aka, The Lottery vs. Megabucks

All of us dream about winning the big jackpot. But how likely is it? Let's find out. The answers may surprise you. 

There are exactly two games that offer multimillion-dollar jackpots: progressive slot machines and lotteries.  Of the two, a state lottery gives you much better chances of hitting the jackpot, and at a lower cost.  The catch is that with the lotto you'll almost always win nothing or just $3 or so, while with a slot you'll sometimes get a decent-sized win.

A table makes this clearer.  For our slot machine I'll use the Megabucks slot machine in Nevada since it's the largest and most famous multimillion-dollar slot, and for the lottery I'll use the Texas Lotto since it has a similar jackpot size.  Here's how they stack up:

The big take-away here is that your chances of winning the Lotto on one play are twice as good as for winning Megabucks.  But it doesn't end there:  A Megabucks play costs $3, while a Lotto ticket costs only $1.  So for the cost of playing Megabucks once, you could play the Lotto three times.  And for $3 played, your chances of winning the Lotto are about six times better than winning Megabucks.  Wow!  So if your goal is to actually win the jackpot (which is why most people play a jackpot game), the Lotto will serve your purposes better.

Megabucks gets the edge on the last row, the percentage returned to players, excluding the jackpot.  That means Megabucks gives out lots more small- and medium-sized pays than the lotto.  But if we equalize the jackpot odds between the two games, we see that the lottery is still a much better bet.

Equalizing the jackpot odds means we figure how much we have to play each game so that the odds of hitting the jackpot are about the same.  My nifty calculator at right makes short work of that.  As you can see it takes two spins on Megabucks to get similar jackpot odds as a single lottery ticket.  But Megabucks costs $3 per play, and if you play it twice, you're forking over $6.  So $6 on Megabucks gets you similar jackpot odds as a single $1 lotto ticket.  So even though Megabucks gives out lots more small pays, you have to pump six times as much money into it to get odds as good as the lotto, so you'll still wind up with losing more money by playing Megabucks instead of the lottery, for a given set of jackpot odds.

Of course, few people play the lottery like they play a slot machine.  With a slot people generally play at least several spins, or maybe an hour or more, at perhaps 700 spins an hour.  But people rarely buy 700 lottery tickets at a time.  So the potential for loss with Megabucks is pretty big.  By contrast, you've really got to go out of your way to lose big on the lottery.

Now, most of you don't live in Texas so you can't play the Texas Lottery, and sorry, I'm not gonna sit here and analyze dozens of individual state lotteries (or other countries' lotteries).  Most Americans do have access to Megamillions, though, so I'll mention that the odds of winning Megamillions from one ticket are 1 in 176 million.  State lotteries are easier to win than national ones.  If you want better chances of winning, skip Megamillions and play your state lottery instead.

Math heads obsess over the "break-even point", which is when the jackpot goes high enough that it's a "fair" bet.  That is, at some jackpot level, the average returned to players for each ticket will equal the cost of the ticket.  For Lotto Texas, that's just over $23 million.  But the math heads are ignoring three important things:

1. Your odds of hitting the jackpot are the same no matter how high or low the jackpot is.
2. The break-even point makes financial sense to the player only if you're playing millions of times.  If you're just buying a handful of tickets each week, it couldn't be less relevant.
3. Most people would be just as happy winning $19 million as they would $26 million.  What can you do with $26 million that you can't do with $19M?
   

Playing the lottery is like any other form of gambling, which is like any other form of entertainment:  Do you get $1 worth of happiness from your purchase of the ticket?  If so, then great, it doesn't matter long the odds are or how low the jackpot is.  (And conversely, if you don't get $1 of joy from your purchase, then it doesn't matter how good the odds are or how high the jackpot is.)

Incidentally, both Megabucks and the Texas Lotto can be paid out over 25 years (the advertised jackpot amount divided by 25), or as a single lump-sum of about 60% of the advertised jackpot amount.

Try my calculator at right to see your chances of winning Megabucks or Lotto Texas over many years.

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 a lot easier than winning several million dollars.

The Texas Lottery has a scratch-off game called "Texas Lottery Black" with a top prize of $1 million even.  There are six winning tickets out of the 6,178,100 printed, so the odds are 1 in 1,029,683 of winning by buying a single ticket.  But the catch is that a single ticket costs $10. If instead we bought ten $1 Lotto tickets then our odds of winning the Lotto would be 1 in 2,582,717. 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.

But 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 about $15M and the odds of winning are about 1 in 50M, that puts the odds at right about 1 in 3.3x the amount of the jackpot.  On a slot with an average jackpot around $500,000, that would put the odds of hitting it at 1 in 1.66M (3.3 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 1.66M chance for hitting the jackpot on a moderately-sized progressive slot are the best odds for hitting a big jackpot of 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 78% excluding the jackpot, that'll come to an average loss 365 x $3 x 22% = $241 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 $241 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.

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, so that we're in a constant state of hoping to win.

But what if going to a casino even once a week is inconvenient, or there's no casino where you live? Thank God for the Internet!  Bodog has a progressive slot called Shopping Spree, whose jackpot is $1.2 million as I write this.  And the odds of hitting it are almost certainly much better than the typical prize-to-jackpot ratio of Megabucks.  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.

So I think Shopping Spree gives the best odds of winning a big prize with the most convenience.  If you know of a game that offers better odds for winning ~$1 million for a $3 bet, I'd like to hear about it! 

References for this article:

• Texas Lottery Commission
• IGT (producer of Megabucks)
• Odds of winning Megabucks
• Historical Megabucks jackpot amounts

Related articles:

• Million-Dollar betting system

 Last update: November 2011