Formulas?

Ok, I've read and read and read and decided to now ask because my head is now spinning. I play 3 games; BJ, Poker, and Craps. I play the way I play and haven't had to work the proverbial M-F 8-5 in almost 3 years. I'll never be rich the way I play, but my intent is to never work again unless I want to. From this site I've read systems are a wash (and when put to the 1Bil test, I agree), but there are many pro gamblers out there, so I'd like to know how they do it. My 1st step is to analyze myself; I want to see if my way of playing makes sense mathematically, or am I just one of the luckiest people on earth. I'm sorry if this question is elementary compared to other question, with that said, here is my question...

1...I play BlackJack, 3 hands equalling 1 segment...how do I calculate how many combinations (Win, Push, Loss) are possible in each segment? I assume 3^3=27?

2...Probability; how do I calculate the probability of each combination?

Example...Win, loss, win

Assuming win=.4331, push=.088, loss=.4789...do I take .4331*.4789*.4331=.0898? If this is correct then wouldn't that mean any combination of 2 wins and 1 loss would have the same probability? I don't see how that could be correct...please correct my math.

With black jack you have several outcomes : Win, Push, Loss, Blackjack, Double down win, split win (and losses) etc.

But assuming the numbers you give :

Won-Loss-Win can occur in 3 different ways (WWL, WLW, LWW). Assuming the probabilities aren't related (they sort of are in blackjack, as each hand isn't quite independent of the previous one due to the deck changing, but lets ignore that for clarity here) then a 2 win, 1 loss sequence will occur 0.0898 x 3 = 0.269 ~27% of the time. But yes all three should have the same probability... not sure why you'd think they don't?

At this point I'm only looking at the final outcome of each hand, not how I got there. Was I correct that there are 27 total combinations of W,L,P?

Aren't the hands independent when using a continuous shuffler with 5 or 6 decks?

Yes, for all intents and purposes, each hand is independent.

Yes there are 27 possible sequences (3*3*3).

The only reason I mention splits, doubles and black jacks is that the net result to your bank roll will be different in some of the win and loss results.

First, thank you for helping a rookie!

I understand about the splits and doubles. I'm new to the math side of this so I decided to split this up for no other reason than ease. For my preliminary calculations I decided to ignore double and split hands. I assume if I play basic stradegy then when I have double and split opportunities they are mathematically better for me than a normal hand or the stradegy wouldn't tell me to double or split...correct? So, for my prelim calculations I just group them in as normal W,L,P to get a minimum net result for my bankroll. Therefore, when I do get better at this and calculate more precise numbers, they should be better (more profitable) than the prelims...correct?

Yes, that seems like a fair assumption to get a rough idea.

By "more profitable" I would assume you mean "lose less"... you -shouldn't- be able to calculate a positive expected value for blackjack without the blackjack/splits/doubles being taken into account (and even then you shouldn't get a profit on anything but the craziest of rules that are in the players advantage, which mostly revolve around small decks, splitting rules, surrender and 3:2+ blackjacks).

If you do calculate a positive expected value, it's probably a sign you've made an error in your calculations or assumptions.

Yes, when I say more profitable I also mean less loss. I haven't finished calculation, but I'm working on them. I can't program so I'm doing them by hand with excel. By what I've read, my assumptions are there isn't a way to calculate a positive EV. Therefore, I'm trying to get as close as possible to even, although I've read that isn't possible for BJ either. And the rules I most frequently play are 6 decks continuous, split A's once, 1 card on split A's, yes double after split, double on any 2 cards, no surrender, and 3:2 BJ.

My main question is this...

What is your opinion on; if there are no systems that produce a positive EV, how are there pro gamblers other than poker players?

Quote: R6RacingR6

I assume if I play basic stradegy then when I have double and split opportunities they are mathematically better for me than a normal hand or the stradegy wouldn't tell me to double or split...correct?

Well, yes.

