CasinoJunkie
Joined: May 20, 2020
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May 22nd, 2020 at 8:09:42 AM permalink
Can someone go to the mega millions analysis page on WoO and take a look at the “mega million return table - with megaplier” and the paragraph before and after the table and tell me if it makes sense to you?

Where I’m confused is it says “The win column is the base win, before applying the Megaplier” but it looks to me that the win column has been multiplied by the average Megaplier. Also, I’m confused at the break even number in the paragraph below. With an EV of 29.10% at a \$40M jack pot and an additional 11.02% for every \$100M in the jackpot I come up with closer to \$683M for the BE. Someone please help. Thanks.
Mission146
Joined: May 15, 2012
• Posts: 12986
May 22nd, 2020 at 9:34:20 AM permalink
Quote: CasinoJunkie

Can someone go to the mega millions analysis page on WoO and take a look at the “mega million return table - with megaplier” and the paragraph before and after the table and tell me if it makes sense to you?

Where I’m confused is it says “The win column is the base win, before applying the Megaplier” but it looks to me that the win column has been multiplied by the average Megaplier. Also, I’m confused at the break even number in the paragraph below. With an EV of 29.10% at a \$40M jack pot and an additional 11.02% for every \$100M in the jackpot I come up with closer to \$683M for the BE. Someone please help. Thanks.

Looks like he put that sentence in there by mistake. The table that you reference assumes a Megaplier of 3x, which is the average, so is why he used that as the assumed Megaplier for the purposes of the total return of the table.

From:

https://www.megamillions.com/How-to-Play.aspx

Quote:

Most states offer a Megaplier feature to increase non-jackpot prizes by 2, 3, 4 or 5 times; it costs an additional \$1 per play. Before each Mega Millions drawing on Tuesday and Friday nights, the Megaplier is drawn. From a pool of 15 balls, five are marked with 2X, six with 3X, three with 4X and one with 5X. This mix results in the following odds for each of the Megaplier numbers and their associated prize values:

((5*2)=(6*3)+(3*4)+(5 *1))/15 = 3

So, he used the average multiplier value of 3x to calculate the return. The sentence that you're describing was probably either not meant to be there at all or not meant to say that. Either that, or an original version of the table did include just the base pays, but then Wizard decided it more prudent to do a table based on the average in order to calculate a total expected return.
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CasinoJunkie
Joined: May 20, 2020
• Posts: 5
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May 22nd, 2020 at 10:03:00 AM permalink
Thanks for the reply. That clears up the first part. I think the table win and return columns are with the average 3x megaplier applied and that sentence in question is there by mistake.

Does the break even look right to you? \$224M? It seems like the megaplier was removed to get that number because it’s roughly 1/3 of the number I came up with of \$683M. I simply did {(1-.2910)/.1102}*\$100,000,000+\$40,000,000=\$683,375,681

What am I missing?
Mission146
Joined: May 15, 2012
• Posts: 12986
May 22nd, 2020 at 10:44:00 AM permalink
I'm actually not sure what happened there. Even the analysis paired with it:

Quote:

The lower right cell of the table above shows the player can expect to get back 29.10% of his money at a jackpot of \$40 million. The rate of return goes up by 11.02% for every additional \$100 million in the jackpot with the Megaplier option. Before considering the annuity, taxes, and jackpot sharing, the break-even point, where the expected return would be 100% is \$224,191,728.

Does not seem to make sense with the number.

I'm going to do this a much different way by using the \$\$\$ return instead of the Expected Value, which we can just divide by \$3 and figure out at the end. I'm also not going to include the jackpot at all because it's a variable. Therefore, it's easier just to keep it separate and figure the breakeven point at the end.

(1/12607306 * 3000000) + (1/931001 * 30000) + (1/38792 * 1500) + (1/14547 * 600) + (1/606 * 30) + (1/693 * 30) + (1/89 * 12) + (1/37 * 6) = 0.73988264255

Okay, so that is the return, in dollars, based on the average 3x multiplier and before accounting for the jackpot at all. This makes accounting for the jackpot a matter of simple algebra because all I want is for the total to equal \$3:

This is also the added \$\$\$ return that the extra dollar spent gets you, since it does not impact the top jackpot.

(1/302575350 * x) = (3-.73988264255)

x = 683,855,800.471509

So, it looks like I agree with you with any differences being due to rounding.

Also, the jackpot would have to be MORE than it would for the base ticket, unless the Megaplier has by itself a positive expected value, which it doesn't. It is technically less bad (by percentage only) than the base ticket, but even if you could play the Megaplier by itself (ignoring the jackpot) it would not be a positive expectation. So, you have part of that extra \$1 to make a \$3 ticket losing expectation and therefore the jackpot must be higher.

I'm not exactly sure what happened here. I think maybe Wizard got his figure because whatever he was using, for one thing, assumed a base top jackpot of \$40,000,000. The second thing I think may have been a problem is that maybe what he was using thinks the top jackpot triples, which it of course doesn't. His break even point is not exactly 1/3 of what we got, but it's pretty close.
Vultures can't be choosers.
CasinoJunkie
Joined: May 20, 2020
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May 22nd, 2020 at 11:31:04 AM permalink
Thanks Mission!

I think the problem is solved. As for the mystery of why the Wizard had the BE so low I think it might’ve just been a pasting error or something because that number, the \$224M, is mentioned near the end of the article. The expected return for all ticket types (normal, with megaplier, and jackpot only) is the same 49.90% when the jackpot is \$224M. So based on that the Wizard must agree \$224M is not the BE. I don’t think he 3x’d the jackpot because the chart shows \$40M and he mentions in the article that the jackpot is not megaplied.
CasinoJunkie
Joined: May 20, 2020
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May 23rd, 2020 at 1:37:45 AM permalink
Hey Mission,

There’s one more thing. In the “other factors” section there’s a sentence that says,

“By the way, ignoring all factors besides the interest rate, the time value of the win is greater taking the lump sum option at an interest rate of over 3.40%, otherwise take the lump sum.”

That doesn’t make any sense. Do you think it’s supposed to say otherwise take the annuity?
Mission146
Joined: May 15, 2012