How many max bets does a casino need to have?

If one were to run an occasional blackjack game with buddies, how big of a bankroll would he need? Lets assume 6:5 BJ, dealer H17, but all other rules quite liberal. DAS, Split to 4 hands etc...

Around how many max bets would the house need on hand?

What should max and min bet be depending on bankrolls of $1,500-$3,000; $5,000-$15,000?

This should be interesting. Thanks

It depends a lot on what kind of players you are expecting to get, what kind of bets you think they will be making and what the house procedures are. (Rotating dealer? Any player banking? Collection fees?) Uston has a chapter devoted to this in Million Dollar BJ. Basically, you estimate your EV and SD the same as any AP would, then adjust the table limits based on what kind of ROR you are comfortable with.

-Sonny-

Now i wonder

this guy works for casino offering 6:5 Bj and he is clueless whether it is good to offer even money or not..

As Sonny pointed out, chapter 18 in Uston's Million Dollar Blackjack is about being the house (and also about caddy blackjack). To give you an idea, with a $12,000 bankroll, he chose a $50 table maximum for a 5% ROR. And that was assuming the players were not very skilled and played at a 2.5% disadvantage.

Step 1: Using Shackleford's house edge calculator, the game you described will have a 1.5% to 2% edge over perfect basic strategy players (you didn't indicate if you allowed RSA, HSA, or LS). You'll have to decide if you want to adjust your theoretical advantage based on the anticipated skill level of the players.

Step 2: Head over to Norm's CVCX Online Calculators - Risk and plug in some numbers. Using the 1.5% house edge from above I used a 130 unit BR, WR per 100 hands of 1.5, and Std Dev per 100 hands of 11.5 (although this might not be the correct Std Dev for a 6:5 game) to get a ROR of 5.15%.

Step 3: Calculate table max (and min). If you had a $15,000 bankroll you could handle (15,000 / 130) $115 of betting action per round. Now divide that by the number of players per round to get the table max, so if you had 6 players the max should be $19.17, just say $20. But with six hands your risk is dispersed. Uston used a multiplier of .7 for 6 spots (I don't know the formula used for that but it's the same one that shows you can bet 1.5x your bet on 2 hands and have the same risk as 1x your bet on 1 hand), so $15,000/130/.7/6 gives a table max of $27.47, just call it $25. But are all the players going to be betting the max each hand? Your actual max per round is $164.84. If you think most players are only going to play $5-$10/hand then you may want to set the max to $50 to allow a player to occasionally throw out a big bet... unless they're counting, in which case you need to go back to step 1 and re-asses your edge The minimum is pretty arbitrary. Set it to whatever you want, or base it on a desired spread. If you wanted to allow players to spread 1 to 10 and the max was 50 then set the min to 5.

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I'm not working for any casino, I stated in the post that it is a friendly game of BJ amongst friends, which we rotate. I'm pretty knowledgeable in the BR behind an AP player but never as the casino so that is why I'm asking the question.

I'm not really sure what the point of your post is other than to try and attack me.

My head is spinning. I pretty much followed what you said, and appreciate those interesting links. But what does the number of players at the table have to do with anything? Would it be possible to just answer each question I ask above in a sentence or two?

The math will show you how much total action you can handle each round with a given bankroll and a given risk of ruin. This total action has to be equal to or less than the total bets placed by all players each round. If you only have one player then the max will be equal to the total acceptable action. If you have two players, then the max is equal to the total action divided by 2, because if you left the max the same as for one player and both players bet the max (or even if 1 player played 2 hands at table max) then you would be exceeding the total action initially calculated. Do you now understand why the total number of players (actually the total number of hands) each round is important?

So you want me to give you a fish, not teach you how to use a net. OK, if you tell me exactly how big your bankroll is, exactly what the house edge of the game will be, what your maximum risk of ruin tolerance is, the max number of hands per round (or if you don't know this then tell me how many players, the max number of hands each player can play, and the number of betting spaces on the table), and what bet spread you want to allow for the players, then I can give you the answer to both of your questions in one sentence each.

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Hey thanks for your extremely insightful response. I do understand why the number of players at the table matters, but to constantly fluctuate the maximum bet by the number of players who sit in and out seems like a real headache.

Bankroll- $4,220
H/E- 2.0188% (assuming perfect BS play which is not always typical)
Max ROR- 5-10%
1-2 players, 5 betting spots, max of 1 spot per player.
I'd like to know for a 1-20 spread and a 1-10 spread.

What I really would like to know is how much BR I would need for a $200 max bet assuming a 1-20 or 1-10 spread.

Thanks a lot.

The bankroll consideration is the same whether you're an AP or the house.

What is your edge, and variance, and ROR tolerance?

Same 3 parameters.

Generally the house has multiple tables going so that reduces variance.

Honestly though, I would be more concerned about your operations -- making sure nobody tries to beat your game by counting (though if you're doing 6:5 that's pretty much impossible), and that the hole card / next card aren't being exposed, and that nobody's cheating.

You're welcome. I'm glad that helped. For the record, I wasn't suggesting that you vary the max bet each round based on the number of hands played. Instead you should always set the max based on the worst case scenario of the maximum possible hands being played.

OK, I'm going to round the house edge to 2.02%, set your max ROR to 10%, and set max hands at 2. With those values:

About 125.

EDIT: Now that I re-read this and notice the "need on hand" requirement, I should point out that this is using a lifetime ROR calculation, not bounded by a time constraint. So you probably would not need that many max bets with you every time you play. If you can estimate the number of hands played each session, I can give you a more accurate value for how many max bets you would need "on hand" each time you play.

• 1-10 spread
  • max: $30
  • min: $3
• 1-20 spread
  • max: $30
  • min: $1.50

Ah, a third question. For a $200 max bet with all the other parameters remaining the same you would need a bankroll of $25,000. The spread does not affect the bankroll requirement, only the minimum bet. So with a 1-10 spread the min would be $20, with a 1-20 spread, the min would be $10.

WABJ11, feel free to ignore the rest of this post. I include it to show others how I came up with these numbers, either because they're interested in how to do it themselves, or perhaps someone like Sonny or QFIT will deem it worthy of a correctness check and chime in with a "yes, that's correct" or a "no, you're an idiot."

2nd question: Bankroll of 72 units with a WR per 100 hands of 2.02 and Std Dev of 11.25 give a ROR of 9.79%. I ran a quick sim with CVCX and it appears Std Dev on a hand of 6:5 is 1.125 not 1.15. I chose a multiplier of 1.15 for 2 players based on the value for 2 hands in table 9-5 on p134 in Million Dollar Blackjack. Like I said, I don't know the formula. So (( 4220 / 72 ) * 1.15 ) / 2 = $33.70.

1st question: 4220 / 33.70 = 125.2 (is that the right number of significant digits?)

3rd question: ((BR / 72) * 1.15) / 2 = 200. Solving for BR I get (BR / 72) * 1.15 = 400, BR / 72 = 347.826, and finally BR = $25043... which incidentally happens to match nicely with the answer to question 1. :grin:

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Lets assume my BR has doubled, and I'm willing to raise ROR to 20%. Whats the max bet I can safely take without going broke?

$100

...but I don't think I'd call a 20% ROR "safe." :laugh:

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