vpFREE2 Forums

Kelly Criterion

#1

Brian, I've searched my back issue index for "Kelly" and it didn't show up. I did mention Kelly in an article I wrote titled "Money Management, Myth or Useful Tool?" but I don't think that brief discussion was very useful for RoR or bankroll calculations. I can't find any other mention of Kelly in my publications. As I said, I don't feel that the Kelly Criterion is a very good guide for high variance games such as Video Poker. Kelly's main consideration is player advantage, and as I've shown, RoR is not directly related to either player advantage or variance. That is why I felt it so important to include the Sorokin formula evaluation in Optimum Video Poker.
Dan

···

At 11:38 PM +0000 8/23/05, Brian wrote:

At 8:28 PM -0600 8/23/05, Dan Paymar wrote:

Brian, I think you're confusing me with someone else. I don't recall
ever writing about "Kelly bankrolls." I don't think Kelly applies
well to high variance games. It works well for blackjack players, but
not as well for VP players. But whatever works well for you is good.

It was at least six years ago, but I am pretty sure it was an article in VPT. If I recall correctly, the article was not written by you, but by a "guest
author." If this is right, maybe that's why you don't recall it?

--
Dan Paymar
Author of best selling book, "Video Poker - Optimum Play"
Editor/Publisher of VP newsletter "Video Poker Times"
Developer of VP analysis/trainer software "Optimum Video Poker"
Visit my web site at www.OptimumPlay.com

"Chance favors the prepared mind." -- Louis Pasteur

#2

Mathematically, there really isn't any problem with applying Kelly
principles to VP. The main thing to avoid is the usual approximations
that are made when Kelly is applied to games with low variance.
The "heart" of Kelly betting is to maximize geometric bankroll growth
(or equivalently, expected log of bankroll).

The "Virtual Payoffs" method that I use for finding min-risk strategies
can be adapted to finding a playing strategy that is log-optimal when
the bet size is a given fraction of bankroll, and can also be used to
find the log-optimal bet fraction and the playing strategy which is
optimal for that bet fraction.

The end result is that the log-optimal playing strategy is sort of
"in between" the max-EV strategy and the min-risk strategy. The
correct strategy varies with bet fraction, and for very small bet
fractions the log-optimal strategy approaches max-EV strategy.
In contrast, as the bet fraction increase to the point where bankroll
growth becomes zero (this occurs near 2X the log-optimal bet
fraction), the log-optimal strategy approaches the min-risk strategy.

I hope someone out there finds this interesting.

···

On Tuesday 23 August 2005 08:40 pm, Dan Paymar wrote:

At 11:38 PM +0000 8/23/05, Brian wrote:
>At 8:28 PM -0600 8/23/05, Dan Paymar wrote:
>>Brian, I think you're confusing me with someone else. I don't recall
>>ever writing about "Kelly bankrolls." I don't think Kelly applies
>>well to high variance games. It works well for blackjack players, but
>>not as well for VP players. But whatever works well for you is good.
>
>It was at least six years ago, but I am pretty sure it was an article in
>VPT. If I recall correctly, the article was not written by you, but
>by a "guest
>author." If this is right, maybe that's why you don't recall it?

Brian, I've searched my back issue index for "Kelly" and it didn't
show up. I did mention Kelly in an article I wrote titled "Money
Management, Myth or Useful Tool?" but I don't think that brief
discussion was very useful for RoR or bankroll calculations. I can't
find any other mention of Kelly in my publications. As I said, I
don't feel that the Kelly Criterion is a very good guide for high
variance games such as Video Poker. Kelly's main consideration is
player advantage, and as I've shown, RoR is not directly related to
either player advantage or variance. That is why I felt it so
important to include the Sorokin formula evaluation in Optimum Video
Poker.
Dan

#3

Although I do recommend that anyone who is serious about video poker buy
Dan's program, our esteemed administrator has placed in the bankroll links a
link to Cindy Liu's Video Poker Analyzer which quickly calculates the
Sorokin RoR. http://members.cox.net/vpfree/Bank.htm

···

-----Original Message-----
From: vpFREE@yahoogroups.com [mailto:vpF…@…com] On Behalf Of
Dan Paymar
Sent: Tuesday, August 23, 2005 7:41 PM
To: vpFREE@yahoogroups.com
Subject: [vpFREE] Re: Kelly Criterion

At 11:38 PM +0000 8/23/05, Brian wrote:

At 8:28 PM -0600 8/23/05, Dan Paymar wrote:

Brian, I think you're confusing me with someone else. I don't recall
ever writing about "Kelly bankrolls." I don't think Kelly applies
well to high variance games. It works well for blackjack players, but
not as well for VP players. But whatever works well for you is good.

