Barry,
You make a number of excellent points, but you wrote "All Kelly does is minimize the chance of getting to the stop point." This is incorrect. Kelly maximizes bankroll growth which is a trade off between risk and reward. You can play at the smallest stakes possible with a large bankroll and have almost zero chance of hitting the stop point, but also very little bankroll growth.
Chris
---In vpFREE@yahoogroups.com, <b.glazer@...> wrote:
While I don't know the math that well, I do understand the principle of the Kelly system and its application, so I understood that what Jean was saying was that if you play at the same betting level all the time (and I think that WAS what her blog said, more or less), there is a non-zero chance of going broke, and I also understood that the description of Kelly "applied" as described in the post below would assure that you never go broke -- but you might have to stop playing.
The player who does not use the Kelly system is not much different on the "bottom" end of possibilities - even if that player is playing a positive expectation game with correct strategy, which is of course an essential part of any successful endeavor in gambling. That player can just take $2,000 and go play dollar VP until it's gone, and then that "system" tells the player to stop and replenish their bankroll with non-gambling income. That player can extend the time before that occurs by just playing quarters or nickels from the start, or by moving down in denomination when their $2,000 goes down to some pre-determined level (not determined by Kelly). That player can also avoid going broke by stopping their play at a pre-determined level, just like the Kelly player (albeit without any mathematical basis for determining that level). Incidentally, that player has a greater chance of increasing their bankroll more rapidly than the Kelly player, the "reward" for exposing oneself to a greater risk of ruin.
The main difference is that the Kelly bettor will last longer by playing according to Kelly before getting to the "go earn some money" point in their play than the above-described player who is betting more than their bankroll justifies -- in fact, they will last as long as mathematically possible. All Kelly does is minimize the chance of getting to the "stop" point in real life, since there is no way to infinitely play the same game in a casino, even if it has a positive player EV, with progressively smaller stakes, forever. Casinos have minimum bets at all games, eventually (just as the casinos have maximum betting limits, eventually, which prevents the "double-up" money management / betting systems from succeeding, along with the fact that most players, even without casino limits, would reach the limit of their non-infinite bankroll at some point in employing such a system).
In the end, especially throwing in the fact that full pay (positive EV) games are hard to find to begin with and even harder to find as the denominations go down, ANY player playing correctly can still either go broke (by not stopping while they still have money) or be forced to stop (by quitting when they reach their pre-determined stop point, whether determined whimsically or by Kelly) until they can get some more money from somewhere else.
Most (but not all) of us have some other source of money, but I assume that most of us do in fact have a gambling bankroll as well, and that, whether by Kelly or by seat of the pants, most of us try not to go through that bankroll, by playing at a level that we think is appropriate for the money we have. Only a true gambler would "manage their money" by, for example, taking their $1,000 bankroll to the casino and placing the entire amount on a single bet (although I have seen people do that, and although that is, in fact, the best chance of doubling your bankroll if you're playing a game with a casino edge, where dividing your money into smaller amounts just gives the casino more time to realize its advantage).
The real lesson of Kelly, to me, is that many of us don't have a good appreciation of how much money we should have in our bankroll in order to play at the levels we choose to play, and not have to replenish that bankroll too frequently with "outside" money. The second lesson is perhaps that negative expectation games do not have a money management strategy that will prevent losing everything, other than "don't play" -- perhaps obvious, perhaps not (as many of us are recreational players who do not expect long-term winnings, but want to minimize our long-term losses while, in fact, spending our money on a recreational activity).
For the example given below, most players with $14,000 in their bankroll aren't happy playing 10-bet quarter machines. Those that understand that this is an appropriate level to play, will have their money last much longer, if not forever.
--BG
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2a. Re: Jean Scott's Frugal Vegas LVA BLOG - 13 NOV 2013
A perfect player starts playing 10 coin quarter FPDW with a double Kelly bankroll: $14,625. For that player there is about a 15% chance that the bankroll will decrease to $7,310, at which point that player will Kelly switch to 5 coin quarter FPDW. Again, about another 15% chance that the bankroll will further decrease to $3,655, at which point that player will Kelly switch to 10 coin nickel FPDW. There is about a 6% chance that the bankroll will further decrease to $1,462, at which point the player will Kelly switch to 5 coin nickel FPDW. There is about a 15% chance that the bankroll will decrease to $731 at which point the player will quit gambling until they can rebuild their bankroll again with non-gambling income.
Summary: The player is never completely busted. There is however about a 0.02% chance the player will stop with a reduced bankroll of only $731. There is about a 99.98% chance the player will play forever.
A perfect player starts playing 10 coin quarter FPDW with a double Kelly bankroll: $14,625. For that player there is about a 15% chance that the bankroll will decrease to $7,310, at which point that player will Kelly switch to 5 coin quarter FPDW. Again, about another 15% chance that the bankroll will further decrease to $3,655, at which point that player will Kelly switch to 10 coin nickel FPDW. There is about a 6% chance that the bankroll will further decrease to $1,462, at which point the player will Kelly switch to 5 coin nickel FPDW. There is about a 15% chance that the bankroll will decrease to $731 at which point the player will quit gambling until they can rebuild their bankroll again with non-gambling income.
Summary: The player is never completely busted. There is however about a 0.02% chance the player will stop with a reduced bankroll of only $731. There is about a 99.98% chance the player will play forever.
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