July 10th, 2017 at 12:05:39 PM
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Using free on-line slot machines as a guide, I came up with a betting system that provides a decent probability of winning. If you play slot machines and insist that you either win something or lose all of it, the probability of losing is quite high. This strategy increases the probability of winning in exchange for accepting the possibility of losing half or 20% of your bankroll. What you do with that is up to you (take the cash and go home, play something else with it, it doesn't matter).

Obviously you cannot guarantee a win. This "betting system" is a way to guide you in a completely objective manner as to when to press the cash out button (rather than relying on emotions which favor the casino), so that you don't give back winnings too often, but also don't give up too soon and walk away with a very small win.

Here is the way it works is:

1) pick a slot machine

2) decide how much you wish to bet per spin (the minimum, the maximum, anything in between, it's doesn't matter, but pick one and stick with it for simplicity's sake)

3) decide on a bankroll amount

Let X be equal to bankroll

Let N=X divided by bet amount (doesn't have to an integer, if not then round off)

N should be between 10 and 100. You can do less than 10, in fact I've done as little as 1 (put in $5 into a $5 machine and do one spin), but with less than 10, don't bother with all this complication, just play it "emotionally" so to speak. If you go over 100, then you're starting to get into "law of large numbers land" where the probability of winning drops.

Because there are three variables, bet, N and X, you'll need to decide how much X should be which determines N, or decide how much N should be which determines X, and of course you could go back to step 2 and pick a different bet and again figure out N and X.

For example, bet 40c per spin, N=50 and X=$20.00

Or bet $2.00 per spin, N=25, and X=$50.00

Or bet 25c per spin, N=60 and X=$15.00

4) Proceed to playing. If at any time, you win enough for the account balance to climb to 2X (congratulations, you've doubled your money), cash out. If not, after N spins have been completed, if your account balance >= X, cash out.

Counting spins gets tedious, but if the player's club card will easily tell you how much you've wagered, this is much easier (i.e., 1 point per dollar wagered, then simply take your starting points balance and add X, and that is when you stop.)

5) If you are down after N spins, then you are in one of three categories:

balance<0.5X (the worst type of loser)

balance>=0.5X but <0.8X (middle category of loser)

balance>=0.8X but <X (best category of loser)

Continue to play, don't bother counting spins, and if you are in the middle or best category of loser, set a floor equal to 50% of X or 80% of X, respectively. There is a built-in floor of zero for the lowest category of loser LOL.

If you win enough for the account balance to promote you up to the next category of loser (but not winner), move the floor up accordingly. If you lose and are at the floor (or the difference between floor and account balance is less than one bet), cash out.

For example, suppose you are betting 40c per spin, N=50, and X=20, and after 50 spins, you have $12.52 left. The floor is $10.00. 80% of $20.00 is $16.00. Should you win and the balance goes up to $17.24, raise the floor to $16.00.

If you can get the account balance back to X at any time, cash out.

The result of all this is that you will be in one of four categories at the end:

biggest loser: lost everything

middle loser: lost 50%

best loser: lose 20%

winner

I did 1,000 trials using this method playing 50 lions at a free play site. The results are as follows:

Breaking even is counted as a "win". The probability of breaking even on a slot machine doing more than a handful of spins, especially a penny machine, is very very small.

"Double winners" refers to those who were able to cash out with a balance at least double the bankroll.

Note that even though a win can be as little as zero by the rules of the game (e.g., start with $20, do 50 spins, then cash out $22, for a 10% profit), that average includes a few very large wins, making the average just over double, but the median only a 1/3 profit. Slot machines have a pretty high variance!

Prob(win)=35% and prob(double)=10% implies that the probability of winning something less than 100% of bankroll is 25%.

Granted, this was only one type of slot machine, so in real life the probabilities and averages will differ, but this is a general guide. The average payback for this test was 97.1%, so in real life you can expect a bit less, but at least this gives you a pretty good idea of what to expect.

Basically, the probability of winning is 1 in 3, the probability of losing half your bankroll is 1/3, the probability of losing everything is 1 in 4, and the probability of losing 20% is 1 in 12.

Because the probability of losing 20% is the smallest, by quite a lot, I ran the test again eliminating the 80% threshhold, but what happens is about 80% of the time, you go from losing 20% to losing 50%. I figure losing only 20% is not such a bad thing and should not be re-wagered. The median loss on a slot machine doing 50 spins is around 20% anyway, so if you lose 20%, you're in the middle of the curve of outcomes and should stop and not risk losing more.

edited to add... if you decided on a bet of 40c and N=whatever, if you wanted to, you could bet 80c but then you have to count 2 towards the total of N, or if you bet 1.20, then count 3 towards the total

Obviously you cannot guarantee a win. This "betting system" is a way to guide you in a completely objective manner as to when to press the cash out button (rather than relying on emotions which favor the casino), so that you don't give back winnings too often, but also don't give up too soon and walk away with a very small win.

