Good cube action increases your equity. Bad cube action decreases it.

For X, no double/win means he leads 3-away, 28-away, for a Match Equity of 99% (actually 99.74%!).

Double/win means that he wins the match and goes to 100%, a gain of 1%.

No double/lose means that he leads 11-away, 20-away, for an ME of 82%.

Double/lose means that he loses the match (because 0 will redouble) for an ME of 0%.

We can see that doubling for X risks 82% to gain 1%. How big a favourite must X be in this game to make the bet cost effective? We do a risk/gain analysis. The formula is Risk/Risk+Gain or here 82/82+1 = 82/83 = 99%. X needs to win this game 99% of the time for a double to be correct. Can he do that? Pretty clearly not. If X rolls less than 4-4 (33/36) and 0 rolls 6-6 (1/36) that equates to 33/1296 losses which is 2.5% straight away and of course 0 has other winning sequences.

We can ignore future cube action if X doesn't double, because in fact he will never have a correct redouble. Cubeless, he wins this game 96% of the time.

If he doesn't double then his equity will be 96% x 99% and 4% x 82%, = ME 98%

If he does double, then his equity will 96% x 100% and 4% x 0 = ME 96%.

Good cube action increases equity, bad cube action decreases it. A redouble to 16 reduces X's equity from 98% to 96%. No double is correct.

The instinct to avoid massive overage provides the right answer. This is just the theory behind the instinct.