The following game came up, and while I know it was a double, take situation, I cannot work out why. Surely I am just hoping to roll a double, while hoping my opponent fails to roll one?

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You are right. It is simply you are waiting for doubles. This is the latest you can take (4 rolls vs 4 rolls). You can roll doubles and cube him out, and you have a few rolls to do it. 3 rolls vs 3 rolls is simply not enough time.

But surely he is just as likely as me to roll a double? In other words, my advantage is cancelled by his? How am I 27% to win here, when I have to roll a double, while he has to not roll one, and both events are equally likely?

I've broken it down into the following scenarios:
1) Neither team rolls a double, he wins. (most likely)
2) He rolls a double, I don't, he wins. (50/50)
3) We both roll doubles, he wins.
4) I roll a double, he doesn't. I win. (50/50)

Where is the 27% winning percentage coming from here?

My heart was in my teeth with this take, which I knew to be correct, but absolutely could not justify. Waiting/hoping for a double just doesn't seem right...?

Numbers 2 and 3 are redundant. They shouldn't be counted twice. Also, if you roll doubles your next roll before he does, you can recube and he has to pass, denying him a chance to roll doubles again for the win.

Thanks for taking the time to go through this.

The chances of me rolling a double are 1 in 6. (as are his chances) That's well below the 25% needed for a successful take. If I am relying on that, where is the maths? I just don't understand...

This is a drop if he just has 8 guys on the 1. You have like 19% equity from winning the doubles battle and another 9% from him bozoing a bunch of small numbers and missing a bearoff.

The white three point in particular. If white rolls two threes before he rolls two higher numbers, he misses and blue can cash.

I disagree with the posters. This is an easy take on 2 or 4 cube but a drop at 32 cube! At best a take and beg to settle!!

I can't do the supporting math, but here are winning chances for no-miss positions.

2 roll: 86% - 14%
3 roll: 79% - 21%
4 roll: 75% - 25%
5 roll: 72% - 28%
6 roll: 70% - 30%
7 roll: 68% - 32%

As people already mentioned your position is a bit better than a four roll position. Why?

a) He has more potential to gap (the two threes before a four thing)

b) He has less working doubles than you do. for example, Double 3's saves a roll for you but not for him.

I think a take at 32 but drop at 64. Only kidding. Mathematically the same at 4 or 32. Not sure if you were joking.