It was at least six years ago, but I am pretty sure it was an article in
VPT. If I recall correctly, the article was not written by you, but
by a "guest
author." If this is right, maybe that's why you don't recall it?

Brian, I've searched my back issue index for "Kelly" and it didn't
show up. I did mention Kelly in an article I wrote titled "Money
Management, Myth or Useful Tool?" but I don't think that brief
discussion was very useful for RoR or bankroll calculations. I can't
find any other mention of Kelly in my publications. As I said, I
don't feel that the Kelly Criterion is a very good guide for high
variance games such as Video Poker. Kelly's main consideration is
player advantage, and as I've shown, RoR is not directly related to
either player advantage or variance. That is why I felt it so
important to include the Sorokin formula evaluation in Optimum Video
Poker.
Dan

--
Dan Paymar
Author of best selling book, "Video Poker - Optimum Play"
Editor/Publisher of VP newsletter "Video Poker Times"
Developer of VP analysis/trainer software "Optimum Video Poker"
Visit my web site at www.OptimumPlay.com

"Chance favors the prepared mind." -- Louis Pasteur

vpFREE Links: http://members.cox.net/vpfree/Links.htm

Yahoo! Groups Links

#4

Video Poker Times Volume 8 Number 5 September/October 200
Bankroll Requirements- A simple approximation.

This was Tomski's simple approximation to calculate bankroll

···

----- Original Message ----- From: "Dan Paymar" <Dan@OptimumPlay.com>
To: <vpFREE@yahoogroups.com>
Sent: Tuesday, August 23, 2005 7:40 PM
Subject: [vpFREE] Re: Kelly Criterion

At 11:38 PM +0000 8/23/05, Brian wrote:

At 8:28 PM -0600 8/23/05, Dan Paymar wrote:

Brian, I think you're confusing me with someone else. I don't recall
ever writing about "Kelly bankrolls." I don't think Kelly applies
well to high variance games. It works well for blackjack players, but
not as well for VP players. But whatever works well for you is good.

It was at least six years ago, but I am pretty sure it was an article in VPT. If I recall correctly, the article was not written by you, but by a "guest
author." If this is right, maybe that's why you don't recall it?

Brian, I've searched my back issue index for "Kelly" and it didn't show up. I did mention Kelly in an article I wrote titled "Money Management, Myth or Useful Tool?" but I don't think that brief discussion was very useful for RoR or bankroll calculations. I can't find any other mention of Kelly in my publications. As I said, I don't feel that the Kelly Criterion is a very good guide for high variance games such as Video Poker. Kelly's main consideration is player advantage, and as I've shown, RoR is not directly related to either player advantage or variance. That is why I felt it so important to include the Sorokin formula evaluation in Optimum Video Poker.
Dan

#5

Bob Webb wrote:

Although I do recommend that anyone who is serious about video poker
buy Dan's program, our esteemed administrator has placed in the
bankroll links a link to Cindy Liu's Video Poker Analyzer which
quickly calculates the Sorokin RoR.
http://members.cox.net/vpfree/Bank.htm

I've been intrigued by Paymar's program, but not sufficiently to pop a
few bucks for it. My vp software arsenal is pretty satisfactory as it
stands.

Liu's online program satisfies general bankroll/ROR interests -- the
extra bells and whistles of Optimum VP (principally having bankroll
related focus) I largely satisfy otherwise in rudimentary form or are
relatively esoteric to practical considerations of my play.

I sense many have similar perceptions -- there's no buzz at all about
the program here ... particularly in the form a convincing testimony
that it's a "must have" addition over and above (or substitute for)
WinPoker and Frugal VP.

I wish a limited capability demo version of the program were available
... say one with a JB/DB, single paytable, game limitation. More
often than not, I'm a sucker for a whistle or two once I get my hands
on them.

