alanback: "As White Tower suggests, the laws of probability do not apply to infinite sequences. They are meaningful only in the context of a finite sequence."

Actually we can't blame the laws of probabilities for not being meaningful at an infinite number of rolls, but our brain's incapability to understand the infinite........


playBunny: "What is the probability that the sequence "Endless 5-5s" exists in the infinite set of all dice roll sequences?
A: 1 "

Since this infinite set contains ALL dice sequences, it's reasonable that it will contain and the "Endless 5-5s".......
So it's 1 or 100%....


Now, what AbigaiIII said about different possible Backgammon games was correct and his proof was correct, but i have found a link that states that the number is 10^140 and not infinite. Perhaps it defines with another way the "game". I will investigate this tomorrow..........

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

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.......?!?!?!?

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.....

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......

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.........

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.......

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.....

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.........

grenv: Pedantic? No, it's just a logical fact......
And for all: you should stop looking for an international set of Backgammon rules, as there isn't such thing........FIDE is for Chess but for Backgammon there isn't any.......

playBunny: Lolol re "Serious about the tricky one". Pgt is right, of course. Having legally taken the last piece off with the higher dice it is then impossible to use the other value.

Q1: Do you agree that the procedure of play at Backgammon should be :
- Making a move
- Investigating if it is legal
- Investigating if this move ends the game
A1: YES

Q2: Do you agree that the game SHOULD end with a legal move?
A2: YES

Q3: Do you agree that after 2-off the move ends illegally?
A3: YES

The above conversation implies that 2-off is an illegal move.......

So where do you have a disagreement? I guess it's on the question's 1 procedure that
should be according to you:
- Making a move
- Investigating if this move ends the game and then everything else stops and we have a winner
- Investigating if it is legal


Now don't you see that the second procedure is not so logical...........?!?!?!?

But it's over with an illegal move (haven't used both dice numbers). We should investigate after every move if the move played was legal or not.

If we don't do that as you suggest, someone can for example in the start of the game having a 42 to play, to take all checkers claiming that he won........

So since the move 2-off is illegal the game can't be over with an illegal way.......

I'm always serious.......!

It depends of how you define maximize......
The rule is simple without using the maximize word anyway:

If you can use both dice you should do it.

If you can use only one then you should use the higher one.

If you have a double you should use the maximum number of rolls possible. 4 or else if you can't use 4 you should use 3, or else if you can't use 3 you should use 2, or else if you can't use 2 you should use 1.....

And a tricky one:
Suppose you have a single checker remained at 2-point and your opponent has one at your 1-point and you have to play 41 for example.
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 ?

AbigailII: I don't care about any other argument i'll see, i just say that anyone who wants to play Backgammon on this site should use both dice-numbers when he can or the higher when he can use only 1 of the 2.
Every other behaviour will result to a game that is not Backgammon........
I will accept the "illegal" move, if my opponent does it, but the game then will not be Backgammon. I don't care if the Brainking rules are wrong(they are), i just would play Backgammon without care if my opponent does not......

The point: Since Brainking allows you to choose according to your personal advantage, the players who don't care if they are playing Backgammon they should do it. The players that want to play Backgammon they should not............!

Imagine a Chess bug that allows Castle when King is threatened. Then if someone would make this castle and convert the position to a good one for him, in contrast of what would happen if he wouldn't castle, then a decent Chess player would feel completely disgusted by this.........
The fact that Brainking rules are wrong and refering to a well-known game, should not mean that we should follow them forgeting what we know about this well-known game.........

grenv: ........

If your games against your mother, would consist of many early resignations or with really stupid moves that would be away from common logic, then this would be cheating.......But i'm sure this is not the case with you of cource........

Andre Faria: I didn't said that users who will be identified using the same computer would be immediately declared as cheaters, but that this would be just an indication and that these user's games should be observed to find any clues........

Hmmm, yes this is a way too, but i was thinking about detecting the internet connection of a player....
Detecting different users that have "something" in their connection with Brainking the same, such thing that they should not have the same, then this would be an indication of multiple ID's....
Only an indication because of cource members of a family could use a computer and this is perfectly normal. But then, games of these users will easily show if they are actually cheaters or different persons........

I wonder if Fencer has any "tricks" that would find all those with multiple ID's........?!?!?!? A good clearance is necessary........

