Ed Miller writes: "First is the assumption that this bankroll is unreplenishable out to
infinity. This is the money you have, and you will never have a penny more
that you didn't win playing the game."
You don't need to make that assumption, of course in the real world there are likely to be other sources that add to your bankroll, but more likely to leaks that deplete your bankroll. These should be accounted for as adjustments to EV, which is what they are.
Ed Miller writes: "But the Kelly number isn't some magical bright line across
which no bankroll shall survive. It is a maximum, and for practical
purposes, numbers slightly to one side or the other are also fine."
Somewhat correct, but be carefull where you take this. The Kelly number is a mathematical inflection point. On one side is a region where risk is proportional to gain, in other words the more risk you take the more gain you get. This is the rational region, this is the region rational people want to be in. On the other side of the Kelly number is the region where increased risk actually yields less gain, this is the looney side.
Ed Miller writes: "I'm not arguing that people should run around playing games for which they
are underbankrolled."
Define "underbankrolled". The Kelly criterion is one definition of "underbankrolled".
Ed Miller writes: "Overestimating edge and underestimating variance are
the bane of many gamblers."
Absolutely, also the bane of "investors".
Ed Miller writes: "But at some point if there's a machine you want
to play and you have a nice edge and your bankroll is close and you're
willing to accept some risk of ruin because, hey, you still have two hands
and a brain and these are not the last dollars you will ever see, just play
the darn game."
Define "bankroll is close". Close to what?
[Non-text portions of this message have been removed]
Posted by: nightoftheiguana2000@yahoo.com
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