lilredrooster
• Posts: 6698
Joined: May 8, 2015
May 8th, 2021 at 2:12:04 AM permalink
....................

this is something I learned from Don Schlesinger - BJ Hall of Fame member
I didn't know this and I was quite surprised

his exact words were:

"Kelly tells us that overbetting by more than twice your edge leads to eventual ruin"

after reading this I then asked him if this meant you were doomed if you did this - just to use a stronger word and hear his answer

to clarify for those who are not familiar with "Kelly" is that it basically states you should bet in accordance with your advantage

Kelly is one of the most important concepts behind AP blackjack

so, if you have a 1.2% edge your Risk of Ruin will fluctuate depending on what % of your total bankroll you wager on each hand

*
the foolish sayings of a rich man often pass for words of wisdom by the fools around him
pwcrabb
• Posts: 185
Joined: May 15, 2010
May 8th, 2021 at 5:11:48 AM permalink
The background and the derivation of the Kelly Criterion are well presented in the book by William Poundstone entitled Fortune's Formula.

Exposure of some percentage of your bankroll is the essence of any wager. When you are matched against an infinite bankroll, your tendency toward overexposure is likely to be fatal. Even if your wager is probabilistically favored, it must be limited in magnitude. The Kelly Criterion analytically optimizes that magnitude.

If your wager is probabilistically disfavored, then the magnitude limitation becomes even more urgent. Purists may insist that the only rational magnitude is zero.

For punters who will make probabilistically disfavored wagers anyway, gains will come only during short term favorable fluctuations in the natural volatility of their games. That volatility is prospectively described in terms of variance. In the short term, notions of Expected Value and optimal wager magnitude fade in significance compared to notions describing experienced volatility.
Last edited by: pwcrabb on May 8, 2021
"I suppose I was mad. Every great genius is mad upon the subject in which he is greatest. The unsuccessful madman is disgraced and called a lunatic." Fitz-James O'Brien, The Diamond Lens (1858)
sabre
• Posts: 1172
Joined: Aug 16, 2010
May 8th, 2021 at 7:17:22 AM permalink
Quote: lilredrooster

"Kelly tells us that overbetting by more than twice your edge leads to eventual ruin"

In reality table limits prevent you from continuing at double Kelly until ruin.
lilredrooster
• Posts: 6698
Joined: May 8, 2015
May 8th, 2021 at 8:39:24 AM permalink
Quote: sabre

In reality table limits prevent you from continuing at double Kelly until ruin.

that's not correct - you are mistaken - one Kelly could mean a small bet depending on your bankroll

*
the foolish sayings of a rich man often pass for words of wisdom by the fools around him
sabre
• Posts: 1172
Joined: Aug 16, 2010
May 8th, 2021 at 8:58:04 AM permalink
Quote: lilredrooster

that's not correct - you are mistaken - one Kelly could mean a small bet depending on your bankroll
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I'm not mistaken.

A player with a small bankroll who starts betting double Kelly is not guaranteed to go bust because he could reach a point where he can't continue making double Kelly bets due to table limits.
lilredrooster
• Posts: 6698
Joined: May 8, 2015
May 8th, 2021 at 9:58:03 AM permalink
Quote: sabre

In reality table limits prevent you from continuing at double Kelly until ruin.

Quote: sabre

I'm not mistaken.

A player with a small bankroll who starts betting double Kelly is not guaranteed to go bust because he could reach a point where he can't continue making double Kelly bets due to table limits.

with the word "could" in there you are not incorrect
without the word "could" you are incorrect

if an AP starts betting at a \$10 table betting 2 times Kelly and his max bet is \$160 it would take him a very, very long time to exceed the table limits (due to bankroll growth) which is likely to be at least \$500 and more likely \$1,000 or \$5,000 or \$10,000 - when I was playing in the 90s in A.C. the table max on a \$5 table was often \$5,000 - I don't actually know what it is likely to be now - but still

either playing for a very, very long time or having a very unusual positive drift (luck) if it's a short amount of time

the usual situation is that he would finish his session long, long before he reached the table limit

I believe a mathematician could actually make this calculation:

these figures are just speculative estimates referring to an AP betting 2 times Kelly

the AP has a 25% chance of going bust after 50 hours of play

a 50% chance of going bust after 100 hours of play

and a 75% chance of going bust after 200 hours of play

edit: actually it would be much more accurate to make the calculation based on number of hands played then hours of play

but I wouldn't ask anybody to make those very difficult calculations which I believe would take a lot of time and effort

*
Last edited by: lilredrooster on May 8, 2021
the foolish sayings of a rich man often pass for words of wisdom by the fools around him
TomG
• Posts: 2428
Joined: Sep 26, 2010
Thanked by
May 9th, 2021 at 6:21:39 AM permalink
Quote: sabre

I'm not mistaken.

A player with a small bankroll who starts betting double Kelly is not guaranteed to go bust because he could reach a point where he can't continue making double Kelly bets due to table limits.

In Las Vegas, it is not that hard to find blackjack tables with \$10,000 limits. If that was double kelly, that means full kelly would be \$5,000. With a 1.2% edge on an even money payout, that would require \$400,000. There are some people who do not have that much money.

