"Post-Game Review" - $1.58B MM Jackpot This WeekPrev TopicNext Topic

• Orange71

  

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  Aug 12, 2023, 12:53 pm

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  A single winner in Florida hit the "$1.58B" Mega Millions this week. The cash value (I saw on TV anyway) was about $783M. This begs the question: playing a regular $2 ticket, did a player have a positive return expectation (expected value of return > $2 bet)?

  Answers:

  1. Before income tax - yes, roughly $0.11 gain per $ bet (about +11% return)

  2. After income tax - no, roughly $0.28 loss per $ bet if you assume a 35% tax rate on winnings. (about -28% return)

  First, I looked up the number of tickets sold for this drawing, and it was about 171.7 million. Given that sales, we have to judge down the cash value jackpot expected value given the possibility of multiple winners. I did that and with 171.7M tickets, using the Binomial Distribution, we get about $597.5M Cash Jackpot Expected Value, given that you are a Jackpot winner.

  

  OK, so now we calculate the overall EV of the return, assuming a tax rate. Let's start with no income tax:

  

  Yea! We are ahead with about 11.1% positive expectation!

  Now, here comes Uncle Sam (and state tax collectors, as applicable)...

  

  Aw shucks! Now we have about -27.8% return.

  No doubt some will argue that most people won't actually report and pay the taxes on the small returns (which, arguably, they don't owe given offsetting losses). Maybe, but most of the overall expected value of the game comes from the jackpot. You most definitely will get a W2G on the high tier prizes. Pay up my friend!
• Wavepack

  

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  Aug 13, 2023, 10:18 am

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  The rule of thumb that I bother to remember is that the expected loss is about 90% for a typical MM or PB player.   By typical, I mean the player will never see a 5 or 6 ball hit.
• Orange71

  

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  Aug 13, 2023, 1:09 pm

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  In response to Wavepack

  Quote: Originally posted by Wavepack on Aug 13, 2023

  The rule of thumb that I bother to remember is that the expected loss is about 90% for a typical MM or PB player.   By typical, I mean the player will never see a 5 or 6 ball hit.

  At least. You can fairly easily calculate conditional probabilities and EVs given the assumption that the player never hits 5 main balls (with or without Megaball) over a lifetime. Just keep the same numerators and subtract off 25 from the denominator from my posted table to get the (new) conditional probabilities for the lower tier prizes.

  How likely is that 5 + 0 or 5 + 1 is never hit? Let's say a player buys 6 Quickpick tickets per week (3/drawing). The player does that for 40 years. That's 6 x 52 x 40 plays (= 12480). The probability of never hitting 5 main balls with or without Megaball is [(302575350 - 25) / 302575350]^12480 = 0.99897. So basically 99.9%.
• Wavepack

  

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  Aug 17, 2023, 7:19 pm

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  The 25 should be larger, primarily because the 4+1 win has (5 choose 4) * (65 choose 1) = 325 combinations out of 302575350 to win.   The 25 should be 325 + 25 + 1.
• Orange71

  

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  Aug 18, 2023, 10:12 am

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  In response to Wavepack

  Quote: Originally posted by Wavepack on Aug 17, 2023

  The 25 should be larger, primarily because the 4+1 win has (5 choose 4) * (65 choose 1) = 325 combinations out of 302575350 to win.   The 25 should be 325 + 25 + 1.

  Yes. I had erroneously not counted "4 + 1" as a "5 ball" win.
• Wavepack

  

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  Aug 22, 2023, 11:24 pm

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  a = 302575350

   ((a - 350) / a) ^ 12480 =  0.9857

   

  A 98.57% probability that you'll lose ~ 90% of ~ $25,000 lifelong ticket cost.   MM and PB are mostly loser games.