betting question

[michael990]

If I sit down at a blackjack table with a $2500 bankroll, betting $100 per hand, playing perfect BS, what are the chances that at some point from the first hand on I will find myself up $100 for the night? In other words, what are the chances of me reaching $2600 before reaching $0?

I ask this because I saw in another post that there was a survey taken at casinos and it showed that 75% of all people leaving a casino were showing a profit at some point in their visit. This puzzles me because if all games have a house edge, then shouldnt the % of people that were ahead at some point be equal to the average house edge of all games played (which would then mean that maybe 45% of all people should have been ahead at some point)? That survey would imply that people lose simply because they dont know when to stop, and I always thought people lost because the games were in the houses favor.

[LeonShuffle]

All this talk of walking away doesn't make any sense to me. Ask yourself what your plan is. Is it to go to the casino, win $100 and leave happy that you've won $100. Then go back the following week and try it again? Well, if it works, why wait a week? Why not go to another casino and do it again? Or another table. Or the next shoe. Or immediately. You could just keep pocketing that $100 and start all over again.

Well, unfortunately, it doesn't work that way. If you've played a fair amount of BJ you'll have had sessions in which you were NEVER up.

If the odds are against you, as they are in BJ or any casino game, and you don't keep track of which cards are gone, there is ABSOLUTELY NOTHING you can do to change that.

You could go with a million dollars, win $10 and go home happy. You could probably do that a few hundred times in a row. Then one day, you'd lose the million, but hey, at least you've "won" hundreds of times compared to just one loss.

I apologize if this comes across as sarcastic. I've heard too many people with sure-fire ways to beat the casino (I'm not saying you're one of them). I GUARANTEE NONE of them works.

In the early 80's, my father went for a few years without a job. He played blackjack for a living. He made enough to support himself (he had stopped supporting us some years earlier). He did this by counting cards. That is the ONLY way to beat this game and I'm not so sure that THAT is even possible anymore.

Leon

[wds_42]

I don't believe that counting cards is the only way to beat the game. Maybe if you play proffesionaly, but not recreationaly.

I've been playing BJ for over 20 years, never counted cards because it was too much like work and I ain't all that smart. I go to the casino to have a good time. If I make a few bucks, then that makes the time all the better. I've kept track of my wins and losses and I can honestly say that I'm on the positive side of things by a few thousand bucks. Not a great return from an investment standpoint, but how many hobbies give you a positive cash flow?

Talking about walking away makes perfect sense. For whatever reason, bad karma, phase of the moon, brain farts, too much to drink, whatever, a player wil have bad days and needs to recognize that they are simply tossing money. The key is to be able to walk away and find something else to do instead of walking to the next table/casino.

I'm sure one of the stats boys here can give you the probability numbers of your $2600 vs. $0 question, but just from a logical stand point, I would say that your survey makes sense. Yes, a good number of people would have to be up at some point during their play or people would not contiue to play. How many people would sit for hours constantly losing? The casino edge comes from the fact that people just don't know when to quit.

[Nickels_n_Bullets]

Interesting question. I won't go the full route of stats because there is one important factor left out. How much is the return per hour YOU wish.

All the numbers don't mean squat if a) you don't obey them and/or b) the unit size risked is too high.

For example 1 std. deviation for BS is about 11.5 units per hour. You come armed with $2500 expecting to play 25 hands at $100. Thats 1/3 of an hour. Lets call it 4 units for 1 std. dev. By bringing 25 units you apparantly cover a 6 std. deviation loss. IN 20 MINUTES. Play longer, and you erode this protection, and lessen the chance of gaining the amount proportional to your extended play (Re: playing 40 minutes has to win or lose 8 units.) Apparantly, you should play to win or lose 4 bets.

But, you might be happy winning 2 bets, and leave before the 25 hands are through. And you might have to suffer an 8 bet loss, never being ahead.

So if the financial goal is better expressed as a $ amount, rather than a unit amount, one has to size the units properly. Playing for +/- 4 bets would be better siuted to a $50 bet IF $200 is your financial goal. As you wrote it, it would appear that winning 3 or 3 1/2 bets ain't makin' it.

[Ray]

Your very best shot at 2600 is on the first bet...47.5. After that no one
can tell because the game of blackjack has swings that take on a vast
number of shapes. At times it looks like a mountain range and other
times more like a table top or a mixture of both. The very best one can
say is at some SD you can play so much time with some percentage
chance of not going broke. Example: (2) SD(money) will allow you to
play (x) time with a 75% chance of not going broke.

