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How to win $1 million at a table game with a $10 bet

Parlay 17 times by Michael Bluejay

In an earlier article we looked at the odds of winning $1 million or more with the lottery or progressive slot machines. (see article) In theory, you could get much better odds of winning $1 million by betting $10 on a table game (say red or black on roulette), winning 17 times in a row, and doubling your bet every time you win. I say in theory because probably no casino on the planet will let you double up a table game bet this high. Table limits usually limit maximum bets to around $5000. But it's still interesting to see how such a series bet could work, and it's certainly possible to double up to a nice jackpot of $1,000 or more, so let's take a look at how it works. Which game to play? To use our double-seventeen-times strategy, we want to pick a game with a high chance of winning and a low house edge. That narrows our choices to baccarat, roulette, and blackjack. Let's examine each in turn, assuming we start off with a $10 bet and double our bet after every win until we've either won $1 million or had a losing hand. How can the odds be in your favor? How can the casino offer a bet that you're more likely to win than to lose, such as the banker bet in baccarat? Simple: You win less than your bet. The casino takes a 5% commission on banker bets that you win, so a $5 bet wins you only $4.75. In other words, when you win you win less, and when you lose you lose more. You'll probably win a majority of your bets, but you'll still be behind because the winning bets don't pay as much as the losing bets lose. Let's use a hypothetical game to demonstrate this concept. Let's say we have a special roulette wheel with only ten slots, six red and four black. If you bet on red, you're clearly more likely to win. But if you win a $10 bet, you win only $6, while if you lose then you lose the whole $10. Let's say you played ten times, wagering $10 each time, and the results were the expected six red and four black. Each time you win you get the $6 prize plus you get your original $10 bet back, for a total of $16. When you lose you lose the whole $10. Here's how it would play out: Spin # Result Amount Bet Amount won 1. Red $10 $16 2. Red $10 $16 3. Red $10 $16 4. Red $10 $16 5. Red $10 $16 6. Red $10 $16 7. Black $10 0 8. Black $10 0 9. Black $10 0 10. Black $10 0 Total 6 red, 4 black $100 $96 So even though you were more likely to win any individual bet, your $100 of wagers returned $96, meaning you lost $4. Baccarat works the same way. In an eight-deck game, your odds of winning the banker bet are 50.685%, slightly better than a coin toss. But if you win the casino will take a 5% commission. (And no, you don't subtract the 5% from the 50.685%, they're measuring two completely different things.) Considering the commission, the house edge on the banker bet is 1.06%, meaning your expected return on any individual bet is 98.94% of the bet, which is pretty good odds for a casino game. That means that after making one hundred $1 bets on banker, you could expect to walk away with $98.94, losing only $1.06 for your fun. Of course, you won't lose exactly the amount of the house edge whenever you play, because the universe is random. Sometimes you'll win more and sometimes you'll win less. That's why they call it gambling. The point is to understand how much the odds are stacked against you. The longer you play, the closer your losses will be to what the house edge predicts. Baccarat has a peculiar feature: If you bet on banker the odds are actually in your favor to win. How can the casino offer a bet that you're likely to win? Simple: When you win, you win less than the amount you bet, but when you lose, you lose the full amount. (See sidebar.) In an eight-deck game your odds of winning are 50.7%, according to the Wizard of Odds. We're ignoring ties, because if you tie you didn't lose and you can just bet again. Starting with a $10 bet, seventeen consecutive wins yields $1,310,720, and after the 5% commission you'd wind up with $1,245,184. The odds of doing this are 1 in 103,996. But hey, that's better than the 1 in 48 million of winning the Megabucks slot machine or the lottery. Saving for Commissions. There's a catch, though: You have to pay 5% on every banker bet you win, even if you lose everything before you hit your million. (Binion's Horseshoe in downtown Vegas used to offer a game with only 4% commission, but they went out of business.) So if you've won $655,360 and then your winning streak ends, you'll owe $32,768 in commissions. Ouch! So you have to make sure that as you win, you save enough to pay for the commissions. But when you save some of your winnings to pay for the commissions, your bets don't grow as quickly. That means it will take 18 consecutive wins to make your million, not 17. That increases your odds to 1 in 205,179, way better than the 1 in ~50 million odds of winning the Megabucks slot machine or the lottery. The following table shows how it would work if you saved for commissions. We'll ignore the commission until it's bigger than $1. Win # Amount Bet Total Bankroll Saved for Commission 0 10 1 10 20 2 20 40 $1 3 39 78 $2 4 $76 $152 $4 5 $148 $296 $7 6 $289 $578 $14 7 $564 $1128 $28 8 $1100 $2200 $55 9 $2145 $4290 $107 10 $4183 $8366 $209 11 $8157 $16,314 $408 12 $15,906 $31,812 $795 13 $31,017 $62,034 $1551 14 $60,483 $120,966 $3024 15 $117,942 $235,884 $5897 16 $229,987 $459,974 $11,499 17 $448,475 $896,950 $22,424 18 $874,526 $1,749,052 $43,726 Securing your winnings. Looking at the last line in the table you may have thought, "Hey, I only wanted to win a million dollars, why am I wagering $874,526 to win $1.75 million? Why not just wager half a million to win the million, so even if I lose I have $374,526 in my pocket?" That's a good point. We can take it further and see what it would be like to start socking away some of our winnings once we've made around $2000, so we have the opportunity to walk away a winner early on, even if our streak ends way before we get to a million. Of course, you could always bail completely before you hit your million dollars and just take whatever you've won up to that point. Probably most of us would. Who has the stomach to let a $10 bet ride up to $1 million? I'm sure I'd bail at $2200 