Hmmmmm, OK thanks.......

Longjohn/Jameshird/DragonPope/Wayney????
WOW! I didn't know that.... I suspected to be the QWERTYGirl (OldDear now) but Wayney too?
That's why he accused me of intentionally playing slow in a Backgammon game and did it a big matter.........And now that i think about it, the behaviour was exactly the same as with QWERTYGirl(OldDear).........He is the same!

Pedro Martínez:
Where can anyone find this list you gave:
http://brainking.com/en/ArchivedGameList?u=11991&op=14225&tp=66
I mean from where on the main page i can go there.......? I can't find a link........?!?!?!?!?

I guess since a Backgammon game is a war, it's reasonable to have you on his enemies list.....:-)
So you will have to wait the war to over, for not being his enemy anymore.......

But a little more seriously what are the consequences of having you at his ememies list? If i remember correctly you can't send him a message but except this, is any other thing.........?

playBunny:
Your question was not in the post of 24 June 14:04 but 24 June 16:04.........:-)

It is the: but are you saying, George, that everyone should be deprived of the ability to offer a draw?

Well no, if some people want to offer a draw they should offer, so the feature should remain, because there are some people that want this.......
But i would never offer a draw or accept one (in the Backgammon game), even if i'm losing the game and my opponent suggest to have a draw or even if my opponent desperately wants it......It's just my pedantic nature.......:-)


WhiteTower:
BTW a draw in Anti-Backgammon might be considered, as I have experienced the utter and chaotic hopelessness of finishing such games...

I know what you mean but this is again a bad choice......We should keep our position of no-draws-in-non-draw-games and remain fantasyless.........~*~ Even if we have to play a 87.000 moves on a Anti-Backgammon game.....:-)

AbigailII:
Finally, there's a tactical element. Suppose you're in a 6 player section. Your current score is 4 out of 4, your opponent has 4 out of 4 as well. There's one other section, and it's already know there's a single winner there. Suppose you, your opponent, and the winner of the other section are all equal in stength, so you estimate a 50% chance of winning any game between any two of you. If you play for a win, you have a 25% chance of winning the tournament - 50% chance of beating the current opponent, and 50% chance of beating the other winner. But if you go for a draw, your chance of winning the tournament increases to 50%! (25% of being a solo winner, 25% of joined winner).


First and since you accept equal strength of the opponent, we must assume that the opponent should also have equal cleverness in his decisions. So he would accept the draw as then he would have more chances to win the tournament (50% instead of 25% as you said-i don't agree with the 50%-number but only with the conclusion (that he would have more chances to win)).......

So after accepting the draw both 2 players would advance to the final, so the final would have 3 players of equal strength that would take the same decisions in draw cases.

But there is one important thing also: What a tie does? Forgetting about Sonneborn-Berger criterions of ranking we have the following cases:

We assume that in the final ranking if there is a tie of 2 or 3 players, then all players win!
That means and since all players have the same smartness, they will agree all games to a draw and all be the winners with a probability of 100%! If they risk one or more games by not offering a draw or rejecting one then they would have less than 100% chance of winning. So they would all offer a draw from the beginning and their equal-generally opponents will accept and win......

But since you assume that the 50% number, is the probability of winning at the final between 2 players, by having the statement: "and 50% chance of beating the other winner.", you assume that a tie repeats the game. Having that in mind.......:

We assume that in the final ranking if there is a tie between 2 or 3 players, then all series of games are repeated.
This means that the probability a player has to win the final is 1/3 or 33.3...%
If he didn't offered a draw at the first round he would then had 50%·50% = 25% chances of winning at the final.
So the player who offered the draw to achieve better chances to win the final, was correct in his decision. The same conclusion with yours but the probability to win is 33.3...% and not 50%.


And we can find a general statement with this observation: If we have for example 2 groups of N equal players each, that would compete for the final.
Then if a specific player tries to win to advance in the final he would have (1/N)·1/(1+X) chances to win the tournament, assuming a tie repeats the games (X (0<X<=N) number of players from the other group that promoted to the final).
But if the specific player offered draw in every game and his opponents accepted and did the same to all of their games(same IQ), they would then have 1/(N+X) chances to win the tournament, assuming a tie repeats the games.
And since (1/N)·1/(1+X) < 1/(N+X) the smart players of the one group that drawn all their games will have better chances to win the tournament than they would have if they fight for having wins.....
But all these are impractical cases as there are no equal players.....

