grenv:
There are probably more accurate rollouts available but they seem pretty good.

They say:
4-1 = 49.8%
2-1 = 49.9%
6-4 = 49.9%

Do you mean that if I'm from 1 point of winning (for example 6-0 in a 7 point match), I should drop the cube if my chances on that game is 49,8%? That would mean that if I'm on the losing side, I should wait until my chances are 50,2% and not to double before that. That happens almost in every game, and thus I would get one point after another until the game would be even.

Or is the situation different in games when the losing player are not as close as 2 points away?

playBunny: hmm, I thought the rollouts were essentially random, so the number of iterations being a multiple of 36 seems a little arbitrary. However if the first 3 moves are selected, rather than random, then it makes sense.

4-2 comes out better than 6-1 according to the site, but it's close.

grenv: I'm off to bed so just a quickie..

46656 / 36 = 1296 and 1296 / 36 = 36. Such a number ensures that each dice roll is represented fairly for the first three moves.

I've done rollouts to 1296 and to 12960. Similar principle; 10 goes each for each pair of opening rolls in the latter case.

The 1296s were just so many wasted CPU cycles. Even at 12960, though, the expected error value exceeded the difference between the top moves in many cases. Getting the error values small enough to reliably decide between two moves would require rollouts of 500,000 and more.

I agree with 3-1, and 6-1's up there too. Whether the results can reliably differentiate between the least popular rolls I'm not sure. I'll have a look at what I found in a few hours...

playBunny: Well I can't remember where I originally saw that, some book years ago.

I just looked them up at bkgm.com. Apparently they use 46,656 iterations (seems like a funny number) and assumes cubeless play for a frame (which is essentially what we were talking about). There are probably more accurate rollouts available but they seem pretty good.

They say:
4-1 = 49.8%
2-1 = 49.9%
6-4 = 49.9%

Important to note that 6-4 has many gammon wins compared to gammon losses so is usually a better roll, but if gammons are not important as in the last frame then it's a bad roll.

Best roll in all cases is 3-1 obviously.

Also even 4-1 is winning if gammons are taken into account. Moving first gives you an advantage in most cases.

grenv: Which rollouts are you talking about here? How many iterations and what's the error margin, etc, etc?

Czuch Chuckers: Well, it's just how the rollouts work.

with 3-2 the best move in a single point game (which is what the game in question is) is 24/21 13/11. This is not as bad as the best 4-1 (24/23 13/9) probably because the back checker is better situated on 21 and the checker on 9 can be hit more easily than on 11 where it is relatively safe and a good builder.

It's very marginal though, 3-2 isn't that good either.

grenv: I guess i dont understand why 4 1 is so bad? what about 3 2 then?

Czuch Chuckers: Essentially the point about dropping when losing is a good one. It isn't always easy to tell of course :)

After one move apparently 4-1 is the only way someone playing first can actually be considered to be losing (on rollouts), hence my suggestion that you refuse the double if you played 4-1 and are immediately doubled. Some might argue 2-1 as well, but that works out to about 50-50.

BIG BAD WOLF: I think you got it!

I know some of this is already covered, but my thoughts in my own words on the subject.

If your opponent only has 1 more point to win the match, then for you - it is beter to double early so the game with worth 2 points so if you do win, you will win twice as many points. (If you lose - well no mater if it is worth 1 or 2 points, you will lose the match.)

If your opponent only has 1 more point to win the match, and lets say you wait for a few moves into the game before you double - then your opponent has the basicly "free" oppertunity to either accept or deny the double and get to play again - and only giving you 1 point. That is your opponent only needs 1 point to win, and if he is already in a losing position, there is no point in him accepting a double - it is beter to just give you the point and start the next game. (Where as if you doubled early, he would already be in the losing game worth 2 points)

(This is of course after the Crawford match where 1 game is played without the cube)

http://www.bkgm.com/articles/mpd.html

Czuch Chuckers: Because of the Crawford rule, after the leader gets one point away from the match, one game has to be played where the trailer hads no right to double. So at 5-0 the trailer needs four wins, not three.
As for doubling strategy, the case where the leader is one point away from the match is about the only simple one. That is what makes cubed backgammon great !

Czuch Chuckers: 4 games actually, you forgot about the crawford round.

And if you lost 5 in a row you probably lost the match already unless every game was worth a single point.

Czuch Chuckers: Depends upon when you are measuring the advantage. At the start of the game, it would be unfair to say "Player X needs 7 wins, Player Y only needs 4." However, once you make the assumption that one player is ahead 6-0, you aren't at the start of the match anymore. I don't care who the players are, I'd rather be ahead 6-0 than tied 0-0. At the start of the match, both players have an equal likelihood of getting to 6-0, so the rules don't favor either of them.

alanback: Sorry... I think I will have to find my answers online somewhere. There must be a good doubleing strategy found online somewhere....

alanback: It's a good idea to read a book (or a chapter) on doubling strategy. Many of the answers to these questions are common sense once you think about them, but wouldn't be intuitively obvious to a beginner. A good example is the take/drop question. You know that the outcome of the match will be decided by the result of the current game if you take, and by the outcome of the next game if you drop. Your chances of winning the next game are 50-50 (modify this if you think you can estimate the relative skills of yourself and your opponent); you should take if your chances of winning the current game are more than that, drop if they are less.

alanback: But a person who has lost 5 in a row in a 6 game match, really only needs to win 3 games for the victory....

