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The Odds of Winning a Million Dollars or More

How hard is it to win the lottery? Here are other things that have about a 1 in 50 million chance of happening. Odds of dealing out 13 cards to each of four players using a 52-card deck and all four players having a straight from two to Ace: 1 in 61 million (WizardOfOdds.com) I have a stack of 64 Bibles. I pick a single word from one of them. Odds of you picking the exact same word (same instance) from the same Bible: 1 in 50 million Flipping a coin 25 times and getting 25 heads or 25 tails: 1 in 34 million Odds of being dealt a sequential royal flush (forwards or backwards): 1 in 40 million (WizardOfOdds.com) Odds of #7 hitting in roulette, five times in a row: 1 in 79 million Chance that radioactive monkeys will kidnap Britney Spears and convert her to Buddhism: 1 in 46 million (estimate) All of us dream about winning the big jackpot. But how likely is it? Let's find out. The answers may surprise you.   Multi-Million Dollar Jackpots There are exactly two games that offer multimillion-dollar jackpots: progressive slot machines and the state lottery. Which is the better bet? Well, that depends on what your goals are. If you want the best chance of winning the jackpot, the lottery is your best bet. But if you want the best chance of breaking even or winning anything, you'll want to go with the slot machine. Let's take a look at the odds in more detail. For our slot machine I'll use the Megabucks slot machine in Nevada since it's the most famous multimillion-dollar slot, and for the lottery I'll use the Texas Lotto since it's the game I'm most familiar with. (You can look up the odds for your own state lottery on your state lottery website.) As I write this, the Megabucks slot machine jackpot in Nevada is around $16 million, and the Texas State Lotto is also around $16 million. The odds of winning Megabucks are 1 in 49,836,032 according to the Las Vegas Sun, and the odds of winning the Texas Lotto are 1 in 47,784,352. The prizes and the odds are almost the same. So what's the difference? Well, there are two differences. The first is that the odds of hitting a smaller jackpot with a slot machine are much, much better. Slot machines are far more generous in giving small and medium sized wins. You're less likely to win anything with the Lotto, and if you do you'll probably win only $5. A progressive slot machine generally returns around 90% of all the money ever played, while the lotto returns only around 52%. The lotto has the worst paytable of any game on the planet. Figuring the odds for multiple plays If your odds of winning a game with one play are 1 in 2,000,000, you might figure that if you play two times then your odds are twice as good -- 1 in 1,000,000. This shortcut works for estimating the odds when the odds are very large and when we're talking about only a small number of plays. But if the odds are small, or if you're playing many, many, times, then that shortcut no longer works. For example, if the odds were 1 in 2,000,000 and you played a million times, you might think your odds have increased to 1 in 2, or 50%. But in fact your odds of winning are only 39%. Here's another example: Let's say you're trying to roll a #5 on a die, and you get three chances to roll the die. Your odds aren't 50%, of getting the 5, they're only 42%. How can this be? Think of it this way: If three rolls meant your odds were 3/6, then six rolls would mean your odds are 6/6, or 100%. But you obviously you don't get a 100% guarantee of rolling a #5 just because you roll the die six times. So we know that you can't just divide by the number of trials. So how do we calculate our odds? The answer is that we take the opposite of the odds of losing, which must be the odds of winning. In the case of trying to get a 5 with three rolls of a die, your odds of losing on the first roll are 5/6, and on the second roll are 5/6, and the third roll are 5/6. That's 5/6 x 5/6 x 5/6, or 125/216, or 58%. If we have a 58% chance of losing, then we have a 42% chance of winning. Here's the general formula for finding the odds of winning when you repeat the bet with certain odds (d) a certain number of times (n), which you can type directly into Excel: =1-((1-d)n) For example, if the odds of hitting a jackpot are 1 in two million (or 1/2000000, or 0.0000005) and you play one million times, the odds are: 1/(1-((1-0.0000005)1000000)) = 39% On the other hand, even though we're less likely to win anything with the lotto than with a slot machine, the lotto actually gives you better odds of winning the jackpot for the amount of money you spend. A shot at Megubucks requires $3 while a Lotto ticket is only a dollar. For for the price of a shot at Megabucks you could buy three Lotto tickets. And buying three lottery tickets increases your chances of winning to 1 in 15,928,118. So which is the better bet for $3? It's a tradeoff: If your goal is to have the best shot at winning the jackpot, then your chances of winning with three $1 Lotto tickets are almost three times better than winning with one $3 spin on Megabucks. But if you're hoping to win anything and have at least a small win, then a spin at Megabucks is the better bet. Million-Dollar Jackpots As you might suspect, the bigger the prize, the harder it is to win. To improve your chances of winning, you can simply go for a smaller prize. Winning just a million dollars is easier than winning several million dollars. The Texas Lottery has a scratch-off game called $1,000,000 Classic. There are eight winning tickets out of the 8,095,350 printed, so the odds are 1 in 1,011,919 of winning by buying a single ticket. But the catch is that a single ticket costs $20. If instead we bought twenty $1 Lotto tickets then our odds of winning the Lotto would be 1 in 2,389,218. So that's quite a tradeoff: We doubled our chances of winning by going with the scratch-off instead of the Lotto, but now we'd only win a million dollars rather than several million. (I'm not going to cover every lottery game that exists, but the one with the best odds of winning a million dollars that I could find is the Georgia Lottery's Millionare Raffle,with odds of 1 in 125,000 to win a million bucks with a $20 ticket.) The Texas Lottery also has a $20 scratch-off game with a $2,000,000 top prize, with odds of 1 in 2,680,000 of getting it. But that's worse than the odds of buying twenty $1 Lotto tickets (2,389,218). With this particular game you get worse odds to win a smaller amount of money, so it's definitely a bad bet. So while going for a lesser jackpot with the lottery might not improve your odds as much as you like, going for a lesser amount on a slot machine probably does. We don't know the exact odds of hitting a jackpot on a machine whose average top prize is about half a million dollars, but we can make an educated guess. Since the average Megabucks jackpot is $14.4M and the odds of winning are about 1 in 50M, that puts the odds at right about 1 in 3.5x the amount of the jackpot. With a slot with an average jackpot around $0.5M, that would put the odds of hitting it at 1 in 1.75M (3 x 0.5M). Again, we don't know these odds for sure, but it's a very educated guess. Turning all this into a strategy The 1 in 1.75M chance for hitting the jackpot on a moderately-sized progressive slot are the best odds we've seen for anything we've examined so far. So how can you turn this into a playing strategy? First, let's assume that you can afford to lose a couple of dollars each week on average while trying for the big prize. Let's also say that you want to play fairly frequently, because you want frequent opportunities to win, which keeps things interesting. One way is to play one spin a day. That shoots your odds of hitting the jackpot up to 1 in 4,795 over that year. And how much will it cost you to play every day? If the machine you play pays back about 90% (typical for progressive slots), that'll come to an expected loss 365 x $3 x 10% = $109.50 for the year. Of course your actual results could be anywhere on the map for only 365 spins, but this gives us a frame of reference. And if $109.50 is more than you care to lose in a year, you can always play once a week or a couple of times a week rather than every day -- though naturally that makes you less likely to hit the jackpot. Another way to get a million dollars Could you live without your car? No? What if someone offered you $2.3 million to give it up? That's how much you'd have if you invested the $7,754 in average car costs every year from the ages of 25 to 67 with an 8% annual return. Staggering, isn't it? (read full article...) Of course, it's a hassle to go to a casino every day just to make one spin. We can accomplish the same thing by going to a casino once a week and making seven spins at that time. We could take it even further and play 365 spins once a year, but that wouldn't be in keeping with our goal of playing frequently so we have frequent opportunities to win. But what if going to a casino even once a week is inconvenient, or there's no casino where you live? That's why we save the best for last: Our preferred solution is to play the Major Millions progressive slot at Captain Cooks online casino. The Major Millions jackpot starts at $250,000 and has gone as high as $1.6 million. (In fact, Captain Cooks awarded the very first $1 million+ jackpot ever won online to a lucky Major Millions player in May 2002.) Using our educated guess from earlier, we estimate the odds of hitting this jackpot to be the same 1 in 4,795 for 365 spins. And since you can play from your home or office, you can easily play one spin once a day or seven spins once a week. Major Millions gives the best odds of winning a big prize with the most convenience. In fact, if you know of a game that offers better odds for winning $1 million+ with a $3 bet, I'd like to hear about it. You can try Major Millions yourself at Captain Cooks.   Odds for winning various large jackpots based on the amount wagered Game Number of Plays Jackpot Odds of winning are 1 in.... $1 bet Texas Lotto 1 ticket $4 - $47 million 47,784,352 $3 bet Major Millions online slot at Captain Cooks 1 spin $250k - $1.6 million 1,750,000a Texas Lotto 3 tickets $4 - $47 million 15,928,118 Megabucks Slot 1 spin $6 - $39 million 49,836,032 $10 bet Baccarat Series Bet 1 series $1 million 205,179b Major Millions online slot at Captain Cooks 3 spinsc $250k - $1.6 million 583,334a Texas Lotto 10 tickets $4 - $47 million 4,778,436 Megabucks** 3 spinsc $6 - $39 million 16,612,011 $20 bet Baccarat Series Bet 1 series $1 million 103,996b Major Millions online slot at Captain Cooks 7 spinsc $250k - $1.6 million 250,000a $1M TX Scratch-Off 1 scratch-off $1 million 1,011,919 Texas Lotto 20 tickets $4 - $47 million 2,389,218 $2M TX Scratch-off 1 scratch-off $2 million 2,680,000 Megabucks Slot** 7 spinsc $6 - $39 million 7,119,434 NOTES: a. Odds are an educated guess. b. Odds are theoretical, because likely no casino would let you take a series bet high enough to win a million dollars. (more) c. Megabucks bet amounts are actually $9 and $21 instead of $10 and $20, because Megabucks requires $3/spin. References for this article: Texas Lottery Commission IGT (producer of Megabucks) Odds of winning Megabucks Historical Megabucks jackpot amounts Captain Cooks Online Casino (where to play Major Millions) Average Major Millions jackpot Odds of winning a bet with multiple trials

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