As for the r being smaller than s, in your below example, i think that this is not a good thing to happen in such a game-site as it should be s=r. And the fact is that at Braiking and specifically at Backgammon it is r=s=8 for players rated above 2100. In fact for players with more than 2100, the system is easy: "+8 -8 =0" with equal(in a +-400 range BKR points) BKR points and "+1 -16 =-14" for players with not equal(in a range more than +-400 BKR points) BKR points.......

I don't like this system at all but...........I would prefer the range factor to be smaller and the rating change to be more wild.....
For example:

A game against opponents that their BKR difference is less than or exactly 100:
A win for the "stronger" player = "+10 -10 =0"
A win for the "weaker" player = "+10 -10 =0"

A game against opponents that their BKR difference is less than or exactly 200 and more than 100:
A win for the "stronger" player = "+8 -12 =0"
A win for the "weaker" player = "+12 -8 =2"

A game against opponents that their BKR difference is less than or exactly 300 and more than 100:
A win for the "stronger" player = "+6 -12 =0"
A win for the "weaker" player = "+12 -6 =2"

and so on........

That would tend to rise the BKR average but that's not bad at all and it happens in many Chess lists........

Lacking fantasy.........??????
RYTFBE!

wayney: A weekend is coming, so 2 days are added to most people as vacation days, because most people have Sat/Sunday as their standard vacation days.....

Hrqls: Suppose you play with other 10 players the following game.
Each player plays with each other one game. So we would have 45 matches.

We have in a black bag 2 balls. One white and one black.
The game is simple. One of the 2 players, picks a ball, without being able to see the color, and if he chooses the white one he wins. If not he loses.

The first 2 of the group win 50.000$ each!
And after all the matches except one, that of player-A against player-B, we have the following ranking:

Hrqls      = 7 points / 10 games
Player-A = 7 points / 9 games
Player-B = 7 points / 9 games

And the 2 players agree to a draw and win 50.000$ each one. Perfectly fair right......?

Backgammon could be at the position of the aforementioned game......Backgammon has no draw! So the arbiter should not accept draw as a result.....

Draw at Backgammon......? That is one of the most ridiculous things that Brainking has.......
Since the game itself CANNOT be draw in any way (this can be easily proven) i completely support that players should not be able to agree on this.......

Chess offers the draw as an option for a player to offer, but that is because the game itself can be drawn by some rules (50 move rule, 3-fold repetition,...,etc).

Chess:
1 move has about 30 possible ways to play.......

Backgammon:
1 move has about 21·X possible ways to play........
This X is about 8 to 40 and depends on the position. For looking 8-plies/4-moves ahead it would need for X=35(in a simple middlegame position):
(21·35)^8 = Oh my God!
So no minimax or alpha-beta would help.........

Note:
21 is the number of different possible rolls.
X is the number of different possible plays for a single roll of the possible 21.

Walter Montego: Does the form of Backgammon that we play have anything to do about these assessments the machine spits out? Single game strategy is different than gambling for money and that's different than playing a set match. And then there's the way that I would play, just a series of games counting gammons and backgammons but no doubling cube.

I believe that the PlayBunny took into consideration, what kind was the game (single or not etc...) for making his analysis with GNUBG. The results and the suggested better moves are very different of course if the game is a single one and it even depends from the current result of the match (In a single game of course is 0-0)........

BIG BAD WOLF: I guess if i and BBW play such a long AntiBackgammon game, with our regular super-quick play, we will finish when the sun becomes a red giant............!

Damn! 550 moves????????
This is boring of fun........?

If you are obsessed of having GNUBG i can e-mail you an old but VERY STABLE version of it. It has almost the same strength (the newer one is a little stronger) but not the newest great graphics and all the fancy things! Comparing the old with new:
Old strength = 98
New strength = 100
Old total features and graphics = 12
New total features and graphics = 100

The whole package is arounf 12 MB so my e-mail will compain with a dial-up connection but if you want it, i can send it..........?!?!?!??!

I have the same problem. After 5-10 minutes and when i'm trying to maximize the window it crushes!
When i asked what is the possible cause of the problem they said: update your graphic card and get Windows XP! (I have ME)

Yes it doesn't........But some graphic cards probably don't "fit" with it......
Of course there are millions of other possible reasons that it doesn't run.......

