Peeky: The weaker player loses more than the stronger player in the case of a loss and gains less with a win. Or two players can play two games and after each having won one game both their ratings will have increased.

Can I explain? No. But I can join you in a complain. It's a terrible formula that we have.

playBunny: Are you sure about that?
Yes, I am...:)
Does not the infinite set contain everything?
Yes, it does...:)

Pedro Martínez: "The probability of any specific roll or sequence of rolls is lower than 1, no matter if you consider the number of moves finite or infinite."

Are you sure about that? Does not the infinite set contain everything?

Pbarb2: Yes, it is relatively new. For the future, just make sure you don't accept invites or sign up to tournaments that have a red dot next to their "time control"...:)

Pedro Martínez: Is this something new? I knew that was there but didn't know what it meant. I sure know now.LOL My first time out or use of the auto vacation. In this case non use. I will make sure I don't get one of those games again. In my case you never know what is happening health wise with me. Thanks for the quick reply.
BARB

AbigailII: I believe that proves an infinite game, not an infinite number of games. Small but important distinction.

Pbarb2: If you see "No days off" written in red in a game, the auto-vacation will not prevent its timing out. See this:
http://brainking.com/cz/Help?ht=13

I guess that the no days off makes the difference and makes the automatic vacation thing useless..........

Pedro Martínez: I see that Pedro.. But why did I run out of time with my automatic vacation on?

Pbarb2: Tournament: The Delete's Gammon Fest #1
Game ID: 890904
Score of finished games (Pbarb2 - MsDelete, Backgammon Race): 0 : 1 (= 0) (show games)
Time per move (?): 3 days, no days off
Public game (visible for other players)
Rated game (the result will be calculated for players' BKR)
Board size: 1 (change)
Layout: columns (change)
White ran out of time.
Black is the winner.

I just got this in my message box that I timed out in this game. I have my automatic vacation box checked so it is in use. Just wonder WHY?
Tournament: The Delete's Gammon Fest #1
Game ID: 890904

grenv: One piece all works as well. Put them anywhere on the board, under the condition they still have contact. Now let them roll only 1-1s. Neither side will be able to bear off.

Pedro Martínez: lol...indeed ..but nobody24 and me are friends and we often play together on the same computer ..That's why we just noticed the difference :)

playBunny: The simple case is always the best place to start, and I agree it was a clever proof.

One piece each wouldn't work, it relied on players hitting each other's block.

Peeky: Yes, but you can see only how your rating will change in case of win, draw or loss. You cannot see the opponent's rating chnages...

You can see it underneath the game board ....in every game there's mentionned how your rating will change in case of win, draw or loss

Peeky: How did you learn how many points would nobody24 lose?

Just noticed something strange . I'm playing a normal BG game against nobody24 .... he has a rating of 2134 and I have a rating of 1805. When I loose the game my rating will go down with 30 points . When he looses the game his rating will go down with 11 points though his rating is much higher than mine .I thought it would be opposite because my rating is so low. Can somebody explain this to me ?

playBunny: In other words, if you make a roll, the probability that something will appear on the dice is 1. The probability of any specific roll or sequence of rolls is lower than 1, no matter if you consider the number of moves finite or infinite.

Pedro Martínez: Aye, and the "something" in question is the endless sequence of double fives.

Or did I miss something? I wasn't sure whether you were agreeing or challenging?

Perhaps by the probability of "something" = 1 you mean the probability of any of the sequences implying that the probability of a particular sequence is less than 1? As I understand it, that's true when considering the finite but not when considering the infinite.

grenv: "the simple case with 2 pieces each left." Lol, I think that's actually quite crafty.

But why complicate it? Let's use the case of only 1 piece each. ;-)

playBunny: The probability of rolling "something" is 1, i.e. 100%.

Chessmaster1000: Excuse my ignorance, I'm a logician more than a mathematician, but I would have thought that the probability of an endless sequence of 5-5s is exactly 1.

Consider every single possible infinitely long sequence of dice rolls.
Surely 5-5, 5-5, 5-5... is among them? If not, why not?

