Kelly Criterion

[pangga]

Can someone calculate for me the correct amount of bet for a bankroll of 500 dollars according to the Kelly Criterion?
Also can someone tell me when to increase my bet according to the count?
The type of Game is 6 decks, about 1 deck cutoff, BJ pays 3:2, Insurance 2:1, split up to 3 times, double after split, one additional card only for splitting an ace.

 

[FLASH1296]

You need to provide the name of the count you are using, or the card tags at least.

Before you run the data via computer you need to understand that the Kelly Criterion will set a "Risk-0f-Ruin" of 13.5% when looking to optimize your "betting ramp"

What you do not yet realize is that there is no optimal betting if you are using a Play-All approach with such a small bankroll. With $500 in the game you are specifying your minimum bet would have to be $.50. Fifty Cent games have not been seen since the 1950's

However, you have enough money to spread 1-2 or 1-3 using a Wong-In approach and not entering a game at your "point of first advantage" - but waiting until you have more than a 1% edge before you bet. The problem with this approach is that even if you bet $25 - $50 this way -- your expectation will be to BET perhaps 15 hands per hour and that would probably yield you projected earnings of somewhere in the neighborhood of $9.00 per hour (by my back-of-the-envelope estimate) - around minimum wage in my State -- and with the inherent RISK of losing your $500.

Back to your original question re: When to raise your bet.
It depends primarily on the House Advantage and the efficiency of the Count you use. It always assumes that you are well capitalized, which you are not.

e.g. The game that you are describing is -.41 off the top. That is the ".e.v." The expected value - before a card is dealt. Let u ssay that you are using Hi-Lo, the most popular Count. Each digit of True Count moves that expectation (either Plus or Minus) by approximately .50

So ... A +1 True Count negates the House Advantage and leaves you with a miniscule advantage of .50 - .41 = .09 That is LESS than 1/10 of 1% of your bet. If you have bet $10 your "expectation" is an average win of nine (9) cents. Hardly the time to risk betting extra money.

However at +2 your advantage will be modest but tangible; rising to .59%; and now for each $10 wagered your expectation is to profit by almost fifty-nine (59)cents. This will justify a minimal increment in your betting.

Typically, Pro BJ Players look to get their Max bets out on the felt when their advantage exceeds 2%.

Folowing the examples thus far. If the Hi-Lo player has a +5 True Count then his advantage is 5 x .50% - .41 This equates to 2.50% - .41% = 2.0.9%

As such, out ten dollar better may be betting $150 with an expectation of earning 2.0.9% of that $150. That equals $3.27

At negative counts the House Advantage grows following the same principle.

 

[Kasi]

A +1 True Count negates the House Advantage and leaves you with a miniscule advantage of .50 - .41 = .09 That is LESS than 1/10 of 1% of your bet. If you have bet $10 your "expectation" is an average win of nine (9) cents. Hardly the time to risk betting extra money.

Except for, despite the fact you mean 0.9 cents, not 9 cents, probably because I'm using smaller fonts and not bolding renders this invalid, if only I used a bigger and bolder font in a dramatic color just to make it more true, not to mention that in this game, even by your "about standards", you are not even close to the advantage at that count, it actually is probably the count at which a play-all bettor would be increasing his bet.

I feel your pain playing with those innumnerate ploppies lol.

But, you still make some general valid points despite almost every detail being, in my world, what I would call "very poor" estimates of reality lol.

 

[blackjack avenger]

Kelly Criterion Betting

In this situation it is probably bet 0 because you probably have a 100% certainty of going broke and according to the Kelly criterion you should bet nothing!:joker::whip:

 

[SleightOfHand]

In this situation it is probably bet 0 because you probably have a 100% certainty of going broke and according to the Kelly criterion you should bet nothing!:joker::whip:

as long as he was betting low at - counts and high at + counts, hes playing a +EV game, no? mebe a 75% RoR, but not 100%. Give him some credit. hehe

 

[blackjack avenger]

Ok Ok

Given a 75% chance of going broke, he should probably bet 0!

 

[Sonny]

As others have said, you really shouldn’t be playing with only a $500 bankroll. You should aim for at least $5,000-$10,000 for card counting. To give you an example, here is what your bet spread might look like with a $500 bankroll:

<1 = $0
+1 = $1
+2 = $3
+3 = $6
>3 = $11

EV ~ $2/hour
RoR ~ 13%

Obviously you’re not going to find a $1 table, so here’s one for a $5 table:

<3 = $0
+3 = $5
>3 = $11

EV ~ $0.40/hour
RoR ~ 12.7%

That 40 cents per hour isn't going to have your bankroll growing very fast at all. But even a $5 table is going to be very tough to find, and even if you did it would be full so you couldn’t backcount it. Most tables are at least $10 minimums, which you really can’t afford to play yet.

