 2 each game, and lost all 4 games I'd be -8 points (that's twice as bad). If, however, I thought I could win (on average) one of those four games, then taking the cube on 2, I'd end up like the first example on -4 points. (-6 +2 for the game I won). Therefore if you think you can win one in four games, or 25% of the time, you will break even by taking the cube. Let's take another example ; if you have 20% winning chance then I suggest you drop, because if you only win 1 in 5 games then you will earn -8 +2 = -6 points, (versus the -5 points you would gain by dropping the cube straight away). Therefore, with 20%, you reduce your losses by dropping, and increase your losses by taking i.e. you will lose money faster (not good). Holding the cube has some value (equity) and cube decisions are much harder in match play. Match winning chances, or equity tables, suggest that when you are trailing by a large score, your take point lowers to 20%, 15% or even lower. Likewise, when trailing heavily in a match, you may not need 75% to double, but only 65% or less especially if Gammons are abundant and increase your score efficiently. In some cases it may be correct to double with less than 50% winning chances. But that's match play.... money play cube decisions are what you should practise first, because they are more regular and consistent.

Estimating your game winning chances : How do I tell if I have 25% or just 20% winning chances. ie. Do I take or drop ? Well what starts out as "guestimation" ends up as accurate assessment with time and experience : Most positions are compared to models or template positions to which you know the answer. I am going to give you a classic mid-point-clearance template which will come in useful time after time : This is only one template, but you will build up others with experience. This is how it goes ; Your opponent doubles & you are holding his 5 or 4 point. He has yet to clear his mid point, and you are less than 25 pips behind. You have a classic take (he has to clear his mid, which you might hit, and you have some race, if you roll big sets (doubles), or just roll high). The exact positions look like this : First (on the left) is the take for orange with 25% down 18 pips and then the drop with 20½% down 28 pips (Snowie 4.5 on 108 Truncated Cubeful rollout). This reference position is not in the "Standard Backgammon Bible of Reference Positions", as I just made it up. But something very similar certainly is!

Orange should TAKE ! Orange should DROP !

Some positions can be calculated according to race. Some bear-offs also according to race but taking account for gaps (Kleinman & Thorpe counts). Some positions can be calculated according to your opponents good vs. bad numbers... and extending that, your chances could be his bad numbers x your good numbers (how many you have.) For example 9 bad rolls equate to (36/9)=25% and 7 to (36/7=19.444) just under 20%.

Simple Bear off Models : To prove that most players already have a set of models or templates that they follow (consciously or sub consciously), I am going to illustrate 3 simple Bear off positions that most people know are from left to right no double / take / drop.

No doubleDouble / TakeDouble / Drop

Let's say Blue is on roll (but it could be orange, in which case blue is being cubed). Orange has 32% in the 10 on 10 men bear off position, and blue (68%) should not cube. With 8 on 8 orange has 26.1% = Take! (Snowie Bear off database) and with 6 on 6 orange has 19.2% which is a money drop, but could be a take at certain match scores (should you have a low take point). The above positions are sometimes called 3 or 4 roll positions.

A Simple Bearoff Winning-Chance Calculation : Recently I was asked this question : What are blue's game winning chances in this bearoff ? Orange is on roll.

The answer is that blue will win all the times orange does NOT throw a double AND blue does NOT throw a single 1 (a double 1 is ok). So blue wins 30/36 (6 rolls are doubles and 30 rolls are no doubles) x 26/36 (10 rolls have a single 1 in them and are no good for blue) = 5/6 x 13/18 (simpler fractions) = 0.60185 or expressed as a percentage 60.185% and to the nearest decimal 60.2% which is what the Snowie database answer is. If you're not sure how to multiply fractions, just plug them into a calculator one at a time (30 / 36 * 26 / 36 =) or you get the same answer with (5 / 6 * 13 / 18 =). In the playing field, you could simplify the fractions to 5/6 x 2/3 (this would be 12/18 instead of 13/18) to get 10/18 or 5/9ths of the time which is easily over half the games. It's a good enough calculation to tell you orange should not double (and blue should beaver if orange does !). It is worth pointing out that if blue has 60% winning chances, then obviously, the remainder of the games are won by orange who has 40% (and in this case that's accurate to the nearest integer).

