Before you come at me and tell me I'm wrong (which I probably am), at least let me explain the questions in order to get an answer to the actual math as to WHY I am wrong. Thanks! :-)
So at my local casino, you can bet between $10 and $1,000 on black jack. And conversely $100 and $10,000 in the high limit room. The basic premise of the martingale is that you keep doubling your bet to get back to your starting point, and you will never lose! (or at least break even). The problem of course occurs when you lose enough hands in a row that you reach your table limit, and therefore are out of luck. For example, on a $10 to $1000 spread you can bet $10, $20, $30, $60, $120, $240, $480, and $960 before you reach the table limit. That would be seven hands in a row which you lose, to where you would be out of luck, and lose your entire stack.
Now, before I looked into it, it didn't seem like losing seven hands in a row happened very often. Well, I did the math, which was .59378 (percentage chance of losing with basic strategy) raised to the 7th power, which came out to 0.01545, or about 1.545 %, or 1 in every 64.72 hands. Not as rare as you would think, right?
So, based on that number, you would lose your $960 bet every 65 hands on average. If you played that exact number of hands on average, only taking 1 to 1 from your wins, you would expect to win .40622 times 65 hands, or about 27 hands. At $10 each win, you would win $270 on average, and lose $960 per 65 hands. Obviously, that's a losing proposition every single time.
So, my two questions are as follows:
1. What if you only play to a certain "win point" per session, for example $100. Based on averages, that would only take 50 hands to reach $100, as opposed to the 65 on average it would take to lose your $960 bet. So you are shaving 15 bets off the average, for less money. Conversely, could you choose a lower "max bet point", lets say the $240 bet in this example. As the bet you wouldn't exceed no matter what. That would be losing six hands in a row. Or 1 in every 23 hands on average. Of those 23 hands on average, you would win 9 hands for a win total of $90, and if you lost it all, you would be down $240. It seems like the less number of hands you play per session, the less likely you are to bust out. With $10 hands, it's pocket change. But let's say you were betting $100 a hand instead. In that instance, you would only have to be up one to three units depending on where you want to end up at the end of the day. So, would betting more, and playing less hands (say you would be thrilled to end with just $100 to $300 profit a session) make any more sense? Assuming you had a huge bankroll? ($10,000 or more in this instance)
2. The odds with martingale never seem to factor in 3 to 2 blackjack pays. Odds of hitting blackjack are 4.62%, or 1 in every 21 hands on average. With this kind of system, you could be betting anywhere from 1 to 7 units when a black jack would hit. If you were betting just $10, you would get $15 back. But if you hit when you were on the 7th loss in a row at $960, you would be getting $1,440 back. Let's assume you were playing $100 a hand, at a $9,600 bet, you'd make $14,400. That along would be enough to quit for a month. Obviously, the majority of your bets on average will be one and two unit bets, but you have to assume that at nearly 5%, you're gonna hit blackjacks on bigger bets at some point. How you would figure that out, I have no idea.
Again, I am a new person to this, and I am just getting my feet wet with the statistical significance of this system. Thanks in advance for any and all replies!
Originally Posted by JonGotti81
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