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%
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(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