Overbetting can definitely limit profits. Imagine a casino that pays out 2-to-1 on a coin flip, with no limits. I could turn \$1 into \$1,000,000,000 in a day or two at that game. But if I overbet and bet everything I have, then I would soon lose everything, have zero, and be unable to make another bet, and not earn anything
Moraine
• Posts: 71
Joined: May 12, 2021
May 12th, 2021 at 5:54:00 PM permalink
Hi, Greetings:

THE KELLY CRITERIA FUNDAMENTALS FOR ONE HAND BLACKJACK:

One KELLY BET = 0.77 x Players' POSITIVE Expected Value (in %) x The size of the Bankroll (in \$)

Bet one Kelly is the optimal bet to achieve the FASTEST Bankroll Growth Rate.

Bet more than One Kelly incurs UNNECESSARY Risk without the accompanying benefit.

Bet more than TWO-Kelly will result in a NEGATIVE Bankroll Growth Rate, leading to EVENTUAL BANKRUPTCY.
aceside
• Posts: 529
Joined: May 14, 2021
May 15th, 2021 at 8:30:39 AM permalink
This does not make much sense. I would say that bet one Kelly is the safest bet for a player not going bankruptcy while securing a reasonable bankroll growth rate.
aceside
• Posts: 529
Joined: May 14, 2021
May 15th, 2021 at 8:36:55 AM permalink
Quote: lilredrooster

....................

to clarify for those who are not familiar with "Kelly" is that it basically states you should bet in accordance with your advantage

*

The Kelly wager basically states that your bet size should be proportional to your advantage and inversely proportional to your instantaneous variance. The variance part is the trickier part.
Moraine
• Posts: 71
Joined: May 12, 2021
May 16th, 2021 at 3:31:45 PM permalink
Moraine would like to add to his May 12th comments on Kelly Criterion.

Formula:
One Kelly Bet in Blackjack = (1/Variance) x Players' Positive Expected Value (EV) According to the True Count x The Size of the Bankroll
= 0.77 x Players' Positive EV (in %) x Bankroll (in \$)

Where,
1. Standard Deviation for most common blackjack is 1.14.
2. Variance = Square of Standard Deviation = 1.14 x 1.14 = 1.3; and 1/1.3 = 0.77.

NOTE: Once the Rules of the Blackjack Game are fixed, So are the Standard Deviation and the Variance. BUT THE PLAYER'S BANKROLL may change after each hand. So. to the extent practicable, a blackjack player must re-size the bankroll after a significant win or loss.
Last edited by: Moraine on May 16, 2021
TomG
• Posts: 2428
Joined: Sep 26, 2010
May 16th, 2021 at 8:40:28 PM permalink
Quote: aceside

This does not make much sense. I would say that bet one Kelly is the safest bet for a player not going bankruptcy while securing a reasonable bankroll growth rate.

Kelly criterion is maximally aggressive. It will maximize growth and there will be huge losses along the way. On close to even money bets, for every 250 bets, there is a 5% chance of losing 60% and a 15% of losing 40%. I don't know anyone who would want to risk those type of losses. Half or quarter significantly cut back on those extreme drawdowns, without losing much growth.

Great article: https://www.pinnacle.com/en/betting-articles/Betting-Strategy/fractional-kelly-criterion/GBD27Z9NLJVGFLGG
Moraine
• Posts: 71
Joined: May 12, 2021
May 17th, 2021 at 11:30:50 AM permalink
Quote: TomG

Kelly criterion is maximally aggressive. It will maximize growth and there will be huge losses along the way. On close to even money bets, for every 250 bets, there is a 5% chance of losing 60% and a 15% of losing 40%. I don't know anyone who would want to risk those type of losses. Half or quarter significantly cut back on those extreme drawdowns, without losing much growth.

Great article: /en/betting-articles/Betting-Strategy/fractional-kelly-criterion/GBD27Z9NLJVGFLGG

One Kelly may be "maximally aggressive", but it is still the OPTIMAL BET for the best long term growth. Also, the safety of the bankroll is assured.

If a card counter is less inclined to accept the huge bankroll swings, he/she can bet HALF-KELLY and still achieve 75% of the growth rate. With Kelly criterion, you can HALF your risk, yet still receive THREE QUARTERS of the benefit.
Moraine
• Posts: 71
Joined: May 12, 2021
May 24th, 2021 at 11:53:56 AM permalink
Quote: Moraine

Moraine would like to add to his May 12th comments on Kelly Criterion.

Formula:
One Kelly Bet in Blackjack = (1/Variance) x Players' Positive Expected Value (EV) According to the True Count x The Size of the Bankroll
= 0.77 x Players' Positive EV (in %) x Bankroll (in \$)

Where,
1. Standard Deviation for most common blackjack is 1.14.
2. Variance = Square of Standard Deviation = 1.14 x 1.14 = 1.3; and 1/1.3 = 0.77.

NOTE: Once the Rules of the Blackjack Game are fixed, So are the Standard Deviation and the Variance. BUT THE PLAYER'S BANKROLL may change after each hand. So. to the extent practicable, a blackjack player must re-size the bankroll after a significant win or loss.

For one hand, Kelly criterion bet is really simple. Discussion on "Betting Ramp" or "Bet Spread" actually is UNNECESSARY AND DANGEROUS. It often leads card counters into thinking it is a sound betting strategy when it is a DANGEROUS ONE.

Many very-hipped counters often talk about "BET SPREAD" and "RISK OF RUIN" as if those were two most important tricks for Bankroll Management.

WATCH OUT, A PRE-SELECTED AGGRESIVE BET SPREAD WITHOUT TAKING KELLY CRITERION into consideration will inevitably lead to losing the entire bankroll. The term "RISK OF RUIN" exists for a reason -- more accurately, for a VERY BAD reason in fact.
Last edited by: Moraine on May 24, 2021