Another way of looking at it is if you lose the first bet, then you need to
win two and your chance of doing that is 22.56%, lose two and it's 10.71,
lose three and it's 5.09,etc. But, don't get me wrong, you could lose 10
in a row and still come back and win the $100 to equal 2600. The problem
is that you can't put a probability on that happening..

Ray

[Nickels_n_Bullets]

For ONE hand the the outcomes are roughly 43% WIN, 49% LOSE and 8% TIE. I consider it as 3 in 7 WIN, 4 in 7 DO NOT WIN (lose or tie).

For the optimists amongst us all its 49% LOSE, 51% DO NOT LOSE (win or tie). Perhaps this way of looking at it better illustrates the house perspective... the dealer collects 49% and does not collect 51%. From this point of view its easier to understand why the player does get ahead.

[Liezel]

hmm, no one still has answered michael's question though... if one has $2500 what's the % that he'll make $100 at a $100 table in x mins or whatever? is there some sort of formula?

Also, what about how long it will last when it comes to x amount after the table minimum bet?

[Ray]

Liezel- Ten birds are sitting on a power line. Counting left to right,
can you tell what percentage of the time bird number 5 will be the
first bird to fly away. In real life, it is possible that he will always be
the last to fly. It's even possible for him always to be the first to exit.
What brand of logic could we use to answer the unknowable.

Ray

[kaiser]

Ray - I'm pretty sure that there's this thing called probability that could answer his question. I just don't remember the formula's off-hand, but you could definitely calculate it. I can do the first couple iterations in my head, but I don't remember how to bring it all together.

But, I think he may have answered his own question. He said that a survey shows that 75% of people at casino's showed a profit at some point. I'd say that sounds about right.

Most games, you'll show a profit for at least a little while. The problem is that you don't know when that profit is coming, and how high it's going to go.

[michael990]

Ran my question by a buddy of mine who was a stats major. To the guy who gave the example of ten birds, you are wrong, it is possible to answer my question. When you know the factors we know:starting bankroll, goal, and most importantly % chance of winning per hand, you can run formulas to figure it out.

He did a preliminary run through for me and came up with 96%. You have a 96% chance of winning 100 before losing 2500. This makes sense because if you did this exercise 100 times you would lose all your money 4 times which would be 10,000 dollars total, and you would win 100 dollars 96 times which would be 9600 total, thus the house edge.

Also, to the guy who said something about it not mattering whether you quit now and come back another day, or quit now and keep playing 5 minutes later..theres alot to be said for leaving the casino with a good taste in your mouth for the game. Look at it like this: if i sit down at a table and get ahead and leave, i have in a sense beat the odds for that session. And when I come back a week or month later, my odds of winning are not lessened because I won the week before. Each time I sit down my chance of success are exactly the same, even if I have won my last 25 times I played. Each session is independent of prior sessions.

[Ray]

Probabilities the universal method:

P(A)=The number of ways an event can happen / The number of possible
outcomes.

In our case..... Win = the number of ways an event can happen(1)

On the first bet the possible number of outcomes = 2 (win or lose)
Thus 50% prob. to win 100(forget the house edge) that is 1/2=.5

If you lose the first bet, the number of possible outcomes remains at 2
win/lose but getting to that outcome for a win has a large number of
possibilities. I can't seem to identify the number of possible ways that
you can get to your goal.

Ray

[Ray]

Michael990- I'm not a stats major and I could be wrong, but I would like
to see the method your guy used. I can think of a "trials" method that
could give some probability based on lets say a 1000 trials of actual play.
The idea behind the trials method is that 1000 samples may reflect the
result of all the possibilities and you arrive at the probability based on
the success that you had.

The reason I question being able to arrive at some number is that I've
never seen such numbers published and used to ones advantage in a
blackjack strategy. It would seem that an individual could arrive at some
strategy that would take advantage of this knowledge. But, the fact that
I've never seen it, may not be saying much..................

***Update...Never mind Michael I found the math and it looks like I was incorrect: %P=BR/BR+W.....So %P=2500/2500+100=2500/2600=96%

Also, 2500 is approx 2 SD for an ave bet of 100. so, you could play
about 2.x hrs at 60 hands per hour.

Ray

[michael990]

not sure if thats the formula he used, but it makes sense since you came to the same conclusion. im not sure though, because yours doesnt take into account the odds of winning a hand.