The 10% Race Trailing rule : If all contact between checkers has been broken, and your pip count is, say, 100 pips and mine is 10% more, which would be 110 pips. Then you'd have a perfect money cube (75%) and I have a perfect money take (25%). Here are two really random examples to show this : Below left, is an illustration the 100 to 110 pip race ; can you see that blue's spare checker would need to move 10 (say, by throwing a 64) to equal orange in pip count ? As blue, I have 25.1% wins (108 Truncated cubelful rollouts) :

Orange on roll. Double takeOrange on roll. Double take

Above right : Orange has 60 pips, blue has 66 pips to complete bear off. (See pip counting tips). According to the Snowie bear off database, blue has an even healthier-than-before chance of 26.7%, (courtesy of the one point gap and the more efficient bear off position of blue... when he rolls (55) for example); so it's still an okay double for orange and an easy take for blue. To calculate 10% of something you just shift the digits one place to the right, so 10% of 45.0 is 4.50, or 10% of 109.0 is 10.90 and 10% of 80 is 8. Working out different percentages is not too difficult either, so 20% of 80 is 16 (just double the 10% figure which was 8) and 15% is 12 (add half of 8 to 8). Another way of working out a percentage is if you want 8 percent, you multiply by 8 and divide by 100. So 80x8/100= 6.4 - now, you might see where I'm going.... the doubling window in pure races is usually between 8 and 12 percent. Therefore is your opponent is on 80 pips, expect to be cubed when you are on 86 - 90 pips. Drop if you're any more than 12% behind, and you shouldn't even be doubled if you're less than 8% behind, say on 84 pips. Let's look at some other examples below : On the left, the count is 45 to 51. Blue should pass if doubled, because 45+12%=50.4, and blue is just outside that.. (though he still has 20%). On the right Orange shouldn't even double (36-38 pips) and is only 2 pips up. However the 8% window starts at blue=38.8 pips, therefore you can see orange is on the verge of cubing in this position (orange has 70.4% and commits only a very small 0.012 error in cubing.) Orange gains -0.012 (or looses 0.012) in equity if he cubes (because of the 29.6% wins blue has including potential re-cubes).

Blue should drop (45-51 pips)Orange shouldn't double

More Random Stuff for Intermediate Players :

What the.. is Equity ? Believe me "Equity" is something you want ! It's the value or strength of your position. If you were playing me in a head to head money game, and we were playing for £1 a point, and suddenly we got thrown out of the club and packed up in the middle of the game, then you'd be disappointed not to get any money from me if your position was worth +0.604 in equity (you may have been about to double me, and I may well have taken the cube... but remember we got thrown out...) then if we were pals (& I were fair) I'd give you 60 pence to settle your equity (. If you were playing some jerk, he'd be happy to pack up & clear off.) Every position has a value attached to it. If you plug the position into a computer it'll let you know what that equity is. By the way, if you have negative equity you are losing. Your equity is your match winning chances minus mine (that does take into considerations how many gammons / backgammons each of us are expected to win). To work out equity say you have 60 % (.6) wins and 20% gammons (.2) and I had 20% wins and no gammons, then you'd have healthy equity of .6+ (.2 x2) - .2 = +0.80 so I'd pay you 80 pence ; unless gammons were off because of Jacoby rule, and I hadn't taken the cube in which case your equity would be +0.40. If somebody else took over the game, at that stage, and the club wasn't closing but you had to catch the bus home, then you'd expect that person to pay you 40 pence to take over your stronger position. This is a fair price for your particular position. If you make a move that loses equity over the best move.... ( say you did a .2 blunder just before you handed over your game (a loss ; ie. -0.20 compared to the top move as you were in a hurry to catch the bus), then the equity of your position would be down to +0.20 and you would have effectively thrown away 20p by making that shockingly bad move. Oh well... You commit an error if your move loses between 0.03 and 0.11 equity compared to the best move, and you commit a blunder if you lose over 0.11 equity over the best move. If you're over -0.2 it's a double whopper ; over -0.4 it's a double whopper with cheese, over -0.6 it's what can I say... Everybody makes whoppers and blunders, just that the Giants do it less often than you and I, but believe me they do them too. So next time you make a blunder my advice is get over it, admit it, study it and move on !

