Quote:
Originally Posted by curious
I I use the kelly criterion and a risk of ruin % of 1%, which makes the unit size basically equal the expected value. Kelly says you should always multiply your bankroll x expected value x the risk of ruin you are willing to accept, since I use 1% as risk of ruin, the risk of ruin falls away and you are left with expected value. I am oversimplifying the formula to make is easy to explain ...
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A more accurate way to simply state Kelly would be that a bettor should set his "to-win" amount to equal his edge.
For example, if you had an edge of 5% (what you're referring to as an expected value of 105%) you'd bet the following:
- odds of +100: bet 5% of bankroll
- odds of -110: bet 5.5% of bankroll
- odds of -200: bet 10% of bankroll
- odds of +200: bet 2.5% of bankroll
You'll note that in each one of these cases a win would net you the same 5% of bankroll.
As to what you refer to as "risk-of-ruin", I'm actually not sure how this makes sense in the context of Kelly. One frequently speaks of a Kelly multiplier, such that a Kelly multiplier of 1/2 would imply a bets of (approximately) half of the full-Kelly stake, and in general a kelly multiplier of κ would imply bets of (approximately) κ × the full-Kelly stake. But of course this has nothing to do with risk-of-ruin in any traditional sense.
Actually, even from an arithmetical perspective, I'm a bit perplexed by your risk-of-ruin coefficient. You state, "Kelly says you should always multiply your bankroll x expected value x the risk of ruin you are willing to accept," and then curiously continue with "since I use 1% as risk of ruin, the risk of ruin falls away and you are left with expected value", which if I hadn't seen you write elsewhere I'd assume to be a typo.
Using Kelly or (much more typically) some fraction thereof, can frequently be a valuable risk management tool for the advantage player. However, what you've described, while perhaps (depending on how you explain your risk-of-ruin coefficient) close to Kelly for bets at odds near even, will drastically diverge as odds lengthen or shorten away from that point.