4 ms·

Not quite; there's no such thing as a geometric EV (EV is by definition always arithmetic). Instead, you calculated the geometric growth rate, which the Kelly c

by n2d4 3y ago

Not quite; there's no such thing as a geometric EV (EV is by definition always arithmetic). Instead, you calculated the geometric growth rate, which the Kelly criterion would then maximize; but it doesn't maximize your average outcome. Try it; run a simulation, and you'll see what I mean! (Some guy already posted his results [1]) If you're curious, I wrote a fairly lengthy explanation in another comment [2] about why your calculation is preferable in many cases, but to maximize average wealth, you really do want to go all-in. [1] https://news.ycombinator.com/item?id=36982560 https://news.ycombinator.com/item?id=36982560 [2] https://news.ycombinator.com/item?id=36986147 https://news.ycombinator.com/item?id=36986147

cubefox 3y ago
> Not quite; there's no such thing as a geometric EV (EV is by definition always arithmetic). That depends on how you define it. The arithmetic mean is usually presupposed when talking about expected values, but the arithmetic mean is not the only mean, and in fact it is inappropriate to use in some cases, so arithmetic expected value is likewise not the only "expected value", and in fact inappropriate sometimes. So yes, talking about non-arithmetic EV should be just as common as talking about non-arithmetic mean, even though it isn't. > Instead, you maximized the geometric growth rate, which is what the Kelly criterion does; but it doesn't maximize your average outcome. Well, it doesn't maximize the arithmetic average, but it does maximize the geometric average. :P There is no point in assuming we have only one kind of average and one kind of expectation. A suboptimal common usage of terms can in fact be a hindrance to thinking straight. You use logarithms to keep talking about the arithmetic mean/average, but in my opinion logarithms just obfuscate the fact that we are in geometric mean territory.
- n2d4 3y ago
  > That depends on how you define it. I agree, this is a semantic discussion. I'm using Wikipedia's definition. https://en.wikipedia.org/wiki/Expected_value https://en.wikipedia.org/wiki/Expected_value

by n2d4 3y ago

cubefox 3y ago

> Not quite; there's no such thing as a geometric EV (EV is by definition always arithmetic). That depends on how you define it. The arithmetic mean is usually presupposed when talking about expected values, but the arithmetic mean is not the only mean, and in fact it is inappropriate to use in some cases, so arithmetic expected value is likewise not the only "expected value", and in fact inappropriate sometimes. So yes, talking about non-arithmetic EV should be just as common as talking about non-arithmetic mean, even though it isn't. > Instead, you maximized the geometric growth rate, which is what the Kelly criterion does; but it doesn't maximize your average outcome. Well, it doesn't maximize the arithmetic average, but it does maximize the geometric average. :P There is no point in assuming we have only one kind of average and one kind of expectation. A suboptimal common usage of terms can in fact be a hindrance to thinking straight. You use logarithms to keep talking about the arithmetic mean/average, but in my opinion logarithms just obfuscate the fact that we are in geometric mean territory.

n2d4 3y ago
> That depends on how you define it. I agree, this is a semantic discussion. I'm using Wikipedia's definition. https://en.wikipedia.org/wiki/Expected_value https://en.wikipedia.org/wiki/Expected_value