However, playing basic strategy is still a losing proposition. I have no idea how do you manage to make full-time profit on gambling without being a WSOP-eligible tourney player or at least a highly skilled card-counter, but then I guess the variance required isn't any more than that for winning a lottery or hitting a big jackpot.

How you size your bets, except in accordance to count, doesn't matter. The math you are talking about resembles that for betting systems, but it's not worth bothering with, if a calculation shows positive EV that way, it's an error in the calculation - the combined EV will always be -HA*sum(B1..Bn). Thus, any bet sizing with the same average bet size will result in the same loss amount.

Quote: R6RacingR6

Therefore, I'm trying to get as close as possible to even, although I've read that isn't possible for BJ either. And the rules I most frequently play are 6 decks continuous, split A's once, 1 card on split A's, yes double after split, double on any 2 cards, no surrender, and 3:2 BJ.

I'm not a Blackjack expert, so can't tell you how close to 0 you'll get with those rules, but you can get pretty close. But I also think doing exactly what you are doing is worthwhile... nothing beats learning this stuff for yourself and seeing how it works out.

EV isn't the be all and end all... variance is also important.

Quote:

My main question is this...

What is your opinion on; if there are no systems that produce a positive EV, how are there pro gamblers other than poker players?

They are either counters, using some other sort of advantage play, have got lucky (variance in some games can lead to winners over the medium term) or are lying to sell you a book/system/course.

"some sort of advantage play" covers a whole heap of ground... including sports bettors with very good knowledge, comp hustling, using vouchers to your advantage, finding edges where no-one expects (and don't expect to have those shared out) and others. Not an expert on those items either.

The rules in question are pretty lousy. Well, mediocre by modern standards. It's a HA of 0.46% for S17, or 0.68% for H17. Such rules can only be beaten by ABC counting (it rarely works today, you get booted), large bet spread, or a skilled counter. Even in the latter case, the earnings to bankroll ratio is small enough to be beaten by good investment with lower risk.

Quote: R6RacingR6

My main question is this...
What is your opinion on; if there are no systems that produce a positive EV, how are there pro gamblers other than poker players?

Systems don't produce positive EV. Positive EV can only be obtained by card-counting, for most rules with large (at least 1-10) bet spread. 1-20 with wonging is preferable.

There is only a very small number of successful card-counters today, almost everyone has either moved up to poker or further up to financial instrument trading, or only plays blackjack on the side, more for recreation than for gain.

As to the mention of sport bettors: advantage sport bettors tend to be arbitrageurs or use another form of exploiting the rules, rather than straight handicapping, and when they are, they tend to make money selling their services rather than betting directly. As for comps, they are fun, but ultimately not something to make your living from.

Gambling period is a losing proposition over time. If it wasn't then there wouldn't be casinos on every corner. Mathematically, I guess all we try to do is get our money in at the best possible time. Mathematically, what else can we do? I'm just now learning about variance and statistics because I want to start risking more. Even though I'm a rookie at math, to me your statement,"but then I guess the variance required isn't any more than that for winning a lottery or hitting a big jackpot" sure sounds like, even a blind squirrel can find a nut lol. Maybe I am just lucky, but haven't you ever been able to do something and don't know how or why? Well, that's why I'm here. I'm trying to find out how or why. Does almost 3 years of consistent play mean I'm a pro...I don't think so. But only because I'm not driving a lamborghini with a huge house. For now my toyota camry and middle class house will do. But if being here learning can help me find the keys to my lamborghini...then why not? :)

Maybe I'll just learn to count cards :)

Quote: R6RacingR6

Even though I'm a rookie at math, to me your statement,"but then I guess the variance required isn't any more than that for winning a lottery or hitting a big jackpot" sure sounds like, even a blind squirrel can find a nut lol. Maybe I am just lucky, but haven't you ever been able to do something and don't know how or why? Well, that's why I'm here. I'm trying to find out how or why. Does almost 3 years of consistent play mean I'm a pro...I don't think so.