From the Frequently Asked Questions thread:

Q: I didn’t realize that I needed such a big bankroll to count cards. Can I still play with a smaller bankroll?
A: Sure, as long as you understand the risks you are taking. If you are able to add some money to your bankroll regularly then you can play a little more aggressively. Here are some tips on playing with a small bankroll and supplementing your bankroll:
http://www.blackjackinfo.com/bb/showthread.php?t=5655
http://www.blackjackinfo.com/bb/showthread.php?t=5939
http://www.blackjackinfo.com/bb/showthread.php?t=9604
http://www.blackjackinfo.com/bb/showthread.php?t=9258

For more information about proper bet sizing, read the Gamemaster's BJ School in the Free Counting Resources thread, the threads on playing multiple hands in the FAQ thread and the book Blackjack Attack.

-Sonny-

 

[Automatic Monkey]

Given a 75% chance of going broke, he should probably bet 0!

It all depends on how important that $500 is to him. In the real world, if $500 is what you have available chances are that's a lot of money to you and playing blackjack isn't recommended.

Here's a quick reality check I do for ruin numbers. Suppose he walked into he casino with his $500 and put it on the Don't Pass line on a craps table. It's close to 50/50 that he will have $1000 at the end of the craps hand. Win again it's $2K, and win again it's $4K. That's enough to play a $5 game under Kelly criterion.

So if the probability of surviving 3 parlayed coin-flip bets is 0.125, and the probability of surviving with a full-Kelly bankroll is 0.865 (1 minus the RoR) the probability of doing both is 0.108. Subtract this from 1 and it shows the RoR with a $500 bankroll cannot be any worse than 89%, and it should be slightly better since advantage BJ bets are placed with a positive expectation even with an insufficient bankroll.

(Note: I am not suggesting putting your money on a craps table to build your bankroll! Just illustrating the math.)

 

[blackjack avenger]

Agree With Math, Not Conclusion, Well Sort of

It all depends on how important that $500 is to him. In the real world, if $500 is what you have available chances are that's a lot of money to you and playing blackjack isn't recommended.

Here's a quick reality check I do for ruin numbers. Suppose he walked into he casino with his $500 and put it on the Don't Pass line on a craps table. It's close to 50/50 that he will have $1000 at the end of the craps hand. Win again it's $2K, and win again it's $4K. That's enough to play a $5 game under Kelly criterion.

So if the probability of surviving 3 parlayed coin-flip bets is 0.125, and the probability of surviving with a full-Kelly bankroll is 0.865 (1 minus the RoR) the probability of doing both is 0.108. Subtract this from 1 and it shows the RoR with a $500 bankroll cannot be any worse than 89%, and it should be slightly better since advantage BJ bets are placed with a positive expectation even with an insufficient bankroll.

(Note: I am not suggesting putting your money on a craps table to build your bankroll! Just illustrating the math.)

My thoughts were also based on what his hourly EV would be, his bank is to low, its not worth it.

Chances are if $500 is all he has then $500 is a lot to him.

While one can start playing with a short bank while adding to it from outside sources. I don't think that equates to one trashing smaller amounts of money and hope to build a bank!:joker::whip:

With small amounts of money table minimums and tapping out during a trip or mid shoe can be very costly!

 

[EasyRhino]

bankroll of 500 dollars.

It's basically going to be kamikaze with just about any sort of realistic table minimums.

That's not *necessarily* a bad thing to do with the money, especially if the alternative was spending it on hookers and blow.

 

[callipygian]

It's basically going to be kamikaze with just about any sort of realistic table minimums.

While that may be true, I don't understand why people assume ROR's of 30-50% are bad for recreational counters, especially since bankrolls that small are replenishable to a certain degree.

ROR's mostly hold meaning for the people who are intent on winning long-term and reaching N0; if N0/hands played is long compared with your life situation, ROR's hold a lot less meaning.

Consider this: How many people in the world can actually tell the difference between a 1% ROR and a 5% ROR? Either way, if you were to go bankrupt, you'd be very unlucky. Neither betting scheme would set off red flags for any mathematical analysis. From a functional standpoint, you'd need to play several hundred bankrolls to tell the difference - and nobody goes through that many in their lifetime.

