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- Thread starter Badbeat
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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.
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.
Risk of ruin (ROR) is something that can be simulated.
Where did you come up with that?
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.
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
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.
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.
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
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.
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?
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?
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.
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.
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.
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.
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.