by Jake Jacobs
10 April 2009

Last Christmas was the first time my daughter was aware of Christmas as something special. She's been going to school in Pattaya, but when she and Ta arrived here in Singapore she couldn't go to sleep before seeing a "Kwissmas twee." (Yes, kids do talk like that, just like in the funny papers.) I explained several times about Santa, I hung up stockings, and, on Christmas Eve put out milk and cookies because "Santa needs quick energy; he's got a long drive."
After she went to sleep I snuck the presents from their hiding place and grouped them under the tree, then carefully ate two and a half of the three cookies, and poured out most of the milk. (I hate milk.) In the morning I woke them up: "Hurry! Come look! Look: the milk and cookies are gone! Who ate those? Look: there are Christmas crackers in the stockings! Look: there is a lump of coal in Uncle Charlie's stocking – see what happens to bad boys and girls? Look: presents under the tree..." She finally got it; she understood Christmas.
That night she went to the fridge. "What are you doing, honey?" She got a plate, put some cookies on it, poured a glass of milk... I hate it when kids are smarter than I am!
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Article text Copyright © 1999-2010 Jake Jacobs and GammonVillage Inc.
I don't believe you should be able to drop a beaver even though Tom Keith's site says that you can. A beaver is not an offer rather it is a statement that the player beavering believes the original double to have been very wrong.
Dear Mr. P:
And an initial double is not an offer, it is a statement that the player doubling believes the other has an unfavorable position.
Imagine this extreme situation. You are visiting a distant city, Ouagadougou perhaps, one that you surely will never return to after departing tomorrow. You visit the local backgammon club, and the very first game find yourself on roll with this bearoff: 111111 vs 111111. It is a perfect 3-roll versus 3-roll bearoff. You own the cube at 256 so you check your pocket and find that (having converted all of your funds from USD) you have about XOF 550,000. Playing for XOF 1000 a point, even if your opponent takes what should be a clear drop, and rolls a double to win, you will have enough left to taxi to the airport in the morning.
So, you redouble, and your opponent shocks you by not just taking, but beavering.
You do a quick reassessment, and discover that the African moonlight has played havoc with your depth perception. It seems that instead of three stacks of two checkers each, one of your stacks has a third checker, and you have thus doubled a 4-roll versus 3-roll position. As doubles go you do not have enough equity to take. And even worse, you do not have the funds to pay if you lose this 1024 cube.
Though you speak nearly sixty of the languages of Burkina Faso Moba is not one of them. Do you still plan to take and rely upon a semantic argument if you lose?
Best,
Jake
I disagree completely. If you make a very bad double when beavers are operative, you should be playing with the cube on 4 as a punishment for the bad double. If you want to bail-out, you should think harder before making the double.
Dear Mr. P:
Should you find yourself in hot water in Ouagadougou, I shall admire your adherence to principles, and will lead the Backgammon community in a memorial toast.
Best,
Jake
hi all, interesiting positiions jake, thank you. i rolled the position out of your match with neil (the 5th in this article)out as a money game position. i used gnu and the result was this: WHITE owns 2-cube: 0.745 0.032 0.000 - 0.255 0.059 0.001 CL +0.463 CF +0.670 BLACK owns 4-cube: 0.769 0.045 0.001 - 0.231 0.065 0.001 CL +1.037 CF +0.933 Full cubeful rollout with var.redn. 1296 games, Mersenne Twister dice gen. with seed 818931132 and quasi-random dice
the good news is gnu confirmed the take by about 0.07 points (on a 1-cube). and now comes my question: how can white win more games and more gammons after giving the cube compared to the times he doesn't redouble?!? by the way i have seen similar things for other positions, too! so it is not specific to this position only. has anyone a sensible explanation for this?!
Yet another example of Neil's expertise, and your writing ability.
Ray appears to have been a pretty good player, but not a GREAT one, he should have doubled the bozo (s) who was ready to pass.
Hi Pfau:
I'm not a Gnuser, so I am not sure what the problem is, but clearly those numbers don't make sense.
Hi Coolrey:
Ray got better with age. ;-)
Best,
Jake
Relative to the very first position in your article, I think the following is most interesting:
1. I did not make up that position...it happened in an actual on-line match I was playing last year; 2. When I put that position in Snowie and played it out, from either side, I initially found my error rate was extemely high. I also found that Snowie played the checkers, from both sides, in a manner most surprising to me. After playing it out many times I realized that Snowie truly did know how to play this kind of position far better than I, and the lessons I learned from this one position have greatly changed my who approach to positions of this nature. Now, if I could only figure out how to get into this position more often, I know I would have a huge edge over most opponents!
Relative to being able to drop a beaver, it is obvious that the bots agree with you. If you give a bad double to GNU or Snowie and it beavers, it does not just beaver and take the cube, it "offers" you the beaver and gives you the option to accept it or drop it. So if the bots say it, even Mr. Pedantic can't argue with that!
Another argument for thinking of the beaver as an offer is this...the doubler has a third option in many games, he can Raccoon. And of course, we now need to discuss whether a Raccoon can be dropped!
Phil
Well Phil, Mr Pedantic can argue with that. Just because a developer programs in one way does not make this way correct. In addition, your facts are incorrect. When Snowie beavers, it does not give you the option to drop. :- )
My mistake about Snowie, but I did check GNU and eXtreme backgammon, and they both give you the opportunity to drop the beaver; eXtreme even gives you the opportunity to Raccoon.
OK, so here's another way of saying what you said: if all other cube actions can either be accepted or rejected, it stands to reason that beavers and raccoons can also. An even stronger argument: if an actual beaver came to my house for dinner, I should certainly have the right to accept or reject it...beaver discrimination is not protected as far as I know.
Pfau (15 Apr 2009),
74.5% and 76.9% are gnu's estimate of white's winning chances if the game is played out to completion. However, these estimates can be different (and/or inaccurate) for at least two reasons:
1. GNU makes checker plays based on the position of the cube. The starting cube position is different in the two rollouts, which may result in different checker plays. The first rollout (74.5% wins) assumes that white starts by NOT doubling. The second rollout (76.9% wins) assumes that white starts by doubling (with black taking).
2. In its rollout games, GNU truncates (ends) the game whenever the game results in a double/pass. It uses its final evaluation (at the point the game ended) to estimate the position's win percentage. It may be the case that this estimate is frequently inaccurate. E.g. it may be the case that in the first rollout the game often evolves into a position which is a double/pass (according to GNU) with GNU often underestimating white's winning chances at the double/pass moment. Note that the winning percentage for the second rollout (76.9%) is probably fairly accurate since most games will be played to conclusion (due to black starting with the cube).
Chris
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