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?

Chessmaster1000:
For every move it's 1/36.
For 2 moves to happen is (1/36)^2
For 3 moves to happen is (1/36)^3
For an infinite number of times it's zero.

When n -> infinite, p -> 0, but it never reaches 0

If p=0, that means there has to be some maximum game length, which is smaller than infinite. What might that be?
If the maximum game length is not infinite rounds, what is it then? Say any number, there is allways 1/36 probability that it goes one round further.

If we count all the possible ends when one player doesn't throw 5+5, we get an infinite amount of games.
The game is at point when endless double 5 results endless game. After that, for every double 5, there is at least 21 other possible games that are different from that particular double 5 game. Wasn't the purpose to count number of possible games? If it is possible to throw 5+5 infinite amount of rounds, there has to be at least 21 * infinite = infinite possible games.

Chessmaster1000: that game would be one single game

If we count all the possible ends when one player doesn't throw 5+5, we get an infinite amount of games.

Chessmaster1000:1st)The probability that both sides will roll a 55 an infinite number of times is exactly zero!

For every move to the infinitum, the probability is 1/36, why would it be smaller at some point?

It's question of possibility not probability.
Ie, if we start counting all the possible games:
....Oh, on this point player 1 can throw 1+1, 1+2 ... 5+5,.. hmm.. let's look more carefully this 5+5. Oh, on this point player 2 can throw 1+1, 1+2, .. 5+5.. hmm.. let's look more carefully this one.. Oh, on this point player 1 can throw ..

Chessmaster1000: But that really proves that the number of different Backgammon games are infinite.....?

I agree, and if you have ever tried anti-backgammon, there is no question about it.. ;-)

WhiteTower: As I pointed out, this question is purely philosophical.. Originally Chessmaster asked, which move would be correct according to backgammon rules and my opininon is that using only one is not honoring the rules.

But your are all right, it doesn't affect the result, so I'll stop whining about this. You all can peacefully keep breaking the rule at that situation.. ;-)

Walter Montego: I could do just the same than if you break the same rule elsewhere in the game. I could ask you to make your move again.. ;-) Well, I guess I really wouldn't mind...

Hmm.. GNUbg offers only one choise on that case.. I wonder what choises for example Dailygammon gives..

Walter Montego: This to me means either way of moving the last man off is OK by the rules.

Not for me.. Law 17 definitely says "Law 13 applies here as in all other situations". Doesn't that mean that you cannot bear off by breaking the Law 13, "Plays must be made for both dice if possible"?

>If I use the 4 and bear my last man off, the game
>is over by Law

As I pointed out, according to Law 17 referring to Law 13, you cannot bear out with 4 without first using 1, because you CAN use both dice.

playBunny: Thanks for the link. Lolol - it's the one I gave in my reply to you earlier

Well, maybe, but I found it from the Finnish backgammon association's pages, http://www.suomenbackgammon.fi/

The question about the tricky last move is purely philosophical, but anyway, there should be some answer to it..

playBunny: "For the sake of expediency because it doesn't affect the outcome of the game."
Yes, true, we know that the player making the last move is the winner anyway. Maybe it really doesn't matter which one the last move is..

What do you think: are both moves legal or only one of them? Why?
If both moves are legal, where is the exception that makes the other legal when it breaks one essential rule of the game?

They are not officially official, but looks the same than official to me ;-)

http://www.bkgm.com/rules.html

About bearing all out with the first roll: If we accept that the last move doesn't need to be legal, then any player could make the first move to be the last by moving all pieces out.

Chessmaster1000: I think this is very clear. There is a rule: "A player must use both numbers of a roll if this is legally possible (or all four numbers of a double)." without any exceptions. Is there any other possibility than to use the both? Using only one is breaking the game rules. Why would the last move be an exception?

If the last move is allowed to be illegal, a player might bear all pieces out at his/her first move, as Chessmaster pointed out.

Chessmaster1000:
>Then is the 2-off (using only the 4) winning the >game, a legal move?
Or do you have to use both numbers with 2-1 1-off ?
I would say the later is correct, but what's the problem, it is also a winning move?

Wil: maximise-dice-usage rule

I'll explain more carefully.. There are rules that require to move both dice if possible and to move bigger one if possible, but there are no rule that require to maximise the usage of dice. The example move I gave is legal regardless of the fact that the move uses only 8 pips out of the 9 possible.

Reading more carefully, I assume Abigail referred to the 'use both if possible' rule.

playBunny: those which go against the maximise-dice-usage rule

Obs! There is no such rule. That kind of rule sounds logical, but it is not part of international backgammon rules. Ie, if I have 2 pieces left, one at 4 and 5, I get 6+4, I can move the 4 first (5 to 1) and then 6 (from 5 to off). Legal move, but not very wise..

Hmm. I get the feeling that people thinks that it would be right thing to do according to the standard rules, but they also think that as long as the site allows the other possibility they cannot require me to do so, because it wouldn't be fare (my opponent might have done the non-standard move)...
I agree.. And we should change the vote to the question "should Fencer change the site behaviour according to the official rules?"
I'll do the standard rule and let it be a "yes" vote to the previous question..
I could also ask Sharon, but as this move is better for her, I guess she won't resist.

Well, there are points that supports both moves:

1) The game is named 'backgammon'. According to 'official' bg rules, they wouldn't allow me to make the better move for me. So I should move both dice. If I was playing on the 'real' board, I would move both dice without asking.
2. This site rules doesn't deny me moving only one piece. See http://brainking.com/en/GameRules?tp=23 The rules are the same for both players.

Since game rules are allways an agreement of a community, I'll do the move players here agrees. Let's make a vote. Give your vote here ('move both' or 'do what you can') and I'll make the vote winning move. You have one day to vote. I'll make the move ~24 hours from this moment. My or Sharon's vote doesn't count.

http://brainking.com/en/ShowGame?g=913674
Move number 19. This site allows me to do an illegal move. Black can move 4 at home and leave 5 unmoved. Is it fare play to do that? I'll wait a couple of days before continuing...