Lottery tickets are notorious for being hugely –EV (negative expected value). In most cases, you are better off to wager $20 on red at the roulette wheel than you are to buy a state lottery ticket. However, there are times in which lottery tickets are +EV.

The problem with lottery tickets in most cases is that your odds of winning money are too low to make it worth spending money on a ticket. For example:

- There are 100,000 tickets left unsold
- Each ticket costs $5
- 100 of those tickets have $50 prizes

This is a –EV situation because even if you managed to purchase every single ticket on the market, you would lose money. You would end up spending half a million dollars on lottery tickets and only have $5,000 in prize money to show for it.

The exact EV of each ticket can be found by dividing the total value of outstanding prizes by the total cost of all unsold tickets. Then you multiply that number by the cost of each ticket. In this case, you divide 5000 by 500,000 and get 0.01. Multiply that by $5 and you get $0.05. That’s how much each ticket is worth. In other words, your expected value is -4.95.

This is an extreme example, but that’s not the point. This is a very basic example of how EV (expected value) works.

Lottery tickets become +EV if the remaining prizes are greater than the total cost of unsold tickets. Another example:

- There are 100,000 tickets left unsold
- Each ticket costs $5
- 50,000 of those tickets have $50 prizes

Each lottery ticket is now +EV. If you were able to purchase all 100,000 tickets, you’d spend half a million dollars. But this time, you’d have a lot more money after scratching off all those tickets: $2,500,000. The EV of each ticket is +25.

In real life, you cannot buy every single unsold ticket in a lottery. But that’s OK, because each ticket is +EV. You are not guaranteed any winnings, but you know that you are making a good bet. The price of each ticket is justified by the odds of winning a prize.

Now here’s where things get interesting:

Some states publish the information you need to do these EV calculations. For example:

http://milottery.state.mi.us/msl-ig-trigps.php

The only thing you’re missing at the above website is the number of unsold tickets. That’s not a problem though – because every ticket tells you the odds of winning a prize. Read the fine print and somewhere you’ll see something like “approximate odds are 1 in 4.51.”

Now you know everything you need to figure out whether or not each ticket in the Michigan lottery is +EV. You can even find out the exact expected value (down to the cent) of each ticket that you purchase.

Here’s what you do:

- Add up the total number of remaining prizes (not the total value of prizes – just total number of winning tickets)
- Multiply that number by second number in the odds (if the odds are 1 in 4.51, you multiply the total number of prizes by 4.51)
- Now you know the total number of unsold tickets
- Multiply the total number of unsold tickets by the price of each ticket
- Add up the total value of remaining unclaimed prizes
- If the total value of unclaimed prizes is greater than the total cost of unsold tickets, you have found +EV tickets

This sounds a lot more complicated than it really is. Just run through the steps one time and you’ll see that it’s actually pretty simple.

The only potential problem here is if the lottery website is updated slowly. I really don’t know how quickly lottery websites are updated. That’s some investigation you guys will have to do on your own.

You also have to make sure you’re getting enough information. I tried this calculation with the Kansas lottery website and found out that they only publish the remaining big prizes. They do not show how many unsold $5 and $10 winners are left. That kills the calculation.

Someone else mentioned that your odds go down significantly if someone has already won a big prize but has not yet claimed the prize. I wouldn’t worry about that though. It’s just like calculating the odds of hitting a draw in poker – you don’t worry about the fact that someone could already be holding the card you need. You consider that an unknown factor and proceed as normal.

And on top of that, you have to consider taxes in your EV calculations. Taxes are a huge drain on lottery winnings. I don’t really want to get into all of that though. This is just an example for you to take to new places on your own.

The lesson here is that with enough information, you can find edges that most people miss. Use your brain, use the internet and get a basic understanding of the concept of *expected value*. That’s all you need to find profitable opportunities in gambling, stocks and everyday life situations.

Credit for this post idea comes from an awesome thread I found last night a while back.