Quote from bwolinsky:
Why do we have to play expiration games every time, atticus?
Can't you just build a system and decide which way it'll move?
I wouldn't ever take a bet just because delta's 0.5, atm, and ready to fall below the strike prior to expiration.
In the sense of probability even if you wanted to say you could flip 2 out of 3 heads in a row without replacement if the second one's tails you'd be out and wouldn't be able to ever flip 2 heads in a row but if the last one or the first one is heads you still have a chance buying the call as long as the second isn't tails hitting two heads in a row depending on sequence, but you must still be right twice consecutively and it doesn't matter if it's the first two or the last two if you've managed to get 2 out of 3 with 2 sequential flips.
You can either do hht or thh, but if you do hth you won't win because of multiplicative compounding. It has to be consecutive and it has to be compounded twice over to beat the delta's 50% probability. Even though I don't like to use delta that way, if we're really close to expiration you could take a chance with it, but you could buy the call instead if you're sure you can flip at least two out of three heads consecutively first or last.