Deleted

[Badbeat]

Deleted

 

[gronbog]

The advantage x 76% number is a decent approximation of the optimal bet and is based on another approximation, which is advantage / variance. A simplified risk of ruin formula was published in Blackjack Attack, 3rd Edition and is RoR = e ^ (-2xExB / var), where e is the base of the natural logarithm (2.718281828459), E is your advantage in dollars and B is your bankroll.

 

[Meistro]

You discount how much you bet because of the possibility of doubling and splitting.

 

[gronbog]

You discount how much you bet because of the possibility of doubling and splitting.

Which is what partly contributes to the overall variance. To explicitly answer the OP's question, the variance of a typical blackjack game is approximately 1.31. 1/1.31 = 0.7634 = 76.34%. So dividing the edge by the variance or multiplying by 0.76 are approximately the same.

 

[DSchles]

You discount how much you bet because of the possibility of doubling and splitting.

And getting paid 3:2 for a natural.

Don

 

[Meistro]

You see, the Kelly Criterion is a recipe for bankroll growth for a series of even money wagers. By betting full kelly, that is to say by betting your advantage, you will experience the most rapid bankroll growth possible. But because blackjack is not a series of even money wagers, it is important to bet less than your advantage, otherwise you will be betting more than Kelly which ultimately is counterproductive for the purposes of bankroll growth as the swings entailed are too likely to cut down on your growing power. Hmm... I feel like this might be a syllogism and I am not explaining myself clearly.

Risk of ruin (ROR) is something that can be simulated.

 

[gronbog]

You see, the Kelly Criterion is a recipe for bankroll growth for a series of even money wagers.

Where did you come up with that?

By betting full kelly, that is to say by betting your advantage, you will experience the most rapid bankroll growth possible

Full Kelly is the bet which maximizes the logarithm of your expected bankroll after the bet is resolved. It is not simply betting your full advantage. Advantage divided by variance is a decent approximation of this. For blackjack, since the variance is approximately 3.1 for typical games, multiplying by 76% is also a reasonable approximation.

But because blackjack is not a series of even money wagers, it is important to bet less than your advantage, otherwise you will be betting more than Kelly

Games in which you do not change your bet also have variance. There are some +EV video poker games. The optimal Kelly bet for these would also consider both the EV and the variance. Hole carding 3 card poker and other carnival games is +EV and has variance and thus a correct Kelly bet based on both

Risk of ruin (ROR) is something that can be simulated.

I know some may consider this pedantic, but I do not. By the definition in BJA3, which is the definition we use when discussing optimal betting and Kelly, RoR is the probability of going broke if you play forever with your bankroll, never resizing your bets. It is not the commonly misinterpreted probability of going broke vs doubling your bankroll. The latter also exists, is different and can be simulated. The former cannot be directly simulated without some sort of stop heuristic for the cycles where the player never goes broke.

It is more correct to say that RoR can be calculated (using the formula I gave above) from data (EV, Variance) collected by a simulator.

 

[JohnCrover]

Let me put it this way. I’ve been practicing for a couple months now and I’m going to get some hours in at a low stakes game to get comfortable and see if I have what it takes to be successful at this. The game has very good rules. $2 min, 6deck, H17, DA2, DA3, DAS, RSA, LS, Pen 1.5-1.75. I haven’t invested in CVCX yet. I don’t want to make any cover plays. I don’t care if I get backed off. I want to play the most optimal game possible. If someone wouldn’t mind helping me out with a bet spread and bankroll size I’d appreciate it.

You say you don't mind getting backed off now. I know you're just trying to play a good game and you're not even sure if you're good enough to beat the game yet but let me tell you, you will care about getting backed off. Take it from me, I was in your position not too long ago. When I got backed off for the first time I thought "oh cool, I'm good enough for the casinos to think I'm a threat. Looks like I'm doing this right. " After my second back off I started to get a little nervous because I was running out of casinos. By my third back off I wanted to cry. I was SOL with no casinos left in the area to play.
Learn from the mistakes of others instead of making them yourself. Take heat seriously, for your name and face have not been burned yet.
As far as your bet spread goes, we need to know how large your bankroll is and how much risk you're willing to take. How much money are you okay with losing?

 

[JohnCrover]

I live in Las Vegas and this will be at a small casino not owned by any of the big companies. There are a lot of casinos to choose from here. If I’ve got what it takes I’ll definitely try to cover when I’m playing higher stakes at bigger name casinos. As for bankroll, since I am just trying my hand at this I’d like to play with as small of bankroll as possible. I’m probably ok with losing a couple thousand but I really don’t have a limit. I would prefer my ROR not to be outrageously high because I don’t want to go bust and never know if it’s me or the variance.

Okay, 2k bank roll 2 dollar min bet, in theory, you shouldn't have a max bet. Your wager should be a percentage of your bankroll that is your current advantage. For example: if your advantage is 5% you should bet 5% of your bank roll so 5% of 2k BUT the Kelly Criterion wasn't made for blackjack so you should be more cautious. For each 1% advantage you have you should bet about 0.75% of your bank roll due to the variance in BJ.
To answer your question simply though: go in with a 2k bank roll and spread 30 dollars Max bet to 2 dollars min bet. This is a very large spread but since the stakes are so small a 30 dollar bet probably isn't going to get much attention, especially on a busy night. If you lose 2k with a 30 dollar Max bet you're probably doing something wrong.

 

[JohnCrover]

A spread shouldn't top out in theory, because it should be a percentage of your bank roll in correlation with your advantage.
You should spread more aggressively because 1.5 to 1.75 decks cut off from the game isn't that great so you're going to want to get your max bet out there sooner to compensate for that.
At a true count of 4 you should have roughly a 2% edge so it's not like you're going to be over betting your bank roll. I suggest you spread 2,5,15,30 .
You should probably buy some software to help you out.

 

[cgasucks]

If I’m good at this I’ll definitely buy some software. Thanks for the help. I just threw $2000 out there randomly when you asked. What I’m gathering though is that around $2000 would be a recommended minimum bankroll for a $2 table. I have read that your betting unit should be 1/1000 of your bankroll. Thanks again. I appreciate it.

I'm new myself (been learning this game for 2 months) and based from extrapolating numbers from the Optimum bet chart from this site I came to the conclusion you need $525 for every $1 of min. bet. In your case it is $1050 (2 x $525). This bankroll only applies to a 6 deck game using a 1 - 12 bet spread as per the Optimum bet chart. If I'm wrong please correct me.