Czuch Chuckers: See my earlier post as to when the leader should take or drop. In general, take if you are ahead in the current game, drop if you are behind.

Czuch Chuckers: It's obviously not true that the early loser has an advantage. I think that what you mean to say is that it's not as hard to catch up as it is to get ahead, and I think that is clearly true. Nor is that necessarily a bad thing.

so being up 6 to 5 you should be given a double offer and refuse it to knot the match?

Czuch Chuckers: Losing early is an advantage? That is not true (obviously in my opinion) and can be proven mathematically. If you want to give me a headstart I'll attempt to prove it

Czuch Chuckers: And if your opponent moved first with a 4-1 he should refuse the double.

If you moved first and this is your second move then he should refuse most of the time.

It almost seems like the person losing early on in a cube match has an advantage....

Czuch Chuckers: Yes. What do you have to lose?

Down 6 to 5 in a 7 point cube match.... do I automatically offer a double?

volant: Thanks to you for putting on the prize tourney. Very nice of you ...YEAH! Volant... 3 cheers.

volant: Lolol. Nice one!

SueQ:
It all fit together so well i couldn't resist

playBunny: How could I resist the start date of Friday January 13

Antje:

Czuch Chuckers: not to mention the interest Fencer will get on the money already submitted

grenv: I do not agree that luck usually evens out in the course of a match. It takes much longer, several matches at least. Certainly I have seen many 21 point matches dominated by luck, though hardly a majority of such matches.

I actually think that doubles are an interesting addition to the positional evaluation that would be missed. They cannot be ignored since they occur 17% of the time. In a multi point match the luck usually evens out anyway.

alanback: It's only exciting when I roll the doubles. It's frustrating when my opponent does!

Groucho: I've never seen it adopted :) Some people probably like the added luck factor, consider it exciting.

alanback: I agree and I think the doubles remove from the game well-played strategies. What has been the response to eliminating doubles in race games?

Groucho: Doubles add dramatically to the luck element in hyper as well as in race situations in other backgammon games. I have suggested eliminating doubles in pure races before.

Has the idea of eliminating the rolling of doubles in hyper ever been discussed? I'm just wondering what others think of the idea at the moment. It seems that by removing doubles, it would add more to the elements of strategy and tactics in the game while eliminating the "stealinng" of a well played game buy the lucky double sixes!!! I've been robbed too many times! ;) OTOH, I've done a bit of robbing myself but with the doubling cube the stakes are higher. What do others think of eliminating (or adding as an option) the removal of doubles in hyper?

Since the prize tournaments have to be paid in advance of the tournament starting, if it takes 10 years to finish, it will be a bargain 13 months membership!

grenv: I think 2 rounds may be optimistic, too. 18 players so far and several weeks to recruit more. Only the board readers know about it so far as it's not on the tourneys front yet. And if volant fancies doing a broadcast to a bunch of players from the Backgammon rankings .... Also, we should go by the average of the slowest rather than everyone, so perhaps 4.88 days per move.

We could have us a 10-year tournament!

Frolind's 21pt tourney from October is racing ahead.

volant: Thanks Volant! That is very generous of you!

playBunny: @ 30 moves per game, let's say about 10 games to finish a set, and some slow players that take and average of 3 days to make each move, that's about 3 years per round, and I didn't even account for vacation.

So if there are 2 rounds, the prize won't need to be bought until 2010 I'd guess.

volant: Very nice of you to create this tourney.

Blimey, it doesn't start for about another 50 days! Any bets on how long it's going to take?

A prize tournament, thirteen point match for thirteen months rook membership.
Please make sure you have at least 10 empty slots.
Best of luck everyone :)

playBunny: The stronger player will win more matches than he loses, but probably not more than he draws, unless the skill difference is great.

The length of a backgammon match is always fixed in terms of a number of points, rather than a fixed number of games (except in the case of a 1 point match which could also be considered a 1 game match). Because there are no draws, BG is almost always played in matches to an odd number of points.

alanback: "BG is never played in 2-game matches for the very reason that the predicted outcome in such a case is 1 win apiece

This puzzles me. Between equal players the win rate will the same for each over the long term. For unequal players the stronger is going to win more matches. "Possible", yes, "predicted", not necessarily.

alanback: Um, that doens't necessarily follow tha the ratings would be even.

However, I believe I showed that the ratings will be affected equally no matter what the skill difference.

grenv: Talk about putting the rabbit in the hat -- how could you have those point changes if the two players are evenly matched? (You must assume equal ratings to make such an assumption meaningful).

tonyh: Reasonable it may be, but the rules of the game don't allow it.

Drawing a 2 game series is only a little better, but I don't agree that the ratings should be affected at all.

e.g if you stood to gain 4, -2, -8 (for w/d/l) and you are evenly matched your expected loss for one game is -2

In a 2 game match:
win 25% = 1
loss 25% = -2
draw 50% = -1
for an expected change of -2. exactly the same!!!

but for example if you were a better player and win 55% of the games then the expected results are:

single game .55x4-.45x8 = -1.4
2 game match
win 30.25% (1.21)
loss 20.25% (-1.62)
draw 49.5% (-0.99)
1.21-1.62-0.99 = -1.4, in fact it's always the same!

QED

tonyh: I have no objection to the draw option. I have had draws on IYT. However, ithe backgammon world it is an anomaly, and would never be allowed in real-life tournaments.