Having recently read a number of analyses (from various sources) of allegedly "too good and not good enough" positions, I've noticed two common mistakes that I think can be readily corrected by a bit of clear thinking. Let me try to explain.
As I mentioned in a recent thread, when one contemplates a doubling decision, one should contemplate both market losers and market freezers. The latter refers to sequences of two rolls that produce a "no double" position, and therefore measure the potential loss from doubling. (Market losers, of course, measure the potential gain from doubling.)
A position can be a "no double" for two different reasons; you can be not good enough (the equity of ND is less than that of D/P but greater than that of D/T) or you can be too good (the equity of ND is greater than that of D/P). In some positions, there are market freezers of both types; that is, some pairs of rolls leave you not good enough, and some pairs of rolls leave you too good. (This can happen even in money play.)
This observation leads to the first of the common mistakes I mentioned above. The mistake is to jump to the conclusion that if a position has market freezers of both types, then it's (very likely to be) ND. After all, the reasoning goes, if my best rolls and my worst rolls are both market freezers, then surely I have no reason to double? But this is exactly the opposite error of the error I complained about in the other thread, namely the error of considering only market losers when deciding whether to double. In reality, both halves of the balance sheet need to be considered in a doubling decision.
For the second mistake, let's take a recent post by Stick as an example.
The score (after 0 games) is: gnubg 2, tchow 3 (match to 5 points)
tchow on roll, cube decision?
| gnubg | 127 |
|---|---|
| |
| tchow | 77 |
Position ID: bdsAgA3F7xsAAA Match ID: cAmgACAAGAAA | |
In the above position, we note that there are some bad sequences for Blue that will clearly leave Blue not good enough to double next roll. What about on the positive side? We note that Blue has decent gammon chances, and that with a moderately good pair of rolls, Blue will still have decent gammon chances (maybe even slightly better gammon chances). Here is the second mistake: to confuse decent gammon chances with being too good. It's true that ATS, by doubling I make my gammon wins worthless, but that doesn't mean that my good rolls are market freezers (i.e., that I lose something by doubling) unless I'm actually too good afterwards. To be too good afterwards I have to have really good gammon chances, especially since I have a considerable number of bad rolls, since those tend to drag down my equity. It's quite possible that the pairs of rolls that slightly improve my situation are simply market losers that result in D/P next turn.
Of course, these general observations don't actually tell us what the correct cube decision for this particular position is. But it does show that if we want to argue that doubling is a mistake, it is not enough to simply note that we have some market freezers that leave us not good enough, plus we have many rolls that preserve decent gammon chances.
Finally, let me say that I don't much like the term "too good and not good enough," partly because it tends to lead to errors like the ones described above. When describing a specific position, I would say either that it's too good or that it's not good enough, and not both. When describing potential pairs of rolls, I'd rather say that there are market freezers of both types, or that there are both good and bad market freezers.