Bearing Off

[diane]

This was my conclusion in this situation too - the 'dreaded' next 22 roll being the prime example - it makes absolutely no difference!!  However, I do take the point that there are situations where not bearing off is better - but someone once told me Kit Woolsey uses greedy bearoffs, since the difference is too minimal to matter.  I am running with that...    

[Hardy_whv]

A pair of 2s is not the example snowjake asked for, it rather makes both moves equivalent ...

I am confident in the computer's numbers, so there must be a mysterious sequence of rolls ...

I've never been talking about a double 2 (representing moving a 2 FOUR times), but two single 2s. Try that. After smoothing, you are able to bear off two checkers with two 2s. After bearing off with 2/0 you can not bear off a single checker with a 2. So after rolling a 2 two times (not talking about double 2s), you are better off one whole roll after smothing. Just count the remaining checkers for both cases.

Don't look for any other "mysterious" sequences, it's the 2s that count here.

Btw, theres a nice article about smooting play at Gammon Village by Walter Trice. Perhaps he has more convincing power than I do: http://www.gammonvillage.com/backgammon/ne...resourceid=4279 (only for GV members).

Hardy ;-)

[Hardy_whv]

... the 'dreaded' next 22 ...

Well, as said in my last post, I never talked about a 22, but about two single 2s.

Trice mentions 259 positions, in which it is correct to smooth instead of bearinf off. Those positions usually look a bit weird, as they consist of stacks and gaps (or possible future gaps). So as long as your position looks "normal", well distributed, greedy bearoff is okay. But if your positions looks a bit stacked, you might consider to not use greedy.

Btw, the 259 positions consist of
- 88 positions, where it's correct to smooth with a 2,
- 121 posision, where smoothing with a 3 is correct and
- 50 positions, where smoothing is correct with a 4.

It's never correct to smooth with a 1 or a 5.

... but someone once told me Kit Woolsey uses greedy bearoffs, since the difference is too minimal to matter.  I am running with that... 

Well, as most of the positions, where smoothing is better than bearing off, look a bit "weird", with stacks and gaps, I guess, that even Kit Woolsey will become alert and switch greedy off, if he faces such a position.

Hardy  

[nabla]

I've never been talking about a double 2 (representing moving a 2 FOUR times), but two single 2s. Try that. After smoothing, you are able to bear off two checkers with two 2s. After bearing off with 2/0 you can not bear off a single checker with a 2. So after rolling a 2 two times (not talking about double 2s), you are better off one whole roll after smothing. Just count the remaining checkers for both cases.

Noooo, I never talked about a double 2 either, a pair of 2s is not a double 2  

Why don't you try a second roll of say 52 ?
snowjake : plays 4/2 3/off (but certainly not 4/off 3/1??)
hardy : plays 3/off 2/off

snowjake and hardy are now in the exact same position.
If there is a second 2 at some point after that, both will probably play it in the same way (2/off) !
What difference can it make whether one plays 2/off at move 1 and 4/2 at move 2 (snowjake) or 4/2 at move 1 and 2/off at move 2 (hardy) ? You need to make snowjake miss twice in order to make him worse than you having missed deliberately in the first move.

[Hardy_whv]

I have to offer my excuses. My explanation was simply not right. At least not in the way given. I should have tried it over the board, not purely in my head.  

Still the fact is true, that smoothing is better here than bearing off. Try the following sequence for example:

62, 65, 52, 52.

After smoothing, your position is 301000 (three checkers in the one-point, one on the 3-point). After bearing off it is 500000 (five on the one-point). So after smoothing you are likely to bear off in 2 rolls (except after rolling 21), after bearing off you will require 3 more rolls.

So my feeling is, that the effect only works, after the remaining checkers on the higher points have been taken off.


Hardy .... promising to check his explanations better next time    

[nabla]

I have to offer my excuses. My explanation was simply not right. At least not in the way given. I should have tried it over the board, not purely in my head.   

Still the fact is true, that smoothing is better here than bearing off. Try the following sequence for example:

62, 65, 52, 52.

After smoothing, your position is 301000 (three checkers in the one-point, one on the 3-point). After bearing off it is 500000 (five on the one-point). So after smoothing you are likely to bear off in 2 rolls (except after rolling 21), after bearing off you will require 3 more rolls.

So my feeling is, that the effect only works, after the remaining checkers on the higher points have been taken off.


Hardy .... promising to check his explanations better next time 

Thank you, this sequence is much better, I should have found it ! First a big roll making the 4 disappear, then there are indeed two misses with the twos. Very nice example, which just needed a better explanation    

[blitzxz]

Intresting discustion. To summarize Hardy's point I would say that at least 4 condition has to be present when it is not correct to bear-off all the possible checkers.

1. Uneven number of checkers. (after you bear-off everything possible)

2. All the checkers close to home and no gaps. (so that you are almost certain to bear-off two checkers every roll.)

3. Lead in race.

4. Bad distribution if you bear-off.

All in all these situations are rare when you play correctly and even then the difference isn't big.