How do I count pips ? (even if I can't count) Pip counting is an integral part of backgammon. There are various ways to count pips. I count cross overs to check if I'm behind or ahead (which might be important when playing say a double 4... do I stay behind & hold my opponent or do I break contact and run ?... ) the solution, as with many problems, is in the Pip count. If I'm uncertain about the value of my cross over count, I count half cross overs. For certain moves I do a comparative count, telling me how many pips I am ahead or behind (but not giving me the full pip count of either side) and lastly, if I'm thinking cube action, or whether to take or drop I do a full count. There are a few more methods (like counting to the 5 point)  that come in handy but here are my tips. Firstly, my counting in 10s system, Below Left ...count 2 checkers, one each on the 4 & 6 points (that makes 10) then do that another 2 times... to get 20, 30, then add 2 from the 5 point to get 40, & another 2 to get 50 pips. Hey that was easy. Try below middle... one checker from the 2 & one from the 3 point, (make 5).... 10, 15, 20, 25... crickey, you're getting good at this! Then just add however many you have on the 1 point... 7 checkers is 7 pips (you'll have to roll 7 numbers as big as or bigger (that's called wastage) than 1 to bear them off). Let's put your skills to the test ; count the pips on the bottom right diagram.

10, 20, 30, 40 50 pips5, 10, 15, 20, 25 pipsclosed board = 42 pips

So a closed home board (42 pips) is worth remembering.. it comes up often. The above system works well, because most people like to count in base 10, but I've often thought it would be more convenient to count in base 6 for backgammon... or at least learn your 6 times table, (it will come in handy) 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120 so that when you come to count 3 checkers on the 18 point, you will jump to 54. Another times table worth knowing is your 13 times table ; 13, 26, 39, 52, 65, 78 etc... as the game starts with the 13 point loaded with checkers. Below : Here's a board you can use to study pip counting :

 Pip Count Board

A comparative pip count is done by comparing each side : On the board, below, (we've seen this position before) blue has to throw 2 7s =14 pips to bring his checkers from his opponent's 5 point to his mid.. then 12 pips (or a double 3) to bring the 2 on his 9 point to the 3 point (the points are marked 16-22 from Orange's point of view), that's a total of 26 pips... oh yes, I almost forgot... to switch the 2 on blue's 5 point to the 4 point (or 20-21 point) add another 2 to make a grand total of 28 pips to equal orange. But I haven't a clue how many pips each side has, I just know that blue's behind 28 pips, and in this situation, anything near 30 pips down seems like a drop.  

A Pip Counting technique using half cross-overs : This method can be quite fast as long as you are prepared to practice it. A full cross over is where you cross one of the four sectors of the backgammon board ; since the sectors are 6 pips wide, you will never need more than 6 pips to do this. And a half cross over can be thought of as 3 pips. Now if all your checkers were on your 5 point you'd have a pip count of 5x15=75. However, all your checkers are probably not on the 5 point ; but count the half cross-overs needed to reach it (if you're on the bar that's an extra cross over just to get to the 24 /23 / 22 point. Also any checker on your 1, 2 or 3 point needs -1 cross over. After having counted all your cross overs (for each checker) multiply by 3 and add 75 pips (as they are now, thanks to the half cross over count)  all in your 5 point sector). Lastly, to refine your count (you may or may not need this amount of accuracy) you can add or subtract single pips, by observing if a checker is in the middle of a half sector or not. The following points need no adjustment 2, 5, 8, 11, 14, 17, 20, & 23. If you have a checker on the 16 point, then you subtract 1 pip from your final pip count, because that checker is one pip closer to home than if it were in the middle of the half sector (ie. the 17 point).

