Just what is meant by the “expected value”?

The mathematical Expected Value is defined as the mean of a probability distribution. For Lottery Games, this means the sum of the prize amounts multiplied by the probability of winning that particular prize.

It can be thought of as what would happen “in the long run” if you repeatedly bought a one dollar ticket under exactly the same conditions. The exact same conditions seldom exist, so here is an easier way to think of “True Value”. It is the expected return per $1 if you bought all of the combinations for a lottery game (all the remaining tickets in the case of a Scratch-off) AND no one else could buy a ticket. This would ensure that you don’t have to share a top prize.

The reason that we say “Expected Value (at Most)” is just because of this probability of having to share the top prize in an online game (Texas Lotto, Texas Two-Step, Mega Millions, and Power Ball). Obviously, the greater the sales, the greater the probability that someone else will also have the top prize combination. IF we had access to the percentage of combinations that were bought by one player, by two players, by three players, etc., then we could refine our expected value. Because that is impossible, we are actually slightly overstating the expected value.