It seems to me that the condition of being too good to double is (primarily) a balance between one's winning chances and one's gammon chances. There are cases where your winning chances are overwhelming, yet a low likelihood of gammons makes it incorrect to play on; you should double (or redouble) immediately and take what's on the table. Conversely, there are other cases where your winning chances may be less than overwhelming, yet a high likelihood of gammons makes it correct to play on for those gammons.

So, in evaluating the condition of being too good to double, is there a recognized rule of thumb or even a weighted average that one might employ in measuring the relative balance between winning chances and gammon chances? Reading recommendations would also be welcome.

Yes, but focus on your losing chances relative to your gammon chances. For money, double if your gammon chance is less than double your chance of losing (assuming it’s a pass). Here’s why:

Assume money play and your opponent would pass a double. Assume you own a 2 cube (this is only to make calculations; the result isn’t affected by the cube value). The safe play is to double — you win 2. By playing on you risk 4 points for a loss (-2 vs +2), gain 2 for a gammon (4 vs 2), and break even for a single win. We e can ignore single wins then since they don’t affect our result and focus on gammons and losses. If we lose X% that means we lose 4x points for every 100 games. We need to win 4x points when we win gammons to break even. Since each gammon is worth 2, we need 2x gammons per 100 games, or twice the percent losses.

This only applies to money games. In match play there is a score dependent value called gammon price or gammon value. As shown above the gammon value is 2 for money play. For matches, it varies according to score. Some scores are gammon go, meaning the gammon value is <2 — you should risk more losses than normal to win gammons. Conversely other scores have gammon value >2 meaning you should be more cautious and less willing to risk losing to win gammon. As an extreme example, if you need 1 point to win the match, you should risk nothing to win gammon; gammons are worthless. Of course you wouldn’t double in that case, but it’s still a consideration for checker play.

You have my head reeling, stremba70, but I got exactly what I asked for - a rule of thumb:

I read this as being equivalent to:

>>For money, you are too good to double if your gammon chances are better than twice your chance of losing.

For example, if you feel that you're an 85% favorite to win a money game, then your gammon chances need to be better than 30% (twice your chance of losing) to warrant playing on for gammon.

As a useful rule of thumb, this could hardly be nicer, and your well-presented justification seems unassailable from a mathematical standpoint. I also appreciate your added perspective on match play. I wasn't familiar with the concepts of "gammon go" or "gammon price," and when I looked them up in the Backgammon Galore! glossary at bkgm.com, I found links to articles on these ideas for further reading. So your post has been extremely helpful in a number of ways. Thank you so much for taking the time!

No problem and your understanding is exactly right. If you lose 15%, you need 30% gammon wins to make playing on break even. More than 30% gammons means too good, less than 30% would be double/pass.

So in one of the articles I referred to on bkgm.com (https://bkgm.com/rgb/rgb.cgi?view+125), author David Montgomery writes:

>> In money play, this simplifies to checking whether your excess gammons (your gammons minus your opponent's) are at least twice your losing chances.

This is a stricter condition to meet than the one you outline, as these so-called "excess" gammons are generally a proper subset of one's gammons. Moreover, the evaluation is more complex since it includes your opponent's gammon chances as well as your own. To add to the difficulty, your opponent's gammon chances would seem a distant forecast given his (currently) weak position.

Needless to say, I hope *your* model is the correct one!

Yes I was simplifying by assuming I could not lose a gammon. This is not really a horrible assumption since your opponent’s gammon chances are typically low in a cash vs play on position. It also ignored the possibility of backgammons. This is also a small possibility typically, though. Unless you have an unusual ability to compute probabilities, you can probably safely ignore both of those as a practical matter. It’s not likely you can compute your losing and gammon chances with enough accuracy that these factors would affect your cube decisions

My feelings exactly - thanks again!