Half cross over pip count
 

Above : An example of a half cross over count. Blue needs 22 half cross overs to get all checkers to his 5 point. His approximate pip count would then be (22x3)+75 = 141. To get his exact pip count we adjust to -4, (the 22 / 24 point checkers are +1 and -1 so they cancel each other out ; the two 13 point checkers reduce our pip count by 2 as do the two 7 point checkers ; the seven checkers in the 5 point sector balance each other out) so the final pip count is 141- 4 = 137. With practice this method can be quite fast.

Remembering pip counts ; you count your pips... then while counting your opponents' pips you forget your own... you recount your own, only.... now you've forgotten your opponents' count ! In the above example to remember 137 place your fist two fingers on your 1 & 3 points, and your left hand index on your 7 point.... now unless you need to scratch your head, your fingers should still be pointing at 1 3 7 after you've counted your opponents'. 

The kind of Stuff Advanced Players think about :

What is match equity ? Here's a match equity table (see below). It's another neatly presented table by Steve Morris (It's rounded up to the nearest integer and is based on a Snowie 3.2 chart I sent Steve, which was accurate to one decimal point.) I'm just going to quote Steve's instructions printed at the bottom : The table below gives the match equity, in percent, for each score in a match to 11 points or less. The numbers on top and down the left hand side represent the number of points to go in a match. For example : You are ahead 8 to 5 in an 11 point match. You have 3 points to go, and your opponent has 6 points to go. Look at the intersection of the third row and the sixth column, and you find the number 71. This means that your current probability of winning the match is 71%. That's what match equity is. It is also called Match Winning Chance in Snowie, MWC%. Although not as accurate, you can download Kit Woolsey's Match Equity Table here. The doubling cube and gammons affect match equity, and recently it is thought that there are around 23% gammons on average in backgammon games.

Let's take a simple example to calculate manually ; what's my MWC% at 2 away, 1 away on Crawford ? Answer: I win a gammon (and therefore the match) on average 11.5% of the time (half the 23% gammons that happen will come from me). The remaining 40% wins are singles. My chances of winning the next game is 50%, so my MWC% = 11.5+40%x50% = 11.5+(4/10 x 5/10) = 11.5+20/100 = 31.5% MWC. If I weren't on Crawford (so let's say it was post-Crawford) it would be a much higher 48.5 MWC% because I would cube straight away. (And that's why my opponent can in many instances take a "free drop", in the event he doesn't open the last game well (i.e. something other than 2-1 or even 5-1)). If I opened the game 3-1 (or with anything else other than 2-1), he'll certainly drop my cube next go.

What do I care about match scores and match equity ?
or How can match equities adjust my "take point" ?

What is my take point ? It's the probability of winning above which I can take the cube !
If I drop the cube, I will have a certain match equity. If I take either of two things can happen:
From this match equity, the amount I gain by taking and winning is called my gain (or reward)
The amount I lose by taking and losing is called my risk.
My take point is risk / (risk + gain)

Below : A Match equity adjusted cube take / pass decision : Orange is offered the cube; it's a take when playing for money. Now let's see when in a match it could be a drop (pass); if orange were 4 away 2 away, (ie. the score is Blue=3/5 and Orange=1/5) then by dropping he'd have 18% match equity (look up the figure in the table above for 4 away 1 away). However, by taking and winning he'd have 50% (2 away 2 away), and by taking and losing he'd lose the match (0% match equity). Orange risks the 18% he would have by dropping to gain 50-18=32% by taking and winning. We say Orange's take point is his risk divided by his (risk plus gain), which in this case is 18/(18+32)=18/50 or 36%. Now, orange wins every time blue throws a 1 which is 11 rolls out of 36 (ie. 11/36 which is about 31%). That's still short of orange's take point at this match score, but is ample good in a money game (where you need 25% to take). So in the position below orange should take for money but drop at 4 away 2 away. (It would be a double blunder for orange to pass this in a money game, and a double blunder for orange to take at a 4 away 2 away match score.)

