At times I regret the day I decided to teach Barry Fisk how to play backgammon. It is not like he is the stupidest guy ever alive, but when it comes to backgammon he seems to have a blind spot. We have played weekly sessions for a few years, and by now I guess nobody has learnt more about backgammon than Barry without being able to apply it to the game. I am not giving up though, and I have even made a promise for the new millennium to stop shouting at him.

Last night the following position came up, Barry playing blue, cube centered on 4 after two auto-doubles:

153 148

White money game Blue

First of all, lest you start thinking I'm a shark, let me point out that it is Barry that insists on using unlimited auto-doubles. He claims that as the weaker player he benefits from the increased volatility. I've tried to explain that he is getting his concepts mixed up and that the auto-double is just equivalent to playing for 1.25 times the original stakes, but he kept getting lost when I evaluated the infinte sum 1 + 1/6 + 2/36 + 4/216 + 8/1296 ...

Back to the position, Barry immediately handed me the 8-cube which I turned back to 4 and replaced in its centered position. Barry looked truly astonished: "Drop? What drop? If this is a drop then I know nothing about backgammon!"

"No, no, no. No drop," I said, calmly, not shouting and resisting the temptation to comment on Barry's last statement, "I am not dropping - you are not doubling. Why would you want to double here?".

"Well, for starters you might drop. You always say that if it might be a drop, then it is a double."

"So true," I said (see, it is not that Barry doesn't learn, it is just that he consistently fail to apply his knowledge), "yet, you yourself  were sure that it was correct to take this, so then you should assume that your opponent is, too."

"But, I might be wrong," Barry insisted.

"So true," I said, "and everybody makes mistakes. Still our own evaluations are the best available, and playing against them can only makes things worse." ("Except maybe in your case," I thought to myself, but I didn't say it, and I didn't shout either.)

Barry looked at the table a few moments. "I've got several market losers here."

"Some," I answered, "not many. And very few big ones. The small ones don't count, remember. It is only when you lose your market by much that you are really unhappy not to have doubled."

"But surely, with the Jacoby rule I must double to activate my gammons."

"Surely not," I said, not shouting, "I have yet to see an early game position where you are good enough to double only because of the Jacoby rule. The only cases where you lose equity to the Jacoby rule are when you suddenly find yourself good enough to play for the gammon. Now if your position is not good enough to double without Jacoby, then usually it does not have many big market losers. In particular it does not have many sequences that overshoot both the double/take and double/drop regions and leave you too good to double. And the ones that do are not likely to be too good by very much, you see where I'm heading?"

"No."

"I'm saying that even if it is true that an undoubled position may be worth less with Jacoby than without, the difference is likely to be small and make little difference for the doubling decision. Assume you had 6 knockout numbers, which again would leave you too good to double half of the time, and say that your equity after these were on average a big 1.2. Now that is something you won't see too often in a position that is not a double without Jacoby. Surely you're far from it here and now. Yet even in that position the Jacoby rule would still only subtract 1/6 * 1/2 * .200 equity, that is 0.017 which might make a difference but probably would not. You got that?"

"No."

"Well, never mind, the message is: Just don't take the Jacoby rule into consideration when deciding on the double."

"OK," Barry said, "but I still think I should double, as I am probably the weaker player."

"No, no, no, no, no," I did not shout, "this is not match play. In money play it is the other way around. See, the doubling points and cashing points depend on your chances to win the game. If you're the weaker player you need a better position to acquire sufficient winning chances to double, and against a weaker player the better player can take positions that are theoretical drops. And vice versa when you get doubled, against a better player you should drop some positions that are theoretical takes, because it is not enough that it is possible to win 1 out of 4 games, you also have to be able to bring it about."

"OK. OK. So I'm rolling then."

Shake, rattle and roll.

55.

10/5*(2) 9/4*(2).

162 128

White money game Blue

Shake, rattle and roll.

16.

bar/24, forced.

161 128

White money game Blue

Shake, rattle and roll.

21.

22/20 2/1*.

162 125

White money game Blue

"Now what was that?" I asked amazed. And amazed at the fact that Barry still is able to amaze me.

"Well, I thought that if I could close you out ..." Barry started.

"No, no, no, no, no, not the move. The cube. Or rather the no cube. What was that about? You cannot possibly be playing for gammon with the Jacoby rule?"

"But, well, eh, you know, you just said that I shouldn't worry about the Jacoby rule," Barry said sheepishly, "but, yeah, no, that doesn't apply here, does it? Got me there for a second, haha. And, also I thought that doubling now was very inefficient, if I waited I could perhaps get a more efficient cube."

"Yes, right, and maybe even gain your market?"

"Yes!" Barry's face was lighting up noticably.

"Barry, Barry, Barry! To every thing there is a season. Right now this position is worth 4 points to you. Also, no matter what happens, by dropping I can make sure that you don't get more than 4 points. So what good can possibly come from not doubling? Nothing, that's what, Barry!"

Shake, rattle and roll.

11.

bar/24(2) 6/5(2).

158 154

White money game Blue

"See," I said, then added: "What? Double? Barry? Anybody home?" Almost shouting. But just almost. Barry had placed a big 8 on the table.

"Well, I'm not making the same mistake twice"

"No, you do seem to find new ones. Barry, you cannot double because you had a good position. What is gone is gone. Yes, you should have doubled. Then. But not now."

Silence for a while

"But you are thinking about and it, and you always say that if you have to think twice about the take, then ..."

"The beaver," I said, "not the take. I'm thinking about the beaver. Not the take. And now, I'm not thinking about the beaver anymore. I'm beavering".

Turning to 16.

Turning to 32.

"If it's a double, it must be a raccoon right?"

"Right. Only, this is not a double, Barry, it's a beaver."

"It could be both a double and a beaver."

"Yes, there actually is such a position, but no, this is not it"

"Anyway, my dice are hot tonight, and I'm on plus, plenty ..."

"That has got nothing to do with anything, and you know it, Barry! Dice don't remember! And money play scores are irrelevant until it's time to pay up! Now shut up and play!"

"I might roll 44, that might be a market loser."

"Shut up and play, or I will start shouting!".

Shake, rattle and roll.

44.

Move, shake, roll, dance, shake, roll, move, shake, roll, dance, etc., etc., etc., gammon.

"Wow, that's a big 64 to go with my 28, I'm up by 92, good golly!"

"BARRY! I KNOW!!!"

At times I regret the day I decided to teach Barry Fisk how to play backgammon.