I’m very new to the game and struggling with the concept of wanting to double before we “lose our market”. I started off by considering a simplified case with no gammon possibilities. In this case, assuming our opponent responds to our cube correctly, it seems like our EV can never be greater than +1 point (because if double/take would result in >1 EV for us, they would just drop). So even if we wait too long to double and have very high winning chances (say >90%), I don’t see how we miss out on any EV compared to doubling earlier before we’ve “lost our market”. Can anyone help set me straight here? Is this just an artifact of my “no gammons” simplification or am I misunderstanding somewhere else? Thanks!

Scenario 1: You don't double when your opponent has a take, then you get a good sequence so your opponent has a pass, then you double and your opponent correctly passes. You win 1 point.

Scenario 2: You do double when your opponent has a take, then you get that same good sequence. You win more than 1 point on average. You're happy you doubled before you lost your market.

Your equity was < 1 when you doubled, but if it was a correct double, it went up, say from 0.7 to 0.8. It shouldn't be surprising that this can happen. I mean, you're ahead in the game, so wouldn't you win more on average if the game is worth 2 instead of 1?

Which is not to say you should double whenever you have any market losing sequences. It's just that in order to have a correct double, you need at least some chance to lose your market on the next exchange. The more frequently you lose your market, and the bigger the market loss is on average, the more argument there is for doubling when your opponent has a take.

Thanks for the input. I’m totally on board with the idea that if we *know* we are about roll a good/“market losing” sequence (as in Scenarios 1 and 2), we would have been better off if we had doubled before rather than after (because our equity could increase above 1, while losing our market caps it at 1 when it goes double/pass). But we don’t know we’re about to roll one of these sequences — that’s just one possible outcome, and the good rolls that increase our equity are balanced by bad rolls that reduce our equity (our current equity is just an average of all these possible outcomes) — right? And again, turning the cube can never increase our equity above 1 assuming our opponent correctly passes.

So to summarize, if we know we’re about to roll a good/“market losing” sequence, then absolutely, we miss out by not doubling before it happens. But since we don’t know that, and doubling can never increase our equity above 1, I’m struggling to see how we lose *on average* when we wait and lose our market.

Again, thanks for the input — I’m maybe being a little deliberately obtuse/difficult but I really am trying to work through this.

http://www.gammonlife.com/06money3.htm

You have a position where you have a correct double so there a lot of market losing sequences.

The average of all possible outcomes is higher if the cube is at 2 than if the cube is at 1.

If the cube is at 1, the possible outcomes include a lot of sequences that end up with you winning 1.0. If the cube is at 2, then those sequences can have equity 1.4, 1.02, etc.

Your good sequences aren't balanced by your bad sequences. If you're a solid favorite in the position, you have many more good sequences than bad sequences, hence doubling will show a bigger profit than not doubling.

Right, that's missing from my explanation and probably speaks better to what OP is confused about.

In order to really see the imbalance in action, it might help to think about a specific example -- you have 2 checkers on your 2 point, your opponent has 2 on his 1 point. It's your last chance to double, on the next sequence you either win the game (i.e. lose your market big) or lose the game. You're a 70+% favorite, surely you want to double the value of the game now in order to maximize your expected win even though you're doubling the loss on your bad sequences as well.

I see. I think I was just misunderstanding the reason why people say losing your market is bad. The concern isn’t that we hit a very good roll and our EV goes down — it just doesn’t increase as much as it could have if we had doubled earlier. If we have 70% win chances, don’t double, hit a “market loser” that increases our win chances to 80% and it goes double/pass, our EV still went up (from 0.4 to 1). It’s just that it didn’t go up as much as it could have if we doubled at 70% win chances then hit our good roll (where it could have gone from 0.4 to >1). So our good roll didn’t cost us EV, we just didn’t cash in as much as we could have. Does that sound right?

One more thought: I'm reminded of the concept of betting thinly for value in poker. e.g., if you never bet the river except with very strong hands, you'll still win all those pots where it goes check/check and you have the best hand. You don't lose money by not betting your strong-but-not-extremely-strong hands -- you just won't win as much as someone value betting more often. Similarly, if you always wait to double until you have the game locked up and it always goes double/pass, you'll still win a bunch of points (1 per game). But you won't win as many on average as someone who doubles when the opponent still has a take (even though they'll occasionally double and lose 2 points). And because you're winning all of those double/pass games it's probably not even apparent that you're missing out on "value". I'm sure this is obvious to you guys but it was an interesting connection for me at least.

That's exactly correct.