For someone who's going to play a few thousand hands per year, why would it matter of they had a one-year ROR of 50%? That's still one bankroll every 2 years of play, which, given a small enough bankroll, more than pays for itself in entertainment.

 

[EasyRhino]

True, a very small bankroll is almost, by definition, highly replenishable. Actually, *my* BR started at $500, I just didn't realize how lucky I got with early wins until a year or two later.

Playing with a 1% vs 5% ror is unlikely to make a difference in absolute ruin. However, the more conservative scheme is also much less likely to have large drawdowns in general.

 

[Kasi]

My thoughts were also based on what his hourly EV would be, his bank is to low, its not worth it.
Chances are if $500 is all he has then $500 is a lot to him.
With small amounts of money table minimums and tapping out during a trip or mid shoe can be very costly!

Well I guess you always have to keep in mind the game you will be playing lol.

Clearly it will not support a play-all scenario.

But, maybe like Flash said, if he does have access to a 5/6 S17 DAS with a $5min that he is allowed to back-count, why not back-count it and spread 1-2?

$500 would support that in a Kelly-way. With 100 units, his ROR is less than 9%. So he has a +90% chance of doubling his money and winning money forever. What's wrong with that.

Or wait until you have $700 and drop the risk to 3% if you want.

If it's a $10 min, and he can back-count, and he chooses to play at 30% ROR why not - maybe he likes the idea of turning the $500 into $1K more than 3 times out of 4 trading the higher risk for twice the $EV.

Sure his EV is low, maybe $2.35/hr, but only $500 is at risk. If the guy is disciplined, 3200 physical rounds later, he's at N0 and knows he can count and bet. I'd call him an AP player then even if that means he only won $400.

I have no idea where Sonny got his 40 cents an hour figure lol. Not that it matters, if it's Kelly, and you have the game available to play the way you want, take the 86% chance of winning money forever if you have to.

 

[blackjack avenger]

So I Am Clear?

So with small amounts? of money proper money management gets thrown out the window?

What is a small amount?
If the amount was $1,000 then is a 50% ror acceptable?
What about $5,000?

$500 is a lot of money. How many of you have tipped dealers $500 this year? Hey, this is not a lot of money, so why not? (sarcasm)

If the amount that can be made at bj is $2.50 then that is equivalent to about a $1.25 an hour job (certainty equivalent) and that is if playing properly! Throw in a 50% ror and he is wasting his time and money!:joker::whip:

With continuous resizing the growth rate for betting .5 kelly and 1.5 kelly is the same, with the overbetting having approx. 3 times the variance.

Now, if he bets over 2x kelly with continuous resizing his bank will dwindle to nothing!

We are talking some form of resizing upward with the $500, I don't think anyone would suggest he continues to earn $2.50 an hour!:joker::whip:

So according to proper money management and the real world low wage considerations he should not play until he has more money!

 

[callipygian]

Actually, *my* BR started at $500, I just didn't realize how lucky I got with early wins until a year or two later.

sup, $500 starting bankroll buddy

I still remember Wonging in with my "big" bet of $20. Those were fun days.

 

[sagefr0g]

i started with $300, always played $5 tables. luck can go a long way.

 

[Kasi]

So with small amounts? of money proper money management gets thrown out the window?

Can't tell if you are talking to me or not lol.

Couldn't agree with you more though.

I was just trying to suggest a way, if certain game and conditions actually happen to exist, that he could maybe make $2.35/hr with an ROR less than 9% if he chose to.

At least a possible way to avoid crazy ROR's like you say.

Same old song, know what to expect before you bet lol. Then do it if you like it or don't do it if you don't.

 

[takinfromindians97]

Can't tell if you are talking to me or not lol.

Couldn't agree with you more though.

I was just trying to suggest a way, if certain game and conditions actually happen to exist, that he could maybe make $2.35/hr with an ROR less than 9% if he chose to.

At least a possible way to avoid crazy ROR's like you say.

Same old song, know what to expect before you bet lol. Then do it if you like it or don't do it if you don't.

Haha the first time i went to the casino i had $200 with me and thought that was more then enough all i knew was basic strategy, and very basic counting.I won $800, used in the next time and close to doubled it. Haha i cant believe it now, knowing what i know now ugh god i was so ridiculously lucky. As my friend mr frog said luck can go a long way.We have all seen the ploppies who make all the wrong moves and win 10 grand at the tables.lol