Here is the way it works is:

1) pick a slot machine

2) decide how much you wish to bet per spin (the minimum, the maximum, anything in between, it's doesn't matter, but pick one and stick with it for simplicity's sake)

3) decide on a bankroll amount

Let X be equal to bankroll

Let N=X divided by bet amount (doesn't have to an integer, if not then round off)

N should be between 10 and 100. You can do less than 10, in fact I've done as little as 1 (put in $5 into a $5 machine and do one spin), but with less than 10, don't bother with all this complication, just play it "emotionally" so to speak. If you go over 100, then you're starting to get into "law of large numbers land" where the probability of winning drops.

Because there are three variables, bet, N and X, you'll need to decide how much X should be which determines N, or decide how much N should be which determines X, and of course you could go back to step 2 and pick a different bet and again figure out N and X.

For example, bet 40c per spin, N=50 and X=$20.00

Or bet $2.00 per spin, N=25, and X=$50.00

Or bet 25c per spin, N=60 and X=$15.00

4) Proceed to playing. If at any time, you win enough for the account balance to climb to 2X (congratulations, you've doubled your money), cash out. If not, after N spins have been completed, if your account balance >= X, cash out.

Counting spins gets tedious, but if the player's club card will easily tell you how much you've wagered, this is much easier (i.e., 1 point per dollar wagered, then simply take your starting points balance and add X, and that is when you stop.)

5) If you are down after N spins, then you are in one of three categories:

balance<0.5X (the worst type of loser)

balance>=0.5X but <0.8X (middle category of loser)

balance>=0.8X but <X (best category of loser)

Continue to play, don't bother counting spins, and if you are in the middle or best category of loser, set a floor equal to 50% of X or 80% of X, respectively. There is a built-in floor of zero for the lowest category of loser LOL.

If you win enough for the account balance to promote you up to the next category of loser (but not winner), move the floor up accordingly. If you lose and are at the floor (or the difference between floor and account balance is less than one bet), cash out.

For example, suppose you are betting 40c per spin, N=50, and X=20, and after 50 spins, you have $12.52 left. The floor is $10.00. 80% of $20.00 is $16.00. Should you win and the balance goes up to $17.24, raise the floor to $16.00.

If you can get the account balance back to X at any time, cash out.

The result of all this is that you will be in one of four categories at the end:

biggest loser: lost everything

middle loser: lost 50%

best loser: lose 20%

winner

I did 1,000 trials using this method playing 50 lions at a free play site. The results are as follows:

prob(lose all) 23%

prob(lose half) 32%

prob(lose 20%) 11%

prob(win) 35%

prob(double your money) 10%

avg net win for winners 107.5% of bankroll

median net win for winners 32.4% of bankroll

avg net win for double winners 318% of bankroll

median net win for dbl winners 197% of bankroll

Breaking even is counted as a "win". The probability of breaking even on a slot machine doing more than a handful of spins, especially a penny machine, is very very small.

"Double winners" refers to those who were able to cash out with a balance at least double the bankroll.

Note that even though a win can be as little as zero by the rules of the game (e.g., start with $20, do 50 spins, then cash out $22, for a 10% profit), that average includes a few very large wins, making the average just over double, but the median only a 1/3 profit. Slot machines have a pretty high variance!

Prob(win)=35% and prob(double)=10% implies that the probability of winning something less than 100% of bankroll is 25%.

Granted, this was only one type of slot machine, so in real life the probabilities and averages will differ, but this is a general guide. The average payback for this test was 97.1%, so in real life you can expect a bit less, but at least this gives you a pretty good idea of what to expect.

Basically, the probability of winning is 1 in 3, the probability of losing half your bankroll is 1/3, the probability of losing everything is 1 in 4, and the probability of losing 20% is 1 in 12.

Because the probability of losing 20% is the smallest, by quite a lot, I ran the test again eliminating the 80% threshhold, but what happens is about 80% of the time, you go from losing 20% to losing 50%. I figure losing only 20% is not such a bad thing and should not be re-wagered. The median loss on a slot machine doing 50 spins is around 20% anyway, so if you lose 20%, you're in the middle of the curve of outcomes and should stop and not risk losing more.

edited to add... if you decided on a bet of 40c and N=whatever, if you wanted to, you could bet 80c but then you have to count 2 towards the total of N, or if you bet 1.20, then count 3 towards the total

July 10th, 2017 at 12:15:07 PM
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So, I can do this, and if I win, stop... what, like forever? Or, can I stop for a week, and then come back and do it again?