Well done everybody, at the start of the thread I thought I had a problem to solve, but it was already solved by the time I woke up. There are indeed an infinite number of games, as proved by the simple case with 2 pieces each left.

As for the infinitely long game, I agree with Wil. it is possible in theory to have an infintely long game. The idea that it's probability approaches zero only shows us that we have no possibility of ever seeing the game to completion. This, of course, is the point.

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: How do you conclude that.......?

Trivial. Suppose you don't get an infinite number of finished games. Then there should be a finite number. Take the one which took the most moves, say R moves. But then your finite set of games didn't include the game that finished after R + 1 rolls of 5-5 by both sides. So, the assumption that there are a finite number of games is false.

AbigailII: You got it wrong.
Correct! I know.....I felt that my example was wrong, but i never really believed it was. Seems stupid right? It was just a matter of not thinking about it a bit more........

I will add later something to the very interesting point of: "Say there are a finite number of games, call this number M. But that could not have included a game that reached the position I described above and then continued with M rolls of 1-1 on both sides, followed by a roll of 6-6. Ergo, there's no limit on the number of different games.

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

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

How do you conclude that.......?!?!?!?

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: You got it wrong. In the limit, the chance that you roll 5-5 "for ever" goes to zero, that's right. So, the chance for an infinite long game is zero. But that's not the same as an infinite number of games. Here is how it goes:

Take the following position: both players have 13 pieces off. White has its two remaining pieces on his 6 point. Black has its two remaining pieces on white's 5 point. White to roll.

If white rolls 6-6, the game is over. Call this game 1.
For game two, white rolls 1-1 (can't move). Black rolls 1-1 (can't move either). White rolls 6-6. End of game. This is game 2.
For game 3, the sequence goes: white rolls 1-1, black rolls 1-1, white rolls 1-1, black rolls 1-1, white rolls 6-6.
Or more general, for game N, both white and black start with N-1 rolls of 1-1 (this chance is not zero), and then white rolls 6-6.

Say there are a finite number of games, call this number M. But that could not have included a game that reached the position I described above and then continued with M rolls of 1-1 on both sides, followed by a roll of 6-6. Ergo, there's no limit on the number of different 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 ..

playBunny: Both sides roll 5-5 ad infinitum

1st)The probability that both sides will roll a 55 an infinite number of times is exactly zero!
With other words : The game would end in a finite time if every single move is made in finite time.....

2nd)Even if the game will continue with an infinite number of 55 (although this can never happen as i said), that game would be one single game and this doesn't help us in the question of how many Backgammon games exist? Finite or infinite? It's another different subject.......
Well it actually "connects" with the AbigaiIII's theorem, but as i believe this theorem is wrong you understand that.....

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.. ;-)

Hmm i understand. But you must have a mistake in your previous post. Please correct it......

You wrote:
The number of different backgammon games is finite if, and only if, there's at least one game with a position that repeats itself.

I guess you should replace finite with infinite. Right........?

And of cource an easy proof that these special positions exist, is to choose M=N+1 and have both opponents at the bar and choose such a dice roll that doesn't get any of the 2 from the bar, for 2 consecutive rolls........

But that really proves that the number of different Backgammon games are infinite.....? At a first glance it does, as k can go to infinity but perhaps this is not critical......
I will think about it and answer later......

Chessmaster1000: All pieces on the ace point except for two men each. Black has the 15th piece on the Bar and White has the 15th piece on the 5-point. Both sides roll 5-5 ad infinitum.

By "all possible, different Backgammon games" do you mean the variants? In which case we need a list so that we're talking about the same thing. From VogClub I know a few variants:
Tapa, Narde (Feuga) and Crazy Narde (Gul Bara) are finite as there is no sending back to the bar.
Longammon, Nackgammon and Acey-Deucey are the same as Backgammon.
Hypergammon is, of course, ripe with infinity.

Chessmaster1000: AbigailII: there's at least one game with a position that repeats itself.

