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Denver, Colorado, United States
I'm an old time roleplayer who became a soldier who became a veteran who became a developer who became a dba who became a manager who never gave up his dream of a better world. Even if I have to create it myself.

Friday, March 30, 2012

Mega Millions vs Pot Odds

Anyone play poker?

They'd probably beat me.
Poker players that have moved beyond the basics of "wait, does a flush beat a straight?" eventually learn the concept of pot odds.  Basically, if the odds of getting a winning hand are better than the ratio of the bet to the pot+bet, then the player should make the bet.  So if the pot is $90, the bet is $10, and the odds of winning are 20%, then the player should bet, since $10 is less than 20% of $90+$10.

That's intermediate strategy, of course, and advanced strategy can try to outsmart people playing pot odds.

But the lottery doesn't outsmart anyone.  It's just straight odds.  Let's explore that in terms of pot odds.

Given that the jackpot odds in Mega Millions is around 1:176,000,000, if the pot is over 176,000,000, then a $1 investment is actually the correct move - because you are betting properly against pot odds.  Over $352,000,000, and a $2 investment is appropriate.

If you folded a winning hand in poker when pot odds were in your favor, you would usually be a fool.  Why be a fool in the lottery?  Don't listen to the naysayers who insist this is a "bad investment".  They can't do math.

For $640 million (the current estimated pot), up to $3.60 is justified.

What the heck, I'll round up and buy 2 tickets with the megaplier for a total of $4.  I bet it gets higher than $640M given the crazy lines at all the stores.

Hmm.  Maybe the lottery can outsmart me after all!

Besides, like Tenkar says, someone might be able to buy the D&D license from Hasbro for that kind of money.

Good luck in the drawing!

6 comments:

  1. Just got your comment. What kind of dog do you have?

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    1. An adorable sheltie-pom. She is about 13 years old now and she could probably beat me at poker.

      At least, she has no problems convincing me to throw more food into the pot.

      Delete
    2. Very cute. Wiggy just turned one and Bug is still under one.

      Right now both girls are playing with a new toy. Too cute.

      Delete
  2. I stumbled onto this searching for just this type of topic. The payout, even if you opted for the lump sum and even after federal and state (MA) taxes is north of $320m. At first blush, the pot odds are so good that you are fool NOT to play. If it were that simple, then billionaires would stop playing the stock market and start buying out all lottery combinations.

    When we calculate pot odds playing poker we assume that we know the hand we have to make in order to best our opponents. With the lottery, even if we "make our hand" and win the jackpot, we may be splitting it. It stands to reason that the probability of a split jackpot rises with the size of that jackpot.

    I'm not a statistician. Far from it. I'd love to see someone really look into this. I imagine the sweet spot for return on your $1 investment might actually be in some of the smaller lotteries.

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    Replies
    1. Well, in truth all Pot Odds is, is an indicator of how well you will do over a long enough time to render the odds complete. When playing with a deck of cards, that means you can "complete" those odds in a reasonable amount of time (i.e., face the situation often enough to get the payout).

      Playing 1:176,000,000 means it would take quite a few lifetimes, I'm guessing, to reach the same level of solvency...

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    2. I just read that there were over $1.5bn in sales for this lottery. Due to the megaplier that's not 1.5bn combinations but 1bn is probably conservative, right? Assuming an even distribution (it's actually far from it) then you would expect each combination to be played > 5 times. Your pot odds are actually terrible because your expected jackpot is down to $115m or so... before taxes.

      If you could figure out what the least played combinations were then you could up those odds again...

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