vpFREE2 Forums

So you go to the Casino with a plan ?

#61

Let's dispense with all this, and just redefine "kelly". I'd vote for
something like: the main idea behind Kelly (& Shannon's) work was that
if the odds are slightly in your favor (with relatively large
uncertainty), the VP player should not bet his/her whole bankroll at
every hand. And, to ahcheive the biggest long-term bankroll growth ,
the gambler should bet some specially optimized fraction of his whole
bankroll every hand.

Then the particular optimized fraction- which depends on the utility
function-- is outside of kelly.

#62

Perhaps we're talking about different things. You seem to be talking
about probability of success if you set stop limits at "half" and "double",
is that correct? For a player who continues indefinitely, the probability
of a Kelly player multiplying the bankroll by a factor M is 100%, no
matter how large on chooses M (with M > 1). Similarly, for a player
who continues indefinitely, the probability that the bankroll will eventually
dip to half is 50%. That is my understanding. I could be mistaken.

···

On Sunday 25 December 2005 07:35 pm, nightoftheiguana2000 wrote:

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x...> wrote:
> My understanding of Kelly is that the probability of your bankroll

dropping

> to X% is X/100, so that the risk of dropping to 50% is 1/2 and the

risk of

> dropping to 1% is 1/100. This is based on continuously adjusting

bet size

> to be the proper Kelly bet.

The risk of getting your bankroll halved is 1/3, and the chance of
doubling it is 2/3, under Kelly strategy.

#63

Why redefine anything? Following the math based on the original
definition, no Kelly player will _ever_ bet his/her whole bankroll on
a single outcome, because doing so gives an expected utility which
is infinitely negative.

By similar reasoning, when a minimum wager is imposed (as is always
the case in real casino games) then a true Kelly player will stop
playing if the bankroll reaches a point where the minimum wager is
2X the optimal Kelly wager.

···

On Monday 26 December 2005 11:15 am, cdfsrule wrote:

Let's dispense with all this, and just redefine "kelly". I'd vote for
something like: the main idea behind Kelly (& Shannon's) work was that
if the odds are slightly in your favor (with relatively large
uncertainty), the VP player should not bet his/her whole bankroll at
every hand. And, to ahcheive the biggest long-term bankroll growth ,
the gambler should bet some specially optimized fraction of his whole
bankroll every hand.

#64

I don't disagree with this, but it seem rather tautological to me, as
if to say "Kelly is the optimal strategy for persons who choose to
measure performance by Kelly standards."

I don't personally claim to be a follower of the Kelly religion. I
would accept a wager of my life vs. a $10 billion cash prize
(tax free) if the probability of winning was large enough (say,
99.999%). Any true Kelly player would describe such a risk
as completely insane, since the log utility is infinitely negative.

···

On Monday 26 December 2005 10:56 am, cdfsrule wrote:

You see, Kelly provides optimal bankroll growth (independant of
utility function) but it is only applicable to the person who has a
logartihmic utility function. So, Kelly is not the optimal strategy
for anyone, unless that person happens to have a logarithmic utility
function. Do you?

#65

Gee, do you really mean what you wrote? What are the odds of losing
your life? 1 in 100,000 to lose? Odds to win,could we say it's 99,999
to one against? Maybe I figure wrong? Anyway you slice it, Kelly
religion or not, it's a bad bet.

10 billion would be too much to spend in a lifetime. So would 1
billion. Would you take the bet for 1 bill?

Have a good 2006......Jeep

.

···

.--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x...> wrote:

I don't personally claim to be a follower of the Kelly religion. I
would accept a wager of my life vs. a $10 billion cash prize
(tax free) if the probability of winning was large enough (say,
99.999%). Any true Kelly player would describe such a risk
as completely insane, since the log utility is infinitely negative.

#66

For a mere billion, it would be tougher to take the bet. You've got
to account for the probability that some present or future instantiation
of the government will result in massive inflation, forcing retired
billionaires to go back into the work force to pay for gas that costs
$10,000 per gallon and Big Macs that go for $5,000 a pop.

Also, $10 billion isn't that much if you're pumping money into
medical research to cures the really tough diseases like aging,
liver spots, wrinkles and incontenance. A big nest egg comes
in really handy once you extend lifespan to hundreds of years.

···

On Monday 26 December 2005 08:30 pm, whitejeeps wrote:

Gee, do you really mean what you wrote? What are the odds of losing
your life? 1 in 100,000 to lose? Odds to win,could we say it's 99,999
to one against? Maybe I figure wrong? Anyway you slice it, Kelly
religion or not, it's a bad bet.

10 billion would be too much to spend in a lifetime. So would 1
billion. Would you take the bet for 1 bill?

Have a good 2006......Jeep