Bluejay's Half-Bankroll Strategy

Full Bankroll, Up Front In discussing the house edge, we mentioned that anything can happen in the short term. It has to be that way, otherwise no one would gamble on games in which the odds were stacked against them. Your expectation is to lose, but with limited exposure (say, a weekend of play), you might come out ahead. Of course, if the odds are against you, then the longer you play, the more likely you are to lose. After millions of plays, your loss would be extremely close to the theoretical house edge. So how can you use this knowledge to your advantage? Well, if you know that the longer you play, the more likely you are to lose, then that means that the shorter you play, the better your chances of winning. And the shortest term you can have is just one play. And so statistically, that's your best bet: making just one even-money bet, putting all your money on the line at once. Crazy? Sure. Logical? Actually yes, according to the numbers. Fun? Probably not -- if you're going to Vegas you probably expect to spend some time gambling for fun rather than having everything be over after one bet, win or lose. But there are variations to this system that can make this very interesting, which will cover in a minute. First, let's see how the basic system works without modification. If you play this according to the numbers, you place your entire bankroll (the amount you bring to gamble) on a single low-edge, even-money bet, such as a a Baccarat hand, a pass line bet on Craps, or a hand of Blackjack. If you win, walk away. If you lose, walk away. You've either doubled your money or lost your whole bankroll. The pie chart shows your nearly 50/50 chance of winning or losing, based on playing the Pass Line in Craps. System A: 1. Win. (You doubled your money, 49.3% chance*) 2. Lose. (You lost all your money, 50.7% chance*)   See sidebar to find out why the odds aren't exactly 50/50 odds. Why you don't get exactly 50/50 odds Your chances of winning or losing won't be exactly 50/50, because the odds are always against you in the casino. For example, your odds of winning a Pass Line bet in Craps is 49.3% (and your odds of losing are 50.7%). It's pretty close to a coin toss. To win two of those bets back to back, your odds would be 49.3% x 49.3% = 24.3%, not the 25% that we depict in the charts below. In the examples on this page, we draw the pie charts as though there were no house edge. We do this in order to keep things simple, and because the effect of the edge in a low-edge game is not that significant if you're only going to make one or two bets. But realize that you don't actually get those 50/50 odds. It's close, but not quite. But anyway, the whole point of this system is to exploit the short-term variance. After millions of plays in a game with about a 1% house edge (like Baccarat) you could see how you'd probably be down close to 1%. But after just one play, you can't be down just 1% -- you'll have either doubled your money or lost it all. You'll be ahead or behind by 100%. You've reduced your exposure to the house edge, although at great risk -- as well as great potential reward. The point is: the fewer plays you make, the less significant the house edge is. With that out of the way, let's discuss variations of the idea of making one big bet with your whole bankroll. Betting what's left of your bankroll Of course, playing just one hand isn't much fun for most people. So here's a way to make a big bet and still get in a decent amount of gambling time: Gamble normally on your vacation, making lots of small bets. At the end when you're about to go home, gamble what's left of your bankroll all at once, right before you leave. That way, you were able to play for hours with reasonable wagers, and you'll still have the opportunity for one last big-money bet when the odds are most favorable to you. It's still an all-or-nothing deal, but by doing it at the end of your trip you made sure you got to gamble normally, even if you lose your big bet. And this is just the beginning. There are variations that can make an end-of-trip bet even more interesting... Half Bankroll, Two Bets I'm sure I'm not the first person to come up with this idea, but I haven't seen it anywhere else, so I'm calling it the "Half-Bankroll System". The idea is that instead of making one big final bet, you divide your remaining bankroll in two, and make two bets, each with half your bankroll. With the variations, this gives you three or more different ways to play (instead of the lone, single way to play if you bet everything), and this makes it a lot more interesting, as well as less risky. Here's how the basic system works: Remember that each time, you're betting the same amount of money -- half of your original bankroll. System B: 1. Win, Win. (You doubled your money.) 2. Lose, Lose. (You lost all your money.) 3. Win, Lose. (You broke even.) 4. Lose, Win. (You broke even.) With this system, you're most likely to break even, which isn't even a possibility in System A. But in exchange for that chance to break even, you reduce your chances of winning. Of course, you also reduce your chances of losing, so it evens out. Note that if you broke even, you're back where you started, so you might choose to start the sequence over again from the beginning. Half Bankroll, Quit after Loss But what if you decide that if you lose your first play, you're going to quit and not risk losing any more? In that case, the possibilities are: System C: 1. Win, Win. (You doubled your money; 24.3% chance) 2. Win, Lose. (You broke even; 25% chance) 3. Lose. (You lost half your money; 50.7% chance) Now, at first glance it might seem that you have a 33% chance of each of these outcomes because there are three of them, but that's not the case. Your first bet has a 50% chance of being a win or a loss, right? So that means that #1 and #2 together are 50%, or 25% each. Broken down that way, you have about a 25% chance for either of the two "win first" scenarios, and about a 50% chance for the "lose first" scenario. How does this compare with System B? Well, right off, you see that you increase your chances of losing, but if you do lose, you've lost only half your money instead of all of it. In fact, you can't lose all your money under this system. In exchange for the ability to not lose all your money, your chances of walking away as a loser (losing half) are increased, and your chances of breaking even are decreased. Half Bankroll, Quit after Win Here's the opposite of System C: Instead of quitting if you lose, you quit if you win your first play, and thereby lock in your 50% profit. Here's how that could work: System D: 1. Win. (You're ahead by half; 49.3% chance) 2. Lose, Win. (You broke even; 25% chance) 3. Lose, Lose. (You lost everything; 25.7% chance) Now, compare this to System C. Your chances of breaking even in each system are the same. In System D you have a better chance of winning, but if so you'll win only 50% instead of doubling your money. In System D you have less chance of losing, but if you do lose then you'll lose everything, instead of just part of it. Now, what if you decided to quit if you win the first bet in order to lock in your winnings, and to quit if you lose your first bet in order to not risk any more of your bankroll? Then realize that this is really just another variation of System A, since you're making one bet no matter what; you're just betting a smaller amount. Summary Let's summarize the different systems: System A One Bet, Whole Bankroll System B Two Bets System C Two Bets, Quit if you Lose the First One System D Two Bets, Quit if you Win the First One So which one of these should you use? Hey, that's for you to decide -- this is gambling, remember? :) There's no way to predict whether you'll win or lose; my goal here has just been to show you your chances of winning or losing (or breaking even). The way you go about gambling is up to you. Savvy readers may realize that you can expand this system further, by dividing your bankroll into 3 instead of 2, and making up to 3 bets. (Or dividing into quarters and making 4 bets.) That's certainly a possibility, but exploring the different possible outcomes is beyond the scope of this article. And remember, the more bets you make, the more you expose yourself to the house edge, which increases your chances of losing. I hope this provides some food for thought. Good luck!