blackjack theory

Hi Michael,

Love the site and was pondering a question that you may be able to answer. I was wondering if there is math to support a theory I have. If all I am trying to accomplish is be up one hand in blackjack (example: playing $100 a hand and all I want is to be up $100) I wanted to know how often can you be up just one hand versus down 2,3,4,5,6 etc hands. I ask this because if say as an example with no math basis I can be up one hand 90% of the time then by flat betting $100 I could theoretically play to be down 8 hands at $100 a pop before leaving the table and still be up $100 if that 90% held true playing 10 different sessions. So my question is is there a way to figure out the odds of being up one hand before being down 2,3,4,5,6,7,8 etc hands and at each point what is the odds of it ( ex odds of being up one hand before being down 2 hands) Once I see the math then I can play optimally knowing exactly when to leave. Also if its not too much trouble add odds of being up 2 hands or three hands before being down 1-8 hands.

Thank you

Welcome to the forum. Well, I'm not Mike nor am I the most capable "math guy/gal" on the site, but I'm going to comment anyway.

A problem with your theory that has been discussed many times on this forum is the concept of managing sessions. It is better to regard play as one long continuous game with periodic breaks. When you take the breaks (manage sessions) doesn't change the long run results. Your theory of play might lead you to take breaks when you are up or after a loss-limit is reached, but you will not profit long term. You won't break even, either. Not even close.

That said, the analysis you requested will require more information; the specifics of the game you play. The usual stuff. Online or casino. Number of decks. Shoe or CSM. Hit/stand on soft 17. Etc.

If you can program, you might consider doing your own simulation for the answer although it is not an easy problem. The nature of the game isn't single wager, then win or lose and equal amount. Blackjacks, splits, surrenders and double-downs need to be accounted for. I suggest a simulation as that is often an easier way to approximate an answer than doing the heavy-lifting math.

Good luck!

Hi,

thank you for your reply. Lets say for example its a casino. six deck shoe hit on soft 17. I do not know how to program which is why I posed the question. I've only noticed my results and they've been positive to the point where I'd like to see concrete math evidence.
while this issue has kind of been discussed ( /forum/questions-and-answers/math/25942-how-to-calculate-session-odds-with-standard-blackjack/ ) but not throughly enough to truly answer my question.

So from this previous post the OP asked and mustang sally answered that while flat betting you"d be up 3 bets 85.826444% of the time before ruin if ruin was 20X the flatbet amount. So what I get from that is with a $2000 starting stack you could win $300 roughly 17 of 20 sessions but you'd lose $2000 the other 3 attempts. 6000 lost and 5100 gained leaves you at -900.

So my question is is there a number of bets you could be up before being down a certain amount of bets that would make for a positive ROI?

Why do you have to leave after making your $100? Why not just get up and walk a lap around the casino floor then sit back down and start over and make another $100? You could do this 20-30 times a day instead of just making your $100 once a day and going home and coming back

Quote: smkhitaryan

Hi,

thank you for your reply. Lets say for example its a casino. six deck shoe hit on soft 17. I do not know how to program which is why I posed the question. I've only noticed my results and they've been positive to the point where I'd like to see concrete math evidence.
while this issue has kind of been discussed ( /forum/questions-and-answers/math/25942-how-to-calculate-session-odds-with-standard-blackjack/ ) but not throughly enough to truly answer my question.

So from this previous post the OP asked and mustang sally answered that while flat betting you"d be up 3 bets 85.826444% of the time before ruin if ruin was 20X the flatbet amount. So what I get from that is with a $2000 starting stack you could win $300 roughly 17 of 20 sessions but you'd lose $2000 the other 3 attempts. 6000 lost and 5100 gained leaves you at -900.

So my question is is there a number of bets you could be up before being down a certain amount of bets that would make for a positive ROI?

You will never get a positive ROI flat betting.

When I play video BJ, I flat bet, and I start with a bankroll of 10x bet with a very simple strategy... double or nothing.

Quote: michael99000

Why do you have to leave after making your $100? Why not just get up and walk a lap around the casino floor then sit back down and start over and make another $100? You could do this 20-30 times a day instead of just making your $100 once a day and going home and coming back

no need to be rude; if you have nothing of substance to add, scroll on by

Quote: smkhitaryan

So my question is is there a number of bets you could be up before being down a certain amount of bets that would make for a positive ROI?

Hi smkhitaryan, and welcome to the forums.

Not to sound rude, but to give you the answer you need, there is NO WAY money or session management will EVER yield a positive ROI. The house has a built in advantage to the game. Without changing that advantage (aka card counting, identifying when the edge has moved to the player based on effect of card removal) you simply cannot beat blackjack with money or session management. There are some other forms of AP'ing (aka changing the advatage) that are more advanced, and won't get discussed too much online (loose lips sink ships), but the end all to your question is: You cannot beat blackjack without changing the house edge.

Since you want some math, here's some math as to why.

EV(x hands) = (x * AvgBet)*(HouseEdge)

So let's say you play 100 hands and stop, flat betting $100, at an average .5% HE game (possibly H17 with surrender and RSA or something)... What's your Expected Value (EV)?

EV(100 hands) = (100 * 100)*(-.005) = -50

So there's variance in the game, which will allow you to be up or down on any one session, but the more hands you play in your lifetime the more the variance will reduce and you will eventually hit your expected value. That's the math of the game. That's why the casino offer the game. The law of large numbers...

So let's say you play 1,000 hands, at the same game, then stop. What's your expected value?

EV(1,000 hands) = (1000 * 100)*(-.005) = -500

Now 10,000 hands...

EV(10,000 hands) = (10000 * 100)*(-.005) = -5000

...Do you see how since you're never changing the house edge (-.005) that you're NEVER going to be ahead in the game (in reference to winning 'consistently' and over the long run)? Stopping a session does nothing to this math. As BleedChipsSlowly pointed out correctly, you should think of your LIFETIME as one long session. When you leave the table you're just taking a bathroom break in your life long session. When you return (the next day, month, year, whatever) you're just continuing the same session and adding more and more hands to your lifetime of play.

If you'd like to learn a bit more and see a bit more math on why money/session management won't beat the game, and learn a little bit about card counting, please feel free to check out the 3 Articles I've written that are posted in the Articles section of this very site:

https://wizardofvegas.com/articles/A-to-Z-Counting-Cards-in-Blackjack/
https://wizardofvegas.com/articles/A-to-Z-Counting-Cards-In-Blackjack-2/
https://wizardofvegas.com/articles/A-to-Z-Counting-Cards-in-Blackjack-3/

Quote: smkhitaryan

So from this previous post the OP asked and mustang sally answered that while flat betting you"d be up 3 bets 85.826444%

that data was for being up at least 1 betting unit sometime during X rounds played

Quote: smkhitaryan

So my question is is there a number of bets you could be up before being down a certain amount of bets that would make for a positive ROI?

the simple answer is no, but to give any data the rules of the game must be made known.

one could play a 6 deck game with NO double-down or splits
but even with that one could be up 1.5 units and that is different from what you asked.
They could also be up 1/2 unit and that might be fine for some too.

so
one should start with some basic rules and go from there.
also is the player making flat bets and following Basic Strategy
as that would make the math easier

Sally