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.
---In vpFREE@yahoogroups.com, <nightoftheiguana2000@...> wrote:
???
The Kelly system tells you when to stop.
And I stand by my claim that:
"With the Kelly system there is zero chance of going broke, and a very reduced risk of bankroll depletion."
---In vpFREE@yahoogroups.com, <h_dunbar@...> wrote:
You know, rather than admit that your "correction" of Jean was an overstatement, you want to invoke "stop-loss" and "gambling addiction"?!
You initially wrote this:
"Jean wrote: "There is never a zero chance of going broke."
With the Kelly system there is zero chance of going broke, and a very reduced risk of bankroll depletion."
That's simply not true. Now you seem to want to amend it by saying the player should stop before going broke.
Yes, we can all agree on the obvious: The only way to eliminate the finite chance of going broke is to stop playing. In contrast to what you wrote initially, betting Kelly does not change that.
--Dunbar
---In vpFREE@yahoogroups.com, <nightoftheiguana2000@...> wrote:
Yes, if your attitude is: "I'll play until I go broke", which is gambling without a stop loss limit, which is one of the signs of gambling addiction.
---In vpFREE@yahoogroups.com, <h_dunbar@...> wrote:
NOTI, everything you wrote is true, but it's also true, as Jean was asserting, that anyone who plays a particular VP game indefinitely will have a finite chance of ruin.
Your advice on Kelly betting is solid; I enjoy reading your posts, particularly the ones about Kelly and "NO".
--Dunbar
---In vpFREE@yahoogroups.com, <nightoftheiguana2000@...> wrote:
For example, as long as your bankroll is over $7,312.50 you'd play 10 coin quarter FPDW, if your bankroll is between $7,312.50 and $3,656.25 you'd play 5 coin quarter FPDW, if your bankroll is between $3,656.25 and $1,462.50 you'd play 10 coin nickel FPDW, if your bankroll is between $1,462.50 and $731.25 you'd play 5 coin nickel FPDW, below $731.25 you'd have to stop and return to your day job to build your gambling bankroll back up. You would never bust out, but you might have to quit gambling and go back to work at some point. By using the Kelly system to define your stop limits, you would be optimizing bankroll growth, for the bet sizes you have available.
---In vpFREE@yahoogroups.com, <nightoftheiguana2000@...> wrote:
In the real world bet sizing is always discrete, even if it's at the penny level. In the case of FPDW you might have a choice of $2.50, $1.25, $.50, $.25. One of those sizes is more Kelly optimal than the rest for a given bankroll. Multicoin and Multiplay games often provide even more choices of bet size, though not very often for FPDW.
---In vpFREE@yahoogroups.com, <eecounter@...> wrote:
---In vpFREE@yahoogroups.com, <nightoftheiguana2000@...> wrote:
Jean wrote: "There is never a zero chance of going broke."
"With the Kelly system there is zero chance of going broke, and a very reduced risk of bankroll depletion....."
Well, not exactly. The Kelly system does promise a zero chance of going broke, but only if you can continually resize your bets downward if you start to lose. Betting strictly according to the Kelly system requires a re-sizing of bets after every change in bankroll size, even down to fractions of a penny bets if you run particularly bad. (All of this assumes you have an advantage. The Kelly bet size for a negative expectation bet is $0.)
In the real world, this kind of bet re-sizing just isn't possible, particularly with VP. If you start out with some fixed amount of money, *and you maintain a fixed bet level*, you definitely have a non-zero chance of going broke, no matter how much money you start out with.
On the positive side, if you start out with a large enough bankroll relative to bet size, and a strong enough advantage, then we might be able to say your chance of going broke is "just about impossible", even if you can't re-size bets downward.
EE
