playBunny: If it isn't against the rules it should be.

redsales: I'd be very surprised if Pah Tum wasn't a forced win for white. I'll try to figure it out :)

playBunny: But that is because one player has fewer games played. This will only continue to happen if new players are introduced, and the low initial rating will somewhat compensate for the increase... or something like that.

Czuch Chuckers: It's indefinite, but in context it could mean a single thing.

playBunny:

BUT it's a yes/no question in the context you used it, therefore the answer is "yes". I don't think it's ambiguous (except maybe to a lawyer).

Also I've never heard anyone answer No, I have three or anything like that, unless they were trying to be funny.

Pythagoras: You have to be kidding me? Math?

I have a math degree as it turns out, but this is a question of the english language.

If you have borne of many checkers it is also true that you have borne off a checker. If I ask "Has player x has borne off a checker?" the answer to that question doesn't switch to being "No" just because I bear off a second!!!

If you want to ask about one checker you have to use the word "one". i.e. "Have you borne off one checker?". This is probably ambiguous enough to warrant the word exactly being inserted.

The use of "Else" is simple to understand and needn't be complicated by the use of set theory in my opinion. In this case there is no intersection of sets, you can't be gammoned and backgammoned at the same time.

alanback: Automatic resignations would be great!! As soon as one ending is guaranteed. Bring it on.

playBunny: If the resignation text in the application was clear:

"Your opponent offers to resign giving you 1 point. If you feel that you would rather continue and play for a gammon or backgammon you should refuse the resignation offer. If you accept the resignation you will be awarded 1 point."

or something like that.

BIG BAD WOLF: Does that mean if I play a beginner in chess I am cheating by taking advantage of his or her blunder?

Pythagoras:

Since you are being pedantic I will have to disagree with your pedantry.

If you've taken 3 men off, then you have taken a man off. No need to add words like "at least"

"and you haven't borne any off" is not needed since you would have passed the first test and not gone to the else

"if none of the 1) or 2) occurs" is implied by the use of the word "else"

BIG BAD WOLF: The advantage of being allowed to suggest the points is that it speeds up play considerably (rather than waiting to get a piece off for instance).

I know that isn't a consideration for some, but for me it is HUGE. I hate games that drag on..

.. and I can't stand it when people continue to roll when they can no longer mathematicaly win... RESIGN please and get on with the next frame.

Hrqls: What do you mean "you are not sure if you would have been gammoned" ? Of course not, it's a dice game.

There is, however, definitely a chance (probably a little under 10%) that you will be gammoned.


and yes, i agree 3&6 is better if you don't need to get out right away.

Hrqls: This was not a tough decision: Drop. If you accept you will probably lose and may get gammoned. I'd say if you played 10 games you would win once, be gammoned once and lose without being gammoned 8x.

In fact I wouldn't have doubled if I were your opponent and played for the gammon, I think his position was too good for a double.

Hrqls:

3&6: 27.8% chance of going out
4&5: 27.8% chance of going out

They are the same.

Not always the case. For instance let's say you have 7 pips left:

2&5: 52.8%
3&4: 47.2%
1&6: 41.7%

So 2&5 is much better.

pentejr: I'll never be on that list. I hate anti backgammon. How about just back, nack and hyper?

Hrqls: I would only resign if it was mathematically impossible to win. What's the point?

A famous chess player once said "Nobody ever won a game by resigning!"

playBunny: hmmm, I think I was mistaken with my 28% comment. After looking up match equity tables it seems most do say low 30s, which means the action is clear. I need to memorize them better. :)

playBunny: I think, therefore, that on balance you should never accept the double in that game because of the great chance of being gammoned.

In this case though, the gammon was irrelevant since the match would have been over anyway on a loss, and all that you need to consider is the win/loss %ages. These may be tainted by not playing for a gammon, so I suspect that the actual chances are slightly lower than 27% and the rejection of the double is correct, but not by much!!

