Mega Millions - is a $1, $2, or $3 ticket the best value (EV)?

Reply #4

Orange71 — Wed, 27 Jul 2022 21:45:07 GMT

That's not how Expected Value works. Your statement is valid, however, from the standpoint of Standard Deviation. No question JTJ has the highest SD, by far.

Let me give an expository example from Video Poker. Let's say this is Jacks or Better Draw. Suppose we have the following starting hand dealt to us before the draw:

Jack-Spades, Jack-Clubs, 10-Clubs, 9-Clubs, 8-Clubs

The payout chart is per unit bet is:

Royal Flush - 800

Straight Flush - 50

4 of a Kind - 25

Full House... [ More ]

Reply #3

db101 — Wed, 27 Jul 2022 19:57:30 GMT

in practical terms, jtj is the worst play because you are more likely to get bit by a shark while attending bigfoot's wedding than win the jackpot, and you have 0 chance of winning a smaller prize that makes up for what you spent on tickets. With regular plays and megaplier you will sometimes get back your investment .

Reply #2

JeetKuneDoLotto — Wed, 27 Jul 2022 18:49:32 GMT

WTF?

If my brain was more Seagullish

Maybe I could understand.

Reply #1

Orange71 — Wed, 27 Jul 2022 18:19:19 GMT

Sorry, I messed up the Just the Jackpot (JTJ) pricing. It's $3 for 2 tickets, not $1 for 1 ticket.

Comparing JTJ to regular ticket, then, we have the following equation for the equal EV / unit bet:

(2/3)(kJ)p = (1/2)(kJ)p + A/2

Therefore, J = 3A/(kp).

Comparing JTJ to Megaplier ($3) ticket, we have the following:

(2/3)(kJ)p = (1/3)(kJ)p + (3A)/3

Therefore, again, J = 3A/(kp)

To re-iterate Regular Ticket vs Megaplier:

(1/2)(kJ)p + A/2 = (1/3)(kJ)p + (3A)/3

Once again,... [ More ]

Mega Millions - is a $1, $2, or $3 ticket the best value (EV)?

Orange71 — Wed, 27 Jul 2022 00:36:27 GMT

In my state there are three types of ticket options for Mega Millions:

(1) A regular ticket at $2,

(2) A Megaplier ticket for $3 with enhanced non-Jackpot prizes, or

(3) Just The Jackpot , $1 - no non-Jackpot prizes.

Which is the best value ? To make this a tangible question, we need to define value in a statistical probability sense. I'm going to define this as the highest Expected Value (EV) per unit bet option. I've explained EV in previous post.

The best option in terms of EV... [ More ]