or $4290. Even the most hardened among us would likely bail at $459,974. The best thing about socking away some of our winnings is that it doesn't take us any longer to hit a million. That's because if we didn't sock away some of our winnings, we'd wind up with around $1.7 million after 18 wins, overshooting our goal. By setting our bets so that we wind up closer to only $1 million, we're able to save some of our winnings as we go. Here's one way to do it. The "Total Socked Away" column is your consolation prize if you lose before completing your winning streak. Of course you could also walk away at any point before you lose and take the Total Bankroll as your winnings. Win # Amount Bet Total Bankroll Saved for Commission Socked Away Total Socked Away 0 10 10 1 10 20 2 20 40 $1 3 39 78 $2 4 $76 $152 $4 5 $148 $296 $7 6 $289 $578 $14 7 $564 $1128 $28 8 $1100 $2200 $55 $225 $225 9 $1920 $3840 $96 $375 $600 10 $3369 $6738 $168 $525 $1125 11 $6045 $12,089 $302 $825 $1950 12 $10,962 $21,924 $548 $1000 $2950 13 $20,376 $40,751 $1019 $1350 $4300 14 $38,383 $76,765 $1919 $2700 $7050 15 $72,096 $144,192 $3605 $3600 $10,650 16 $136,987 $273,974 $6849 $5500 $16,150 17 $261,625 $523,249 $13,081 $11,500 $27,650 18 $498,668 $997,336 $24,933 So at the end you'd have $997,336, minus the $24,933 in commissions on your last bet of $498,668, plus the $27,650 you've already socked away, giving you a cool $1,000,053. Whew! Roulette. Roulette is tempting because it's so simple and easy to understand. You can just bet red or black, or odd or even, and you don't have to screw around with saving for commissions like you do with baccarat. If you win your seventeen bets back to back, you win the whole $1.3 million. But the catch is that roulette doesn't offer the best odds. You have only a 47.4% chance of winning any individual bet, and the chances of winning all 17 bets are 1 in 328,616. That's certainly better than the lottery (about 1 in 50 million), but not as good as baccarat or blackjack. But there's a catch! You can get better odds by playing on a European-style wheel has only one green slot (0) instead of the American wheel which has both a 0 and a 00. And European wheels aren't found just in Europe, some American casinos have them (such as Stratosphere, Paris, and Monte Carlo on the Las Vegas strip). The odds of getting 17 consecutive wins on a single-zero wheel are 1 in 208,832. That's only slightly worse than the 1 in 205,179 with baccarat, and you don't have to screw around with saving for commissions. Blackjack. Blackjack has some of the best odds of any casino game and not surprisingly it offers the best chances of turning your $10 into $1 million -- about 1 in 148,367, which is far better than the odds of winning with roulette or baccarat. Of course there's a small catch: you can't really double your bet each time, at least not if you want to get the best odds -- you have to have enough money to throw in for doubles and splits, so you can bet only 1/4 of your bankroll each time. Since you're not doubling your bankroll with every win, your winnings grow more slowly, and it will take much more than 17 consecutive wins to get your million -- 51 to be exact, assuming you never double, split, or get a natural, bet at least $10 each time, and round your bets so you're not betting spare change. Of course, you don't have to win 51 bets in a row. Since you're only betting 1/4th of your bankroll you still have some money left if you lose a hand, and so you can continue betting 1/4th of your bankroll every time, until you either win your million dollars or go bust trying. But dividing your bankroll by four for every hand is cumbersome, and even if you're lucky enough to win your million it will take a while. It takes an average of 273 hands to turn $10 into a million this way, which will take at least five hours. And that's just on average. You might actually be cruising along into hour number seven -- and then go completely bust. If you want a shot at actually making your million and don't have a lot of time to kill, you'll need to play a different game. On the other hand, if you do have the time, then trying to get to a million this way will be a lot more fun than with roulette or baccarat, because you'll get to play longer. Table Limits. As we said, this is all theoretical because probably no casino would accept bets this large. If you tried this method and then were lucky to win enough times to bump up against the table limit, you could always ask the pit boss to raise the limit, and if they refuse, see if you can get the casino manager to do so. It can't hurt to ask. Which game to play? That depends on what feature is most important to you. Play Baccarat if you want to be able to use a table we created above to mark your progress, and if you want to bail on bet #17 at close to half a million dollars. Play Roulette if having the simplest game is most important. You won't have to screw around with saving for commissions or dividing your bet by four every round, but you won't get the best odds either. If you do play Roulette, look for a Single-Zero wheel (like at Stratosphere, Paris, or Monte Carlo on the Vegas strip). Play Blackjack if you want the best odds, don't care that you'll have to divide your total bankroll by four every hand, and have at least five hours to kill. Winning a smaller amount So now that you know the theory, you might be disappointed that you can't actually try this since casinos won't let you make bets as large as you'd need to in order to double up to $1 million. What you can do instead is to try to double up to $5,000. And the odds of doing so are much better than the odds of doubling to $1 million. Playing roulette, you'd have to win only nine bets in a row, with odds of 1 in 833 of doing so. For baccarat you'd have to win ten bets in a row, since you have to save 5% of your winnings to pay the commission, so you can't quite double your bet size after every win. The odds of winning ten consecutive banker bets in baccarat is 1 in 894, which isn't as good as the 1 in 833 for winning nine roulette bets. Here are the odds for winning consecutive bets in roulette: Wins in a row Bet Amount Odds of winning (1 in ...) 1 $10 2 2 $20 4 3 $40 9 4 $80 20 5 $160 42 6 $320 89 7 $640 187 8 $1280 395 9 $2500 833

-MBJ, 9/2003

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