White's a big favorite when Black dances, which happens 16/36 = 44% of the time. He also wins plenty of games when Black enters with 5-2, 5-3, or 5-4, and owning the cube he'll also win a few after being hit but then hitting Black as he comes around. So the take is trivial.

Black loses his market after hitting or rolling 5-5 (14 rolls), but that's about it. Redoubling looks very premature.

Thank you! Would any of the above change for the following position, which is actually the original position:

It's still a massive take for all the reasons given above.

I wouldn't have doubled over the board but an XG rollout made the double/no double decision a tossup. Every checker matters in this sort of ending position.

O’Hagan’s law for redoubles – when you know it is a take, redouble with 11/12 net market losers AND you are doing ok in all of the other variations.

Here black has 14 market losers – all hits and 55. How is black doing in the other variations, 16 fans and 5/2, 5/3, 5/4, and 5/6.

First the 8 numbers that come in and do not hit. Black is doing well in these variations, ranging from 64% equity to 79% equity. Let’s average this to 71.5% equity.

What about when he fans? When Black fans he is only 36% to win. And whenever he fans twice in a row, he cannot take a cube. Let’s imagine a 5,3 roll played a 6/1, 3/off. This will occur 256/1296 or about 20% of the time.

(71.5% * 8) + (36% * 16) = 11.5 wins in 24 games or 48% equity

So in this variation, Black is not a favorite in the variations where he does not lose his market.

In variation 2, there is an additional checker off. In this variation, the numbers that come in and miss white’s equity ranges from 75% - 86%. We can average this to 80.5%. (Also, there are some variations where you come in and he does not roll well that would also lose the market. Such as 65 followed by 21.)

When he fans his equity is 46% with the extra checker off. Additionally, you can take the cube after he fans twice in this variation.

(80.5% * 8) + (46% * 16) = 13.8 wins in 24 games or 58% equity in the second variation when he misses or fails to roll 55.

In variation 1, you are not doing so well when you fan. While in variation 2, the extra checker off gives you enough equity when you fan that you are still doing good enough. So it is the difference of being an underdog when you do not roll the market losers in variation 1 versus variation 2 in addition to the extra market losers just by coming in without hitting that makes the difference.

That was a great explanation by JJ of the necessary thought process in these situations.
I jsut want to point out that although it has no bearing on the correct decision, that there are only 6 numbers that come in and do not hit.