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 Originally Posted by Belt
Say you have 100K,
You can bet 1.000 times $100. EV is 10% and you win $10.000
You can bet 2.000 times $50. EV is 20% and you win $20.000
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I offer a counter example.
We start with only $100
I take the $50 bet. I lose.
I have $50.
I take the $50 bet, i win.
I have $100.
I take it 2 more times, and lose each time.
Thus starting with only $100, i then could take the $50 bet 4 times.
The EV's are exactly the same no mater how many times we run this. The only reason you would care about one bet over the other is due to rake or due to variance. With a higher variance we have a greater risk of ruin , so we need a larger bankroll to justify even taking the bet. With rake, the EV's of the bets will change. Depending on structure, the smaller bet could become more favorable (higher ev), the larger one could be, or they could both be the same.
However, I have absolutely no idea how i would figure this out if the EV's and variance's were different and we cared about the variance at all.
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