Quote Originally Posted by James989 View Post
I thought the formula should be, bet size = kelly ratio * bankroll * edge / variance ? where kelly ratio = 1.0
No. I just made a similar post to Nyne's on another thread. The Kelly ratio isn't the operative factor. The important point is that the payoff for a winning bet is a hefty multiple of that for a losing one. For example, it's very easy to conceive of several different scenarios, all of which have the same e.v., but where that e.v. is attained in various ways: win less than you lose, but win VERY frequently; even money payouts where you win more often than you lose; or longshot payouts, where you win much less frequently than you lose, but your win is a large multiple of the loss amount.

As you must understand, the Kelly-optimal wagers in these three circumstances are all quite different, with the first being the highest, and the last being the lowest. And it's easy to understand why: the latter scenario is much more risky than the former, with very frequent losses; so you need to be cautious with your bet size. In those situations, the PRECISELY correct Kelly wager is (bank x edge)/ratio of winning bet to losing one.

Don