House edge and expected value are useless when applied to the lottery (lotto)

Playing lotto games is not stupid.

Last update:  November 8, 2025

As they say, a little knowledge is a dangerous thing.

Some people learn about the house edge and expected value, which are important for understanding casino games.  They then try to apply those concepts to lotto games, where those ideas are all but useless.  As a result, they ridiculously conclude that people are foolish for buying lotto tickets.  That’s flat-out wrong.

Ironically, while these critics scoff at lotto players’ supposedly poor math skills, it’s actually the other way around:  it’s the critics who are bad at math.  They’re trying to compare two totally dissimilar things with the same measure.  It’s not even like apples to oranges, in this case it’s more like apples to roofing materials.

Let’s see why, starting with a quick review of the house edge.

House Edge and Expected Value

The house edge is the casino’s average profit per bet, in percentage terms.  For example, in American roulette the house edge is 5.26%, meaning in the long run, the casino will take 5.26% of all money bet, and return 94.74% to the player.  Different games have different house edges.  The typical Vegas blackjack game is 1.5%, while Lotto Texas averages around 24%.

The flip side of house edge is “expected value”, which is the amount the player gets back.  So if a game had a house edge of 5%, its expected value would be 95%.  On a dollar bet, the casino keeps 5¢ and returns 95¢ to the player (in the long term, over all bets made).  In short, the house edge is what the casino gets, the expected value is what the player gets.

If all things were equal, then games with a lower house edge would always give you the best chances of winning, and give you the lowest long-term average loss.  But the reality is that things are never equal.  Your chances of winning don’t depend on just the house edge, they also depend on how many bets you make.  For a casino game, that’s how many bets you make per hour, times how many hours you play.  Speed varies a lot from game to game.  A slot player bets about 700 rounds per hour while a baccarat player does about 70.  More rounds means a higher chance of losing, and more total loss. 

Next, your average loss isn’t a function of just the house edge and the number of bets, it also depends on how much you bet per round.  Different games have different price points.  The minimum for most table games on the Vegas strip is around $15, while a state lotto game is just $1.

The point is, the house edge is just one variable in evaluating games, and focusing on it exclusively while ignoring all the other variables is wrong.  The house edge shouldn’t be a religion that players follow blindly.

My Average Loss Calculator below shows how all the above concepts matter: house edge, speed of play, and average bet.  Play around with the values so you can see how they affect your average loss.

With that out of the way, now let’s see why it’s ludicrous to judge lotto players for playing a game with a low expected value.  And to be clear, we’re talking about lotto games (with the multimillion-dollar jackpots), not scratch-offs.

Mistake 1:  Thinking that the low expected value makes lotto a horrible waste of money

Let’s see how our aspiring analyst “Bob” goes wrong about this.  He’s learned about the house edge for casino games and knows that games with a high edge are a bad bet because they result in a low expected value.  He knows that lotto games have an expected value of only 50-75¢ on the dollar, while games like blackjack or craps return an impressive ~99¢.  He therefore concludes that lotto is “a tax on the people who are bad at math” and that anyone who buys a lottery ticket is foolish.

Bob didn’t go wrong in just one way, he went wrong in five ways.  Let’s go through them.

1. Lotto losses are actually minuscule

First, Bob failed to consider the practical result, which is that the most you can lose on a $1 lotto ticket is a f**king dollar.  Big freaking deal.  Most of us can afford to lose a dollar or two.  Every damn week.

House edge matters in a casino when you’re playing for hours on end, because you can easily lose hundreds to thousands of dollars in just one session.  That is not in the same universe as a piddling $1 lotto ticket.

2. You lose more on a low-edge casino game than on a high-edge lotto game.

Since Bob blindly zeroes in on the house edge like it’s the only thing that matters, he completely missed the fact that you lose more on casino games than lotto, even though casino games have a lower house edge.  That’s because, as we covered earlier, average loss also depends on how many rounds you bet, and your average bet size.  Buying a single lottery ticket is a common play for that game.  But nobody plays a single hand of blackjack.  Playing a 3:2 blackjack game with proper strategy at $5 a hand for two hours results in an average loss of about $5.  That's more than twice what you’d lose on a lotto ticket.  Great job, Bob, you lost more money than the “foolish” lotto player.

3. You can’t judge entertainment by expected value.

Bob’s third mistake is ignoring the fact that nearly all kinds of entertainment costs money, and it’s normal not to get any money back from those purchases.  When you go to the movies, go bowling, go skiing, or whatever, you shell out some money, and you’re satisfied.  You traded some money for some fun, and it seems like a reasonable deal.  You don’t consider that the house edge on the transaction was 100%, because the value isn’t getting some money back, it’s having an enjoyable experience.

This concept went straight over Bob’s head.  It wouldn’t occur to Bob to judge someone for spending $15 on the movies or bowling, but as soon as someone lays down a mere dollar for a lottery ticket Bob goes apoplectic.  In Bob’s mind, every form of trading money for entertainment is valid, except when it comes to lotto tickets—somehow.