at 4 away 2 away orange must drop

Well, this next example is also clear: Below is a simple position in which you wouldn't hesitate, playing as orange on roll, to redouble in a money game. Well you'd be committing a blunder not to, anyway(with a 0.149 loss, near enough 15%) And of course, blue would have to drop, and if he didn't he would be committing a double blunder (giving you +0.243 or 24%). So this is a clear Redouble / Drop when playing for money. However, it would be a risky cowboy stunt in the following situation: If orange were leading 7,1 in a match to 11 (that's known as 4 away, 10 away) he has 81% match equity (his chances of winning the match at that score). Blue has 19%, and it looks like that's about to become 8%. Now if orange redoubled to 4, and then didn't throw a double, blue could redouble to 8, before having a go at throwing a double himself (he has to throw a double this go or the next to win, but now on roll, he would now have an improved 20% chance of winning this game !) Well, before taking his 20% chances he should redouble to 8 (if not, he would be committing a 0.154 blunder, and orange must take, not to commit a 1.287 blunder!). So, orange's initial redouble to 4 has given blue a 20% chance to take the lead in the match, which would leave orange with a very sorry 34% match equity left, at 4 away-2 away. In fact, at this score, Snowie says Orange would blunder if he redoubled to 4 so it's now a No redouble / Take.

Now let's talk about Blue. A 4 cube comes floating blue's way....if blue passes he'll have a miserable 8% match equity... but if blue takes (and therefore would have nothing to lose by shipping it back on 8) and wins, he would have 66% match equity. If he loses he'll have 0% match equity, and will have lost the match of course. So by taking, blue is risking his remaining 8% (which blue would still have by passing) in order to gain 58%... so you are getting odds of about 7 to 1 on your take. Blue's take point is 8/8+58=12% which he amply surpasses as he has 16.2% according to Snowie's bear off database.

 No redouble at 4 away, 10 away

I still want to show another example. Below, blue is on roll. For money, Orange would commit a quadruple blunder by dropping the cube. At 5 away, 2 away, a drop brings Orange to 16%. Orange's gain would be 25% and his risk 16% giving a take point of 16/(16+25)=16/41=39% which orange doesn't have. At the match score below (0-3 to 5) it would be a blunder for Orange to take !

 

 

How do I use Snowie constructively ? Coming soon....

Chouettes
Here's a nice way to play backgammon when there are not enough players to have a tournament. Chouettes rules adopt money game rules, including Beavers & Racoons, and Jacoby rule (where a gammon cannot be won unless the cube has been turned). Chouettes is a game where 3-5 (or possibly more) players all play together ; one man is in the Box, playing all the other players in a team who are lead by a Captain. The captain will have the final word in selecting moves (which his team member may suggest to him, once that particular member of the team has doubled or has been doubled). No consulting must take place about cube decisions. Every member has his/her own personal doubling cube and will win or lose points according to their cube value. For instance, if the box offers an initial cube (the first cube is usually offered to everyone, rather than select members of the team) and if a player in the team drops, then that team player loses 1 point. If the box then goes on to defeat the team, winning a gammon, the players on the team will lose 2 x their individual cube value. If someone on the team happened to re-cube the box to 4 then that team player would lose 2x4=8 points !). Playing at £1 or $1 a point, that would be a loss of £8 or $8. It is worth noting that the player in Box will experience the biggest loss or win. If the Captain defeats the Box, the Box is overthrown, and the Captain takes the Box, offering the next player the Captain's chair. Initial placing in a Chouettes game is established by rolling dice ; the highest number wins the Box, followed by Captain, and then team members. Chouettes groups of 3-4 people have faster turnaround time and more excitement in general than large groups of 6-8 players. Settlements are possible, as in money games, and a great many variations on the standard rules exist. In fact there are no standard rules. In Bristol we usually play ; Jacoby rule ; It is compulsory for the Box to take or offer the initial cube from or to all team players ; subsequently, cubes may be selectively offered or dropped even if not of different cube values ; Captain beats Box (as opposed to last man standing) ; Auto cubes at the Box's discretion. In very small groups of 3 or 4 players it is possible to have consulting before the cube is turned (at the box's discretion). New players enter the chouettes session joining the team at the bottom of the list. Players should be prepared to cover 50 points in cash before joining. Etiquette on leaving a chouettes session is to give a notice of one hour before leaving, or x number of rounds in order to give a chance for others to win their money back ! Don't expect to be invited back into a Chouettes if you make a lucky run in the box then quit after 3 games, for example.