Can you explain in more details this.........

Eh, you have a game, and the positions (that is, where the pieces are on the board, and whose move it is, and if you have a cube, the value of the cube) after move N and M (for N and M not equal to each other) are the same. If that can happen in a game, you have an infinite amount of different backgammon games (if the position after move N can occur after move M again, it can also occur after move 2M - N, 3M - 2N, 4M - 3N, ..., kM - (k-1)N, k >= 0).

If positions cannot be repeated, the number of different games is finite - as the number of different positions is finite.

WhiteTower:
It depends on how you define "similar"........


AbigailII:
there's at least one game with a position that repeats itself.

Can you explain in more details this.........

Chessmaster1000: The number of different backgammon games is finite if, and only if, there's at least one game with a position that repeats itself. And that's not hard to construct - just take a game with both sides having 14 pieces on their 1 spot, and the remaining pieces not having broken contact. Then repeatedly, knock of the single piece. Eventually, the position must repeat itself.

Chessmaster1000: Yes, calculating the upper bound of possible games in GC does sound similar to what you are asking, doesn't it? :)

WhiteTower: About infinite or not BG games, ask Grim Reaper, he had some fun calculating similar cases for Gothic Chess :)

Similar cases? No! Nothing similar as i remember......
It was just a try to calculate the upper bound of possible arrangements if no pieces were captured. The upper bound and not even the absolute number.
And of cource it can be easily shown without any calculations that the number of possible Gothic Chess games is finite. For the moment i can't easily show that the same exists for Backgammon.......

Chessmaster1000: About infinite or not BG games, ask Grim Reaper, he had some fun calculating similar cases for Gothic Chess :)

As for Fencer's Law - it is as you say, and ends up being in the same way that Anubis existed both as an Ancient and as a Goa'uld (for Stargate fans!)

playBunny: Rule 19 in Connect-4 8x8? lol. What's that one about?

It's a set of rules and procedures that i use, trying to solve with a "computerized" way, the Connect-4 8x8 game............

And about the Fencer's Law. It's obvious that Fencer wanted the Backgammon game to be played correctly, but a programming bug created all these conversations........It was not his intention to play the game with other rules......
Also the Backgammon rules page here at Brainking is wrong.......When do you want to define the rules of a game you should include all possible situations possible.......

By the way, a question that came to my mind now and in the first 2-3 minutes i tried to think about it, i've been confused.
Do you know if all possible, different Backgammon games are infinite or not?
I will think about it at night but if you know the answer and help me save some time from trying to find it, i would be very thankful.....

Wil: DG is much smarter and does take care of all such cases, to the point of pre-playing moves to speed things up. But DG is only for BG, so it can afford the extra system load, whereas BK... ;)

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: Exactly - turning to Wil> - either accept the status quo here and shut up about it, or don't accept it, shout at the top of your (virtual) voice and watch it get lost in the wind ;) (unless your stars are lucky and you make more sense than everyone else here and your request gets some results)

Wil: Yeah, right. Suppose you and I were playing a game and this very example happened in it and I played the four to win the game. If you object to it, just what can you do about it? That's what I thought, now pay up and let's get another game going.

Chessmaster1000: I agree. By "Time we had some" I meant the world. ;-)
Rule 19 in Connect-4 8x8? lol. What's that one about?

WhiteTower: Reality? Where you bin? You've missed a whole huge debate about Fencer's law. ;-p

And back to reality now: Here there is only Law 0: Fencer's Law :)

playBunny: Personally i don't care much about Law 20, but for my rule 19 that is getting on my nerves and prevents me to go into the next step at solving Connect-4 8x8.....

But even if we clarify what Law has the priority it doesn't matter much, as it will be written by a book and not an official, international Backgammon organization.........

Chessmaster1000: It's about time we had some then. We desperately need to know whether Law 20 is the most important in spite of Law 13 overiding Law 17.

Chessmaster1000: ...and that's because there is the element of chance in it. Can anyone tell us if there is an International Roulette/Slot-Machine/etc. Federation? :)