In money play under the fully live (continuous) model, I would never have any reason to double before my cashpoint of 80%, and so this is the lowest point at which I should ever offer a double. Using this logic, I would have assumed that the double point in matches is also equal to my fully live cashpoint, but this is not the case.
I'm not sure precisely which point is being missed, but I think it's either one or both of two points.
First, the continuous model assumes that equity changes incrementally, and therefore your game winning chance never goes over 80% without you having had an opportunity to double precisely at 80%. And the same assumption applies to your opponent's redouble, after your redouble/take.
That assumption is unrealistic in actual money games, and in matches. In an actual money game, your cash point (your opponent's take point) is lower than 80% because your opponent can't count on redoubling optimally. A more realistic take point is derived by applying an estimate of cube efficiency (typically 0.6 to 0.7) to the continuous model live cube equity.
Second, the cash point is the optimal time to double, not the only time. The cash point is the top of your doubling window. Your doubling point is the bottom. The doubling window is the range of gammon-adjusted game winning chances for which you may give a takable double. In practical play, you can't wait until you reach your cash point because equity does not change incrementally. You can't count on doubling precisely at your cash point. If you go over the cash point your opportunity to give a takable double has been lost.
When you are considering a double, you need to examine all of the 1296 2-roll sequences of your roll and your opponent's roll and determine whether on average your equity will be higher if you double now or do not double now. At least that is what you would do if you were a calculating bot; humans know some shortcuts.
Two-roll sequences that cause you to exceed your doubling window are called market losers. If you are in your doubling window and have a proper double/take, it is because the total equity lost by not doubling in all your market losing sequences outweighs the equity you lose (if any) by doubling in all other sequences.
In this 3-away all position:
| White | 7 |
|---|---|
| |
| Blue | 4 |
Position ID: IgAAeAAAAAAAAA Match ID: cAlgAAAAAAAE | |
Blue must double now even though he wins only 56% of all games and White's potential recube is live -- Blue must take White's redouble. All of Blue's winning two-roll sequences are market losers. Blue gains match equity by doubling now.