Note that this is two mistakes in one:  First is failing to consider the intangible value of a lotto ticket purchase, and the second is failing to realize that lotto tickets are super-cheap entertainment compared to other forms.  You’re more frugal by buying a lotto ticket than by going bowling.

4. House edge does not estimate any player’s loss in lotto games.

For casino games, the house edge is a good approximation of almost every player’s loss.  It doesn‘t take much play for the actual loss to get in the same ballpark as the mathematical expected loss.  You'll probably be within 5 percentage points of the house edge after just 100 rounds on a table game.  By contrast, for lotto, the house edge fails to gauge the loss for any player, neither the one winner nor the millions of losers.  Even if you bought a million tickets, your actual result wouldn’t be anywhere close to what the house edge formula suggests.  That’s because lotto is a completely different beast—again, apples to roofing materials.

Let’s use my House Edge Simulator to see how expected value is useful for a casino game.  It plays roulette a bunch of times and you can see the results.

What you saw is that:

1. You’re gonna be a long-term loser
2. Anything can happen in the short term
3. After just 100 rounds your actual losses were likely in the ballpark of expected losses.  The house edge and expected value are useful here because this is a game where you'll likely play a bunch of rounds, and the chances of winning any individual round is almost 50-50.  Wins are frequent in this game.
   

For lotto games, it’s the exact opposite.  The house edge says you’d get back 76¢ on a $1 Lotto Texas ticket on average.  But most players who bought a million tickets would actually get back only 10¢ on the dollar.  That’s because the 76¢ figure includes the jackpot, which 99.999999% of players will not hit.  (And I’m not exaggerating the number of nines in that figure, that’s the actual value.)

So actually, for most lotto players, it’s even worse that Bob thought.  He chastised them for getting back only 76¢ on the dollar, but their actual return is closer to 10¢.  (Who’s bad at math now?)

The point is, the house edge isn’t useful for judging a lotto game, which is fine because getting a great deal is not why people buy lottery tickets in the first place.

5. The whole point of lotto games is the huge jackpot.

The whole point of lotto games, obvious to seemingly everyone except Bob, is that there’s a thrill of the chance to win multiple millions of dollars.  You can’t get that same experience anywhere else, certainly not with low-edge casino table games like blackjack.  It's like if someone were trying to buy a bicycle for exercise, but Bob tried to get them to buy a car instead because it goes faster...missing the entire point of the purchase.

Of course, all the above assumes that you're not buying a gazillion lottery tickets and that you follow the cardinal rule of gambling, which is to never bet more than you can afford to lose.  Buying lots of tickets naturally results in a much bigger loss.  But one or a few tickets at a time is how most people play lotto.

Mistake 2:  Thinking it's better to play when the jackpot goes positive

As a lotto jackpot grows, so does the expected value.  Many state lotteries actually become positive on occasion, which means that the expected value of a $1 lottery ticket is more than a dollar.  Here's how that would work with Lotto Texas:

So, Bob figures that when Lotto Texas jackpot grows to $22,900,000, it becomes a positive expectation game and it’s suddenly worth playing!  According to Bob, those “foolish” lotto players aren’t foolish if they wait for the jackpot to go high enough, because then the house edge isn’t 30-50%, it’s a player edge.  Here again, Bob has ridiculously put all his eggs in the house edge basket, as though the house edge is the only thing that matters.  In fact, with lotto games, it doesn’t matter at all.

What Bob’s missing is that his math works only if you buy tens of millions of tickets, at a cost of tens of millions of dollars.  For the player buying just one or a handful of tickets, there’s no difference between a normal jackpot and a positive jackpot:  They’re either gonna win the jackpot and be elated (even if it wasn’t a “positive” jackpot), or, more likely, they’re gonna lose their whole dollar.  The jackpot size does not affect their odds, at all.  A positive jackpot is exactly as hard to hit as a normal one.

I wrote a simulator to put this into perspective.  Click the button to pretend-buy a whopping 500,000 tickets.

What you likely saw is that even with half a million freaking lottery tickets, your results were exactly the same for both the smaller and larger jackpots.  If you bought ten million tickets the results would likely be the same.  The jackpot size simply doesn't matter.

Also, even if it were a "good" time to buy tickets when the jackpot goes positive, the fact is that when the jackpot grows, more people buy lottery tickets.  Not because those buyers are calculating the expected value (most people have no idea what that is), but because they're more excited about winning a bigger pile of money.  The more people play, the more likely it will be that more than one person picks the winning numbers, so the prize will be split among all the winners.  If two people win a $20 million jackpot, they each get $10 million—the same as if one person won a $10 million jackpot.  Therefore, you can't assume that the expected value goes up in relation to the amount that the jackpot goes up, because if you do win, you're less likely to win the whole thing yourself.

So, there's no point in waiting for a bigger jackpot.  If you want to play the lottery, play it whenever you like, it won't affect your odds.

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