This Too Shall Pass

 

Sometimes the brain and the mouth are in opposition. Four years ago I made it to the final five at the Blackjack Ball, winner to be crowned King of Blackjack. The first challenge was to count down several decks, with two cards removed, and state the count, and what it meant, e.g. “Plus one, with a high card and a zero-value card.” The second part was a formality, in case someone was using a count with different point values than the counts others used. Except I said: “Plus one, with a low card and a zero-value card.”

“Don’t you mean that the other way, a high card and zero-value?” several asked. No, I was sticking to my guns. I knew what I meant, and the fact that what I said didn’t match mattered not to me. (There was quite a bit of Champagne involved.) And so I was not part of the final four.

 

Last week I was commenting, with Joe Urso, on the finals of the Michigan tournament, an eleven-point match between Marty Storer and Nick Murtos. Commenting is harder than it sounds. You have to talk when, quite often, you should be thinking.

The score is tied 4-4 to 11, and Marty redoubled. Nick thought long and hard, while I commented that his cubeless takepoint was about twenty-six percent, and it seemed to me White had “twenty-eight or twenty-nine percent.” Later, I realized I had made two errors, one leading to the other, and White’s chances were less than twenty-seven percent. How much less I didn’t check. But my friend Edward Onny did. As he is likely not the only one looking it up, I thought I would correct the record by writing this.

White’s chances are considerably less than twenty-seven percent, around twenty-four percent in fact. If the cube were fully live, White could take with as little as twenty percent, but here most cubes for White come after Black rolls non-doubles, and White rolls a big set the first or second time around. Only parlays where both sides start with double-ones lead to somewhat efficient cubes. White must pass, though taking is a small error.

It was double-ones which led me astray. For some reason I was seeing them as giving White full value, while practically destroying Black. Actually, there isn’t that much difference.

 

Both players miss on ones, and after two big numbers, White is ahead only because 11 bears off two men on the deuce, whereas it misses for Black’s one on the three and one on the two. Black’s worst parlay not involving a 21, is to end up with two men on the 3pt, whereas the same set of rolls for White leaves a man on the three and man on the two.

 

Meanwhile, both players waste on deuces, but having hallucinated that the difference in double-aces was a big gain for White, I then inverted the value of missed doubles.

 

 

 

A pure three-roll versus three-roll bearoff (six men on the ace versus six on the ace) is worth 21.22% to the taker. The above position is pure for White, impure for Black. Black does not profit from 11 or 22. This brings White’s chances up to 25.6%, an easy take at money, though a tiny pass at the score, as the cube is worthless.

 

 

White gained 4.39% when Black was spread and he was pure. On that basis you might guess that when the situation is reversed he’d lose 4.39%, and would have 16.83% winning chances. In fact, his chances are only 15.33%. The doubling side usually has three chances to roll, but the taker only has two.

 

Had I not been wrong to begin with, there was room for a different, interesting discussion. There is the Fish Factor. I don’t know Nick’s error rate, but Marty has one of lowest in the world, averaging under 3.0 in the BMAB ratings. Almost everyone playing Marty should consider him the stronger player. When and how to apply the Fish Factor when the game is complicated is often debated, but here there is no need for discussion. These are precisely the sorts of positions the Fish Factor is made for.  According to the table for 50-point rating differences found in Can a Fish Taste Twice As Good? (Available from the lovely Carol Joy Cole at better backgammon tournaments everywhere.) the takepoint for a redouble to four at seven-away, seven-away is 23.45%. That’s the cubeless figure, around 2.5% lower than for evenly matched players. The higher the level of the cube, the more it matters. If a 50-point Elo rating is worth about 1.5 PR, and Marty is playing at under 3.0, anyone not averaging under 4.5 is kidding themselves that this is a take.

Actually, it is even clearer than that. An XG rollout found the position to be a 1.025 pass, or not so far from a coin flip. That’s because there is some value to owning the cube. For the weaker player, the value of owning the cube, and potential to send it at eight, is even greater. The bottom line: Unless your name is Mochy, you should take this cube.