# First lottery related question

The odds of winning the megamillions is 1:176000000. Once it gets over that each ticket can win more than the dollar invested. I am sure that gaming theory has a name for this fact, maybe opportunity cost. Does anyone know?

Expected value?

Each ticket “can” win many millions of dollars, but most tickets will win nothing. But this is true with or without the large residual pot.

If you’re asking what’s the term for lotteries where a rational player would actually buy a ticket, you might be looking for “favorable” or “negative vigorish.” However another recent thread seems to conclude that even this MegaMillions phemonenon is not a favorable opportunity.

No, it is not a favorable opportunity at all. The 1:176000000 chance of winning stays exactly the same. Psychologically, that fact that the payout is greater than that makes it seem as though it is a better deal.

Theoretically you could buy all 176M combinations and “make” almost half a billion - provided not too many others either (a) are lucky and win or (b) also buy all possible combinations.

Of course, practically, how would you buy every combination; how long to print all those tickets.

It must not be that hard. A couple of days ago they had sold 400 million tickets for this drawing.

Yeah, but that’s spread over dozens of states. It’s rather difficult for a single person (or even group) to also get that many tickets on top of all the regular folks buying their tickets.

It’s been attempted in the past, with mixed success, as mentioned in this thread.

Yep, It has a positive expectation(if it’s true and I think it is,)

just to make an example by making up numbers:
If we assume a winner this drawing, which isn’t certain, and we ignore the secondary prizes, and we round to 400M spent and 462M awarded, then for every dollar spent about 1.15 dollar would be awarded for an expectation on 115%. Of course there will be one hell of a deviation from the mean.

So if the total awarded to the grand winner exceeds the individual dollars spent on tickets (am I reading that right?) then how does the lottery make a profit on that? What am I missing here?

What you’re missing is that the prize fund includes cash-carry-forward from prior lotteries where no one won the grand prize.

What others in the thread are missing is that, when taxes and certain other penalties are considered, even this MegaMillions phenomenon still offered unfavorable odds. This was discussed and explained in another thread.

The issue isn’t that the odds are unfavorable; it’s that the game has negative expectation. A game with very low odds of winning can still be worth playing if it has positive expectation.

In this context “unfavorable” means “negative expectation.”

Hope this helps.

(ETA: Do you need a cite?)

I’ve done a fair amount of reading in statistics and game theory, and I have never encountered this usage before, so yes, a citation would be nice.

It’s gambling jargon, not strictly statistics jargon. But, yes, it’s quite common. I was actually surprised you’re pushing back on it.

The first page on a google search of the terms “unfavorable game gambling” shows the usage requested. Several of the other sites on the first page of the search also show the same usage.

I’m not completely sure that I would use the terms “unfavorable game” and “unfavorable odds” to refer to the same concept, but if that’s what people say, then that’s what they say.

Edit: Just to be clear, I am a statistician, and so the word “odds” means something very specific to me. Most people aren’t quite so precise with their use of the terminology.

The very first Google hit on “favorable game” is a pdf (math paper – bjmath.com/bjmath/breiman/breiman.pdf) for which the Google excerpt begins “We say that the game is favorable if there is a gambling strategy such that almost …”

The first Google hit on “unfavorable game” is “TopCasino.com - How to Spot Unfavorable Blackjack Games.” This does not refer to the greater than even-money odds offered on Blackjack and Insurance. (And, just to be sure, Blacjack is a favorable game for a skilled player.)

I was not overly surprised that you’d never heard of “favorable games” (though that combined with the “fair amount of game theory” reading does seem odd).

What did surprise me was that you seemed to infer that I thought odds-against bets were always “unfavorable.” I post regularly in threads involving games, even giving the correct answer to the “Second question” twin of this thread. Have I written something to make you think I was stupid?

On reread, it appears yours was all just a nitpick that I truncated “game with odds that make it unfavorable” to “unfavorable odds.”

Whatever.

It’s pretty clear to me that ultrafilter uses “unfavorable game” to mean one that has a <50% of winning whereas septimus is using it to mean a negative EV or positive vigorish.

Anyway, the OP is neglecting to consider that for every 176 million tickets sold, someone will win. That means that no matter how many tickets are sold, each winner only gets a portion of the money for 176 million tickets. I read it’s about a third, so that’s \$50 million before taxes. Any amount higher than that will come from other ticket buyers and thus will be split other winners.

This doesn’t consider carry-forward balances, which really just mean the lottery has already made its money.

No. An unfavorable game is and always will be one with a negative expected payoff.