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Cube action ATS?

Posted By: Daniel Murphy
Date: Tuesday, 17 September 2013, at 7:14 p.m.

In Response To: Cube action ATS? (HOMINID)

You ought not to shy from defending your "heresy," since much of what you say immediately above is valid, minus the ad "hominem," which you have no basis for making. I agree that, often, "Even a sloppy system is far better than none." But no "sloppy" system "is never far from the truth," some sloppy systems are not better than none, and some sloppy system can't be applied at all to many backgammon problems.

Experience and intuition are important, approximate approaches to precise decision making does often work and is what we use most of the time. But not all match problems can be solved by dismissing match equity tables and game winning probabilities as the "domain of the nerds," as you put it. Good backgammon play requires some facility with arithmetic. That's a fact. But another fact is that most of the arithmetic required is not difficult. It is well within the reach of nearly any aspiring intermediate player. It's not right that you dismiss all that as a tool that only nerds, geeks and superplayers are capable of understanding.

In John's problem, your sloppy system had three points:

1. You only win 60% of the time.

That was wrong. You say that was an intentional simplification. I don't get the argument that 3/5 is an easier fraction to deal with than 2/3.

2. If you redouble to 4 the game will always end with the cube on 8.

That was also wrong.

3. Leading 4-0/7, you're better off not doubling, hoping to lead 6-0/7 after a favorable sequence, rather than doubling now and "leaving the outcome to the vageries of the dice."

That is awful advice. There's hardly any content in it that can be rationally applied to the problem — which was: what cube action should White take now given this precise score, the cube value and game winning chances? But all you're saying is: be more cautious with a big match lead. That's true enough, but it's not very quantitative, is it? And in my experience, a very common fault of intermediate players is that they become extremely cautious with cube decisions when they have large match leads. They make huge blunders by not doubling absolutely clear doubles, or by passing absolutely clear takes, all to avoid letting the match be decided now instead of later. And perhaps that is because, without any math and match equity tables, it's impossible to apply the "be more cautious" guideline with any accuracy.

Play and cube problems can be solved in different ways. We can use increasingly accurate methods to identify essential problem elements that must be accounted for in order to arrive at reasonable decisions.

I have, for example, a sometime social opponent who is extremely averse to making any sort of calculation. Fine, then. Won't count pips? Then count crossovers. Or rolls. But without some minimal effort to refine our analysis, we're left with looking at the position and guessing who's ahead. And the guesses, frankly, are often atrociously wrong.

As another example, the so-called "PRAT" system encourages students to identifying particular facets of positions in terms of positional advantages, racing leads and offensive threats. That's great. That's a lot better than guessing. And formulaic "If I lead in two of three categories, then ..." guidelines work more often than not.

But no-math methods are not always enough. I'm not even sure if you're sure of the point you seem to want to argue. Let me remind you of your opening statement:

To answer this question with confidence one needs to calculate the game winning chances then compare it to the MWC equity table, the domain of the nerds. [emph. added]

And that — there's no getting around it — is true. This problem cannot be solved without knowing the MET, being able to estimate GWC, and being able to manipulate those figures to determine the correct cube decision.

From the MET, you have to know that 6-0/7 = 91% ME, 4-2/7 = 65% ME and 4-4/7 = 50% (and that's all). Then you have to be able see that White misses exactly 12 times and loses all those games regardless of cube position, and be able to see that White hits exactly 24 times, winning all of them if he owns the cube and losing some — 1 out of 24 is a good estimate — if he has redoubled to 4.

Then, what a player can comfortably do over the board with that information will vary. Contrary to your jibe, I'm not tied to "decimal" precision. Backgammon math can be done with decimal numbers, fractions and percentages, and combinations of them. Whatever a player is comfortable with, the more practice a player gives himself with simple number problems the better he will become at doing them quickly.

One way to solve the problem is this:

1. If I don't double, I hit and cash 24 times for 91% ME and lose 12 times with the cube on 2 for 65% ME (we'll ignore gammons, since they don't amount to nearly as much as 1 time in 12).

91% of 24 is approximately 21.6. 65% of 12 is approximately 7.8. 21.6 plus 7.8 = 29.4.

Remember that number.

2. If I do double to four, I lose 1 game and the match with the cube on 8. I win the game and the match 23 times, and 12 times the match is tied. This gives us 100% of 23, plus 50% of 12. That's 23 + 6 = 29.

3. 29.4 is more than 29, so the correct cube action is No Double.

Was that hard? I don't think so. The hardest part is keeping more than three numbers in one's head at a time.

John solved the problem differently, basically this:

1. We win 24/36 of the time holding the cube, 23/36 of time if we redouble. 23/36 = ~64%.

2. Redoubling gains 9% when we win.

3. If we redouble, our 13 losses cost us (12 * 15%) + (1 * 65%) ME. (12*15) + 65 = 245. 245/13 = 19%. That's our risk.

4. R/(R+G) = 19/(19+9) = 19/28 = 68%. That's our doubling point.

5. 68% is more than 64%, so the correct cube action is no double.

I have no doubt that John can do such calculations over a board in a reasonable amount of time. I'm sure most players could do the same if they were inclined to learn a MET and practice simple addition and division. Some players are not so inclined. But please, let us not spread the falsehood that such methods are only possible for a handful of great brains. That's not true.

And yes, let's acknowledge that number-free analysis is of great help in solving a vast number of problems, and encourage players to make use of the analytical skills they do have as they improve upon them. But let's not spread the falsehood that backgammon math can simply be done without. No-number backgammon can take one very far, but it's not enough. And some problems, like John's here, just can't be solved without it.

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