I need to respond to this since I read it after replying to your other related post.
Let me say first off, that when it comes to a largely quantitative science, I develop an inate distrust of anyone who'd be inclined to conjure "Rumsfeldian unknown unkowns".
Frankly, that's a bit of hand waving that I could scarcely tolerate that in the context of Iraq and WMD's (but, let's not stray there!).
And is it really necessary to involve black holes and dark (matter)?
Look, I truly applaud the cautionary nature of your post. A few around here seem to advocate wading into uncertain waters rather carelessly.
Bottom line, I'm suggesting that never exceeding a kelly bet (assuming that your primary goal is bankroll growth) isn't a sound strategy. Significant exercise of caution is warranted. But under that goal, I think playing 120% of kelly is advantageous over the alternate of 60%.
ftw, my comments are strictly limited to a stated goal of intelligently maximizing bankroll growth. Personally, this isn't a strategy that I'd adopt.
The prospect of entering a play at one given wager, where my strategy might call for me to drop denom in half after just $2k-$3k of incurred loss doesn't seem sensible (I can see it for others.)
Generally, I'm going to look to keep my wager at 40%-80% of kelly, where my own gut comfort of play volatily and ROR is a more important driver. I grasp what I sacrifice in exchange.
---In vpFREE@yahoogroups.com, <nightoftheiguana2000@...> wrote :
vp_wiz wrote: "For example, generally speaking, betting below Kelly is no more advantageous to bankroll growth than betting above Kelly. So, it's difficult for me to understand why your scheme (that sets a Kelly bet as a upper threshold) stands out as optimal in this respect. "
Sometimes there are two betsizes that yield the same average bankroll growth, but why would you take the higher betsize? It's possible there is a valid bet on the dark side that has a higher growth than the valid bet on the good side, but you're playing with fire. In the real world there are Rumsfeldian unknown unknows, and those are going to get you into trouble on the dark side. On one side of Kelly, the good side, there is always bankroll growth and growth is proportional to risk, the more risk you take, the more growth you get in return. You make a mistake and take a bit more risk than you wanted to, at least you get a better return for taking that risk, up to a point. Not true on the other side, the dark side, there the more risk you take the less growth you get and eventually the growth even turns negative. On this side there be dragons. Actually, a better analogy would be a black hole. The good side has some built in stability, the bad side is unstable and eventually turns ugly, faster than your expecting, that black hole will suck you in. Sure, if you're really really good and really really know what you're doing, you could play around on that dark side, but, as your mother told you, it's not safe, you could shoot your eye out kid. I'd recommend Poundstone's book "Fortune's Formula" for a non mathematical discussion of this topic and its real world implications.
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