- Harry

#6

So, if I understand this correctly:

If a Kelly gambler had a bankroll (total money to be placed at risk on
the gamble) of say $5,000, and could gamble with a 101% return with
variance of 25, the correct Kelly bet would be $5,000 x 1% / 25 = $2
per bet which is 40 coins on a nickel machine. The correct strategy
would be the log-optimal strategy. If in the course of play the
bankroll fell to $2,500, the correct strategy would be min-risk, or
alternately switching to $1 per bet. If in the course of play the
bankroll grew to $10,000, the correct strategy would be between
log-optimal and max-EV, or alternately switching to $4 per bet.

···

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

The end result is that the log-optimal playing strategy is sort of
"in between" the max-EV strategy and the min-risk strategy. The
correct strategy varies with bet fraction, and for very small bet
fractions the log-optimal strategy approaches max-EV strategy.
In contrast, as the bet fraction increase to the point where bankroll
growth becomes zero (this occurs near 2X the log-optimal bet
fraction), the log-optimal strategy approaches the min-risk strategy.

#7

That's a fair overview. I would think that the Kelly formula would
break down for most VP games, since it is an approximation, so I
wouldn't trust it to give the true log-optimal bet size.

···

On Wednesday 24 August 2005 01:46 am, nightoftheiguana2000 wrote:

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:
> The end result is that the log-optimal playing strategy is sort of
> "in between" the max-EV strategy and the min-risk strategy. The
> correct strategy varies with bet fraction, and for very small bet
> fractions the log-optimal strategy approaches max-EV strategy.
> In contrast, as the bet fraction increase to the point where bankroll
> growth becomes zero (this occurs near 2X the log-optimal bet
> fraction), the log-optimal strategy approaches the min-risk strategy.

So, if I understand this correctly:

If a Kelly gambler had a bankroll (total money to be placed at risk on
the gamble) of say $5,000, and could gamble with a 101% return with
variance of 25, the correct Kelly bet would be $5,000 x 1% / 25 = $2
per bet which is 40 coins on a nickel machine. The correct strategy
would be the log-optimal strategy. If in the course of play the
bankroll fell to $2,500, the correct strategy would be min-risk, or
alternately switching to $1 per bet. If in the course of play the
bankroll grew to $10,000, the correct strategy would be between
log-optimal and max-EV, or alternately switching to $4 per bet.

#8

> > The end result is that the log-optimal playing strategy is sort of
> > "in between" the max-EV strategy and the min-risk strategy. The
> > correct strategy varies with bet fraction, and for very small bet
> > fractions the log-optimal strategy approaches max-EV strategy.
> > In contrast, as the bet fraction increase to the point where

bankroll

> > growth becomes zero (this occurs near 2X the log-optimal bet
> > fraction), the log-optimal strategy approaches the min-risk

strategy.

>
> So, if I understand this correctly:
>
> If a Kelly gambler had a bankroll (total money to be placed at risk on
> the gamble) of say $5,000, and could gamble with a 101% return with
> variance of 25, the correct Kelly bet would be $5,000 x 1% / 25 = $2
> per bet which is 40 coins on a nickel machine. The correct strategy
> would be the log-optimal strategy. If in the course of play the
> bankroll fell to $2,500, the correct strategy would be min-risk, or
> alternately switching to $1 per bet. If in the course of play the
> bankroll grew to $10,000, the correct strategy would be between
> log-optimal and max-EV, or alternately switching to $4 per bet.

That's a fair overview. I would think that the Kelly formula would
break down for most VP games, since it is an approximation, so I
wouldn't trust it to give the true log-optimal bet size.

What's the formula for true log-optimal bet size using R(1)?

ln(R(1))/ln(.1)?

···

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

On Wednesday 24 August 2005 01:46 am, nightoftheiguana2000 wrote:
> --- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:

#9

The log-optimal bet size isn't a function of RoR.

Let me try to explain it this way -- for RoR, the formula for the virtual
payoff that is equivalent to a real payoff of N units is given by:

V = (1 - R^N) / (1 - R)

Similarly, the formula to convert of payoff of N units to a virtual payoff
for an optimal bet fraction F is given by:

V = N / (1 + F*(N-1))

If virtual payoffs are computed with this formula, and F is adjusted
until the strategy gives a breakeven game, then that value of F is
log-optimal for whatever strategy was used. The optimal strategy
can be found by using the virtual payoffs to compute the strategy
which maximizes "virtual EV".

Many readers probably won't have a clue what that means, but I
think you might understand it.

···

On Wednesday 24 August 2005 11:09 am, nightoftheiguana2000 wrote:

What's the formula for true log-optimal bet size using R(1)?

ln(R(1))/ln(.1)?