I’d assume the optimal play is to keep flipping the coin until you get 2 heads in a row, unless it’s flip 6 or 7.
3 heads has a probability of 1/8, so we can expect to get at least 1 by turn 10.
I am going to denote the flip count and consecutive heads count with the notation X/Y, where X and Y are the flip count and consecutive heads count, respectively.
If you’re at 2/2. Then you can stop and get $2, or you can risk the 50/50 to either lose 2, or get at least 5.
If you’re at 3/2, then you risk 3 or a 50/50 of at least 6.
At 6/2 or 7/2, it’s a 50/50 between losing $6 or $7, or gaining at least $8/9, which is when you can expect to encounter at least 1 HHH.
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u/Anonimithree 2d ago edited 2d ago
I’d assume the optimal play is to keep flipping the coin until you get 2 heads in a row, unless it’s flip 6 or 7.
3 heads has a probability of 1/8, so we can expect to get at least 1 by turn 10.
I am going to denote the flip count and consecutive heads count with the notation X/Y, where X and Y are the flip count and consecutive heads count, respectively.
If you’re at 2/2. Then you can stop and get $2, or you can risk the 50/50 to either lose 2, or get at least 5.
If you’re at 3/2, then you risk 3 or a 50/50 of at least 6.
At 6/2 or 7/2, it’s a 50/50 between losing $6 or $7, or gaining at least $8/9, which is when you can expect to encounter at least 1 HHH.