If you're ahead over 3 years of gambling, without using AP methods, and not only are ahead, but made a living out of it, however hard it is to believe, but if it's true, you have to consider yourself equivalent to a lottery or jackpot winner.

Quote: R6RacingR6

But only because I'm not driving a lamborghini with a huge house. For now my toyota camry and middle class house will do. But if being here learning can help me find the keys to my lamborghini...then why not? :)
Maybe I'll just learn to count cards :)

This might be not the best forum to find these keys. If you really want to get ahead, you need to shift into more serious fields like commodity trading, which can deliver consistent profit with less variance.

The difference between casino gambling and stock trading is that the former is a negative sum game, and the latter a positive sum game. That is, in the former, the combined EV of all players is negative. It's still negative even with the casino itself included, because of its expenses. In the latter, the combined EV of all players is positive: they may drop short and mid term, but long-term stocks grow with the economy. So while a casino AP has to be constantly fighting a house edge, an investor starts out with the odds being in his favor and uses his skills to further his gain.

I do have another question...

I was reading on this site about the 1 challenge (Rainsong) that was actually put to the 1 billion test and lost. How many of us will ever see 1 billion hands? I play BJ about 3 days a week 4 hours at a time. I believe over time you will lose. So I try to get in and out asap win/lose (within reason) by slowing down when things are bad...and bigger bets when things are good. Almost like a card counter just without the actual counting. Ignoring size of my bets...If there is an average of 60 hands an hour at 4 hours times 156 sessions a year...that's 37,440 hands a year. I'm 35...so lets say I have 50 years of playing in me. Why test a system 1 billion times with the same bankroll? Why not test a system with X(bankroll) by 240 hands (simulating a session), then bringing X back to the original starting point and doing it again 7800 times (simulating 50 years of sessions)?

My question is...Mathematically, had they done that with Rainsong, would it have resulted in the same outcome?

Quote: R6RacingR6

I was reading on this site about the 1 challenge (Rainsong) that was actually put to the 1 billion test and lost. How many of us will ever see 1 billion hands?

Doesn't matter. A billion is just overkill to mitigate variance. Over a million hands, the most likely results will still be close to house edge. But blackjack is a high-variance game, even a million hands can elevate a BS player or ruin a counter.

Quote: R6RacingR6

I play BJ about 3 days a week 4 hours at a time.

That's tens of thousands of hands. And you really keep winning? What is your bankroll and average bet size?

Quote: R6RacingR6

Why not test a system with X(bankroll) by 240 hands (simulating a session), then bringing X back to the original starting point and doing it again 7800 times (simulating 50 years of sessions)?

If you sum up the changes in bankroll, the result will be approximately the same as one 7800*240=1,872,000 hand long session.

Quote: P90

The difference between casino gambling and stock trading is that the former is a negative sum game, and the latter a positive sum game. That is, in the former, the combined EV of all players is negative. It's still negative even with the casino itself included, because of its expenses. In the latter, the combined EV of all players is positive: they may drop short and mid term, but long-term stocks grow with the economy. So while a casino AP has to be constantly fighting a house edge, an investor starts out with the odds being in his favor and uses his skills to further his gain.

Very nice point. Definitely something to look into. I didn't choose gambling, I kind of fell into it and it has worked out...so far.

I'm going to ignore your 1st comment about the lottery winner because I'd like to cling to the notion that I had at least a little to do with my little success. I hope I did just a bit more than the equivalent of buying a lottery ticket at the corner store or dropping a dollar into a slot machine.

Quote: R6RacingR6

I'm going to ignore your 1st comment about the lottery winner because I'd like to cling to the notion that I had at least a little to do with my little success.

Perhaps. But the expectation was to lose. If you keep at that, you will more likely lose than win, unless you count.

