Let's say Alice will be wrong several times and then right once, and Bob will be right several times and wrong once. Both of them start with $10k.
To give Alice every advantage, let's say her bets pay out 10x or nothing, and Bob's bets pay out 4x or nothing. We'll also say Alice magically knows which time she'll be right, but Bob won't know which time he'll be wrong.
Alice will obviously bet all her money on the time she's right, and come out with $100k.
Bob can invest 2/3 of his money each time, repeating every time he's right. Let's say he happens to be right 8 times, then is wrong. After those 8 right bets, he'll have $6.6M. After he makes his wrong bet, his fortune will drop to $2.2M. Then he'll retire.
Looks like Bob has a much better windfall to me.