Those of you who read the comments will have seen Timothy Chow's comment on the last post. I reproduce it here for those who didn't. Thanks Timothy, but I fundamentally disagree with you. Here's why.
"There is one reason you may not want to double at 4a2a as aggressively as the bot says you should. A lot of positions that the bot drops at this score will be easy money takes and therefore will be taken by many players. If your opponent is likely to take next turn even though it is technically a drop, then you can't actually lose your market."
This is worth looking at more closely. The examples that I gave are not early doubles in the sense that they are technically wrong, they are correct doubles and to wait a turn loses equity. If we wait until there has been a market losing sequence and yet our opponent incorrectly takes, we don't gain anything. It's the same game with the cube in the same place as it would have been when we doubled correctly earlier. In order to reach that point we have to make one or more cube errors and then rely on our opponent to make a mistake in order to avoid losing equity by losing our market!
Lastgamephobia afflicts both doublers and takers. If you open with a 3-1 and the opponent rolls a lemon, 6-3 say, then believe me you can and do get wrong passes by correctly doubling immediately. At this score, lastgamephobia sufferers also get sudden attacks of gammonphobia. You can't gain by missing a correct double at this score, only lose.
Traditional cube play technique was to try and double as close to the point where a take becomes a pass as possible. There are several drawbacks to this.
First, it requires very precise judgment to identify when you have reached this point and balance it against market losers. Doubling at the first correct point is a lot easier to spot, because you only need to be in the ballpark.
Second, you almost always have to miss several correct doubles to get to that point. Doubling early means that you might make a mistake when you double, but it will be the only one that you make in that game.
Thirdly, if you double at what was traditionally considered the optimum point, i.e. at the place where you gain a theoretical point by getting a take or an actual point when the opponent passes, it isn't then possible for the opponent to make a mistake! She loses a point either way. Doubling early allows her to make a big mistake by wrongly passing.
The bots, who play better than humans 24/7, double early. The very best players and there are a few who consider a PR in excess of 2 to be playing badly, double like the bots do. We have nothing to lose and everything to gain by trying to emulate them. In the process, we will certainly make matches shorter, but dont be afraid of that. It's a game of aggression. Make aggressive doubles and reap the rewards.
Enjoy the game!