However, there is a lot of variance. Here is a simulating analyzer if you want to try it out: http://www.jacobsongaming.com/Blackjack_Analyzer.html
It essentially just plays out a lot of hands and gives you the bottom line.

Try setting it to 6 decks, 1-20 spread, 70% penetration, H17, DAS, and a count of choice. Keep an eye on the Bankroll field. Notice how even over a million hands, under the exact same conditions, the results can easily vary between -1.5 million and +1.5 million. And that's over a million hands.

Thanks! I'll play around with it and see what happens.

Quote: P90

That's tens of thousands of hands. And you really keep winning? What is your bankroll and average bet size?

We're getting a little personal so here are some numbers...

I rotate table limits depending on how the week/month has been going. I either sit at a $25 or $100 table and bring about 40x the tbl minimum. I don't know my actual average but on the 25 my bets are between 25 and 50 with a few 100 bets. On the 100 tbl they are 100-200 with the occasional 400 bet. Winnings are divided 50% (my weekly paycheck) 25 (bankroll) 25 (savings, not to be touched for gambling). I started at $5 tables and been at 25s about 2 years and started 100s about 6 months ago. I'd get a job if my bankroll was ever gone.

To sum it up, I was making about 60k working and got laid off. My severence financed this and now I'm as comfortable as when I was working but without the 40 hrs a week.

Quote: R6RacingR6

We're getting a little personal so here are some numbers...

It's just that it's quite far out there on the bell curve to turn a consistent gain in a -EV game. I suppose it's possible, the same way as it's possible to be a beneficiary of many other events considered luck. But if you don't believe in luck, don't count on this going on. It won't necessarily reverse, but the odds are against you, and no system (other than counting) can change that.

You've only been through about 100,000 hands, as it seems, which means variance dominates. However, even so, if you try the simulation, you have to hit the button a lot of times to get a positive bankroll change without a count, or a few times with a weak count like A-5. Notice though how massive a difference even a primitive A-5 count makes, from only a 2-3% chance of overall win to about 20%.

What you had to do with it is play your cards right, but the cards dealt to the player, on the average, still lead him down even if played perfectly.

I'm playing with it and honestly I don't know what some of these settings are.

Bet spread...
sit out minus counts...
deck penatration...how does this work assuming continuous shuffler?

It doesn't, the simulator is for evaluating counts. But you can use the minimum setting (25%). It doesn't matter without a count.
Bet spread is just that, max:min bet ratio.
If you don't count, then of course you can't sit out negative counts.

Ok, so for max/min it would be 50 25 for me...correct? cuz at a 25 tbl i bet 100 every once in awhile randomly.

I'll play with it more later. But I'm thinking it doesn't do what I'd like it to do. I'll search around and find one.

Back to your point...I agree with you, 1 day the roof is going to cave in. Which is why I thought I'd start researching and getting better at the math part. But I also play craps and poker. Between the 3 I'd say I play more poker then BJ then craps. Only reason poker is higher is because it's a slower game so I sit much longer. Although, of the 3 I think if I'm going to increase earnings I should start with BJ.

Lets be clear, there have been some hard times in 3 years, it's not all fun and games. Unprofitable weeks mean I don't get a paycheck. So imagine working and just not getting a paycheck for a week. The reason why I'm still above water is because my bankroll hasn't hit zero. It's a grind but much better than my last 8-5.

I would say still focus on poker. Most of your winnings probably come from there anyway. Top 10% of players consistently win at poker (and the full 100% includes tourists and first-timers), but only maybe top 0.1% at blackjack. If you don't believe in luck, poker is where you can keep making money even without it. If you do, a pair of rockets still nets a grand in poker with only $20->$250 risked, but only $400 in blackjack with $100->$200 at risk.

But you can reduce the risk of losses at blackjack by learning BS+CDE and an A-5 count (A-5). It's still not a winning proposition under realistic circumstances, but at least can work out even.