Hrqls: That's the pure mathematical cutoff, however you do gain a slight advantage in accepting so the real number is often slightly less (depending on the match score).

In this case the 28% is your chance of winning the match after rejecting the double. In this case, because accepting basically makes this game the final one, 28% becomes the cutoff.

It seems that the chance of winning this game turned out to be 26.8% or 27.2%, so to say that it would have been a major blunder is a little harsh (unless I am missing something).

playBunny: I'm surprised it was a major blunder, what is the chance of winning the game from that position? It must be significantly 28% for it to be a blunder. What do the numbers actually mean from a statistical perspective?

Hrqls: agreed, the games won/lost is kind of irrelevant. Maybe showing both matches and games would be interesting, but matches is what should be there. I guess it's the default behaviour of the programming rather than intentional.

Hrqls: Very close call.

Your chance of winning from 19-20 down is about 28% (2 in a row is obviously 25%, but you have to factor in the chance of getting a gammon in the next game).

Your chance of winning this game is probably about 28% as well (or thereabouts), so not much you could do to improve your odds (except for hoping he doesn't double!)

Maybe someone could run it through a computer and give us the results? I think it's ok since the double is already rejected.

playBunny: i believe I just helped you already on the move I just made. The chicken was a red herring apparently.

alanback:

alanback: I meant that ignorance should be scorned. Ignorant people should be educated. Who would like to be first?

playBunny: I have no sympathy for the fools. So, for instance, their ratings should suffer from timing out in such a situation.

However I do not condone the guilty party, and propose his account be terminated and he be removed from the list.

So you were only half right, but thanks for trying.

And yes I think ignorance should absolutely be scorned, but corrected rather than looked down upon.

ColonelCrockett: hear hear, stop accepting games that you can't finish, people!

playBunny: I was being ironic, I knew it was a cheat. Each game is 3 moves or fewer.

I don't think any games should be private personally. What have people got to hide?

is this really the best backgammon player? As far as I can tell he is on top of the ratings without making a move.

http://brainking.com/en/Profile?u=4320&eg=23&p=1

alanback: That's not what I meant. I am very aware of the strategic considerations of the cube, having learned to use it about 30 years ago, but most of us can't calculate the winning %ages accurately enough to determine the difference between 49.8 and 50.2 without a computer. And it won't always happen that you get into a position that is obviously a winning one.

alanback: Thanks for clarifying, I was sure we were talking about a 6-5 game from the start, but that was a while ago. :)

Also, you don't get to 50.2% on every game, you could be losing from the start and never come back. Also, how would you know that the chance was 50.2% without a computer? The first move is easy since these roll outs are well enough known.

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.

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.

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.

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.

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: 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.

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.

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.

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.

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: There's no such thing as a draw in backgammon. It should be removed as an option in my opinion.

Czuch Chuckers: That is correct.

If you are 3-4 down and double, your opponent should refuse the double even if only slightly behind, since that is a chance to even up the game again (rather than continue the current game at a disadvantage).

Hence it is important to double before the game gets going.

How about a confirmation page that says: "Are you sure you want to leave a blot there?"

Czuch Chuckers: You can use a remote keyboard with a computer as well, and a large flat monitor is not all that expensive.
Viruses and spyware are overrated, just install some software and forget about it. I recommend using Firefox or Opera instead of IE.

playBunny: LOL. I agree!
Getting a computer that can run a browser should cost about $50 on ebay I imagine. Some ISPs are as little as $10/Mo. So I didn't consider "nothing" to be the alternative.

I really don't get webTV, sounds like more effort than it's worth.

YOu guys must be really click happy. Unlike Fencer I recommend reading at least once before clicking, twice if necessary. Unless you're running out of time for the move or something, lol.

Hrqls: Don't forget to square the hypotenuse before integrating the logarithm, otherwise you might get a result with an uncertainty an order of magnitude higher then optimal.