What Windows version are you using........?
This is most probably a graphic card problem......

Did you save the games..........?
No! (I guess--All beginners with a program don't save nothing!)

I have to add that winning 12 straight 5-point matches against GNUBG in a level of more than Advanced (Expert or more) would make you the best Backgammon player on the galaxy with a huge difference from the 2nd. With few words: It's impossible!
So i guess you played with Intermediate or something like that........

<Go to SETTINGS->PLAYERS and choose Player 0 or 1 depending on where the GNUBG was playing (The other normally would say human).
Then see the Checker play what setting it has........(Expert, Advanced, Beginner.....,etc)

You won 10 5-point matches???????? WOW! Interesting...... And it says you play like a beginner? So your luck should be huge in these 10 5-point games! But this is really impossible (or very difficult) to have in at least 50 games, a huge luck........
On what level GNUBG was playing........? It offers a strong opponent at Expert, World class and above. Advanced or below is just bad (or not so good)..........

Forgeting my pedactic nature for a while and if we want this thread to stay we should stop here......:-)

But on the other way.........:
This defines "centimetre" as a unit name that has a prefix. It doesn't fall into a distinct "prefix-unit" class. Therefore it is treated as per 9.2.
This "therefore" is wrong. From where do you conclude that? With that logic the derived units also should be treated as per 9.2. But they are not.........

Anyway i agree that there should be a discussion board for pedantic, hmmmmm no, i mean people interested at science.......... :-)

Luke Skywalker: Hmmm in this things i'm almost always correct...........:-)
But as i see now i'm not correct or incorrect as NIST hasn't defined clearly what is happening with "prefix"-units.

So from http://physics.nist.gov/Pubs/SP811/sec09.html#9.7 :
"A derived unit is usually singular in English"

And from http://physics.nist.gov/cuu/Units/units.html :
we see that centimetre it's not a base unit, but not a derived one too, it's a "prefix"-unit if we can say that.

So what ist's the final judgement......?


Walter:
I don't said that because you have used "and" instead of "+" but because you hadn't used ( ) between the numbers.
It's wrong to say this is 5 and 1/2 meter tall.
The correct is (5 and 1/2) meter tall.
Because in the first case the meter goes to the 1/2 ONLY while 5 remains a single number and not a unit of length.........

I have to correct your correctness:
A third of a meter is not 33.33 centimeters.
It's not even 33 and 1/3 centimeters.
It is (33 + 1/3) centimeter or (33 + 1/3) centimeters (better not to use plural but it's acceptable too (if you have used the cm prefix instaed of the whole word, then the cms would not be acceptable) ..........

I agree......But it doesn't matter.....

JamesHird:
If he is actually intentionally not playing some games while playing others, Fencer should
1. Give 1st and final warning
2. Force a forfeit

I disagree in both 1) and 2).........
He has every right to play whenever he wants in whatever game he wants. He has also the right not to play at all.......

I find this a bit stupid if it's true..... I mean to delay some lost games, in order to be first for a while.......
Perhaps Fencer or anyone else has a secret prize for the 1st at Backgammon on the 1st of May. It maybe 100.000$ ............. So he knows what he is doing.......

Hmmmmm OK. I understand............!

So you mean that "it seems to us" that the BKR will increase more after a winning streak, than if we won without any streak, so we are wrong.......

But that's not what alanback says: He says that the increasement WITH a winning streak is higher than that of without any winning streak.......
While you say that if you win 5 games in a row (=8+8+8+8+8) then you will have (obviously) more points than 4 wins and 1 lose (=8+8+8+8-8). But this is not what we are saying here..........

But the individual adjustments is the BKR itself! So after you complete a winning strike you have a bonus......?
And what are all these 8's mean.......?

Hmm OK, but i thought that the way your(our) BKR change, is based only on the current opponent's BKR and not on the "history" of the previous opponents you played......
Fencer can you verify that a winning strike increases the normal BKR's increasement of a win......?

wayney: (Still mad about me (because i didn't play quick our game).....?)
I don't support that! I support that i'm at the same level with the best players.........Not above or below........
Perhaps i'm wrong of course......

alanback OK lets suppose what you said is true. But why? The rating page Braiking supposedly based, doesn't give any bonus for winning streaks.....So what is happening it's a mystery..........