Variations in Chouettes
Box must defeat all :
A common rule is that the box must take, or defeat all players on the team to retain the Box. Last man standing rule states that if the Captain drops, and so do other members of the team drop at different stages, then the last man standing who defeats the Box shall earn his place in the Box. The usual rule is that the only game that determines who is next in the box is the game between Captain / Box. For example, if the Captain drops a cube and the rest of the team take and go on to win, the player in the Box has retained his position in the Box. (In this scenario the Captain would rotate to the bottom of the list, and the next player in turn would become the new captain.) Partners : Large chouettes groups, in which weaker players may be involved, the Box may take the player who has just come out of the Box to partner him/her, thereby halving the losses (& wins) that the Box may incur. Consulting with Box partners is usually active on moves and cubes from the beginning. Extras : (sometimes called "props") may be enforced for advanced chouettes ; if one player on the Team decides to take the cube and all other players drop, then the cubes from the remaining players are sold to the taker, who naturally has a great deal of re-cubing ammunition at his disposal, but the player who takes will usually incur large losses. This discourages players / Captains from taking questionable takes in order to beat the Box. Other members of the team who are usually excluded from the game find themselves more involved.

Propositions (Props.)
Props. arise mainly due to a disagreement over whether the cube action in a position is a take or a drop. If I think it's a take, and you think it's a drop, then I'd like to play the losing side. I'd take the cube, for which you'd pay me 1 point. The position is then recorded and played out x number of times. Say 5, 10 or 20 times, at the loser's discretion. If I went on to win the game (played on from the recorded position) I then win 3 points as I own the cube on 2 and you paid me a point. If you win, you win 1 point.. (the 2 cube minus the point you paid me). If I win a gammon it's 5 points to me ; if you win a gammon it's 3 points (4-1) to you. If I recube you to 4 and gammon you I win 9 points (2x4 + the point you owe me ). Why should you give me a point for taking the cube ? Well, because you are saying you'd rather drop and lose a point than carry on. I say I'd rather carry on, and win perhaps more than 25% and I also like holding the cube too (which I can use !).

Prop. Chouettes
This is a form of chouettes or head to head money games where if a cube position is reached the players will hold (or not) a cube in their hand and on the count of 3 will reveal by turning their hand whether they would take or drop the cube. No cube in your hand indicates a drop. All the players who would take the cube then play out the recorded position on the weaker side, taking the cube (but are paid 1 point for each cube by the players who decided it was a drop). Usually it will be Box vs. Captain, or the next team player who play out the prop. After 5 or 10 games or rollouts the players who took may have changed their mind, and decide it was indeed a drop. They may wish to end the session, or if they feel they were right to take, but are suffering higher than normal losses they may insist on playing another 5 or 10 rollouts. Re cubes are allowed, and players always earn the individual value of their cube plus or minus the initial point they paid / were paid. If one side wins a total of +3 and +5 points, then the losing side should usually split the losses equally (-4 -4) (as long as they are equally responsible for the loss).

 

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Last modified: October 06, 2009 00:11