How about I stop for a second, cash out and then immediately cash back in again? Does that mean I can start counting all over again?

What if I don't cash out? Can I arbitrarily decide that one session has ended and another begun?

The machine doesn't know how much time there is between spins, and doesn't count what we consider "sessions" as discrete calculations. It simply collects its edge. I'd say it collects it ruthlessly, but it doesn't care, it doesn't know anyone named Ruth. The only way to win on a slot machine is to get lucky, get ahead (by a penny, a dollar, whatever), and then never play another slot machine ever again.

How about I stop for a second, cash out and then immediately cash back in again? Does that mean I can start counting all over again?

What if I don't cash out? Can I arbitrarily decide that one session has ended and another begun?

The machine doesn't know how much time there is between spins, and doesn't count what we consider "sessions" as discrete calculations. It simply collects its edge. I'd say it collects it ruthlessly, but it doesn't care, it doesn't know anyone named Ruth. The only way to win on a slot machine is to get lucky, get ahead (by a penny, a dollar, whatever), and then never play another slot machine ever again.

NO KILL I

July 10th, 2017 at 12:18:21 PM
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Quote:MoscaSo, I can do this, and if I win, stop... what, like forever? Or, can I stop for a week, and then come back and do it again?

How about I stop for a second, cash out and then immediately cash back in again? Does that mean I can start counting all over again?

What if I don't cash out? Can I arbitrarily decide that one session has ended and another begun?

The machine doesn't know how much time there is between spins, and doesn't count what we consider "sessions" as discrete calculations. It simply collects its edge. I'd say it collects it ruthlessly, but it doesn't care, it doesn't know anyone named Ruth. The only way to win on a slot machine is to get lucky, get ahead (by a penny, a dollar, whatever), and then never play another slot machine ever again.

It's one session. If you win, or lose, it doesn't matter, you can do it again at the same machine or a different machine, with any amount of time in between. It's all the same because each time you start all over again at step 1.

July 10th, 2017 at 1:08:59 PM
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Quote:KevinAAIt's one session. If you win, or lose, it doesn't matter, you can do it again at the same machine or a different machine, with any amount of time in between. It's all the same because each time you start all over again at step 1.

Ah, but it's step 1 with a personal wealth which has been subjected to the wins or losses of the previous sessions.

There are so many ways that you can change the ratio of winning sessions to losing sessions. For example, you could use Martingale and a fair coin toss game to give you an average of 9 winning sessions to each 1 where you lose. These systems all come with commensurate cost in that the amount you stand to lose will be massively larger than the amount you stand to win. . . And that's even before you get whacked by house edge.

Kevin, you may enjoy this. . .

http://wizardofvegas.com/member/oncedear/blog/2/#post1370

Embrace the Variance

July 10th, 2017 at 5:05:39 PM
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Quote:KevinAAIt's one session. If you win, or lose, it doesn't matter, you can do it again at the same machine or a different machine, with any amount of time in between. It's all the same because each time you start all over again at step 1.

Following that to its logical conclusion, then each spin is an independent decision, and there is no system at all.

NO KILL I

July 10th, 2017 at 5:09:33 PM
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My free Craps simulator also works for slots: https://www.qfit.com/calccrap.htm

"It is impossible to begin to learn that which one thinks one already knows." -Epictetus

July 10th, 2017 at 6:10:24 PM
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Quote:MoscaFollowing that to its logical conclusion, then each spin is an independent decision, and there is no system at all.

Yes, each spin is independent of one another, but the probability distribution of prizes for one spin is not the same as the probability distribution of resulting win (or account balance, however you wish to call it) using this system (or any system, such as "put in $20 and do 20 spins of $1 each"). That is the key here.... I have created a betting system which produces a probability distribution of prizes that is A) lose 100% B) lose 50% C) lose 20% D) win something (and the "something" has its own probability distribution of wins which depends on the slot machine; some have more variance than others)

For example, if you loss a coin and say that heads=0 and tails=1, then for one coin toss the probability distribution is 50% 0 and 50% 1. But if you do 100 coin tosses and add them together, the probability distribution ranges from 0 to 100, with a mean of 50 and standard deviation 5 (if I did that math correctly). Graph the results and you see a bell curve rather than just two points with the single coin toss.

July 10th, 2017 at 10:53:39 PM
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Quote:KevinAAIt's one session. If you win, or lose, it doesn't matter, you can do it again at the same machine or a different machine, with any amount of time in between. It's all the same because each time you start all over again at step 1.

I'm gonna try your system out. One question , if I stop playing and walk a lap around the casino floor and then play again , does that count as a new session ? Or do I need to actually go home and come back to the casino another day ?

July 11th, 2017 at 2:31:56 AM
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Is this a serious question or am I wasting my time trying to contribute to this forum?