Megabucks (slot) question - am I missing something?
March 21st, 2012 at 4:37:54 PM
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I've been trying to figure out the problem(s) in this argument pretty much all day. - it's probably one (or more) of my assumptions:
(a) Megabucks slot machines have about a 10% house edge;
(b) The chance of winning the jackpot is 1 in 50,000,000;
(c) The jackpot is usually around $15,000,000;
(d) The third coin does not increase the non-jackpot win amounts (so if, say, three red 7s pays 10 for one coin and 20 for two, it pays 20 for three as well).
Using these assumptions, for every 50,000,000 plays at $3/play, the casinos take in $150,000,000 total, keep $15,000,000, and pay out $15,000,000 for a jackpot, which means $120,000,000 is paid out in non-jackpot wins.
If, instead, the 50,000,000 plays ignored the jackpot and played just two coins each, the income would be $100,000,000, but the non-jackpot payouts would remain the same at $120,000,000 - so the machines have a player advantage of 20% if you're willing to risk the chance of making a major fool of yourself if you happen to get the three jackpot symbols.
Is there something obvious that I am missing? I have a feeling I am just imagining that (d) applies to every casino, just because I saw them this way in a few Strip casinos...
(a) Megabucks slot machines have about a 10% house edge;
(b) The chance of winning the jackpot is 1 in 50,000,000;
(c) The jackpot is usually around $15,000,000;
(d) The third coin does not increase the non-jackpot win amounts (so if, say, three red 7s pays 10 for one coin and 20 for two, it pays 20 for three as well).
Using these assumptions, for every 50,000,000 plays at $3/play, the casinos take in $150,000,000 total, keep $15,000,000, and pay out $15,000,000 for a jackpot, which means $120,000,000 is paid out in non-jackpot wins.
If, instead, the 50,000,000 plays ignored the jackpot and played just two coins each, the income would be $100,000,000, but the non-jackpot payouts would remain the same at $120,000,000 - so the machines have a player advantage of 20% if you're willing to risk the chance of making a major fool of yourself if you happen to get the three jackpot symbols.
Is there something obvious that I am missing? I have a feeling I am just imagining that (d) applies to every casino, just because I saw them this way in a few Strip casinos...
March 21st, 2012 at 4:44:14 PM
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You are approaching this question the wrong way. Imagine if the first player to play the machine hit the jackpot for the, what, $1,000,000? The casinos would be behind by $1m - $3 but this irrelevant. The actual outcome has no bearing on the mathematical house edge.
Vote for Nobody 2020!
March 21st, 2012 at 5:30:06 PM
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There is no slot I know of that has an intentional advantage. IGT mega-progressive games all have a marginally higher return for the last coin. Overall, the return at max bet is about 1% higher than playing anything less than max bet.
I heart Crystal Math.
March 21st, 2012 at 8:23:06 PM
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Quote: bigfoot66You are approaching this question the wrong way. Imagine if the first player to play the machine hit the jackpot for the, what, $1,000,000? The casinos would be behind by $1m - $3 but this irrelevant. The actual outcome has no bearing on the mathematical house edge.
That's true, except that, for all intents and purposes, the "third coin" is really a side bet - either you win the progressive, or you win nothing extra.
However, there is a possibility that I didn't take into account - when I said "Megabucks machines have about a 10% house edge," that wasn't the mathematical/theoretical edge, but based on a Nevada Gaming Control Board report over a one-year period, and for all I know, the date range for the report was one in which the jackpot was not hit (it's sort of like using a Monte Carlo method to calculate the ER for Video Poker and getting an undervalue because you never got a Royal Flush).
March 21st, 2012 at 9:20:50 PM
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So I was googling and stumbled across a great website that explains Megabucks:
Wizard of Odds - Megabucks
But seriously, you made a very bad assumption in your original post:
The non-jackpot payouts would NOT remain $120,000,000. You forgot to take into account that payouts are multiple of the bet. So at 2 coins, using your logic, the payout would be $80,000,000.
EDIT: Here's the paytable:
Wizard of Odds - Megabucks
But seriously, you made a very bad assumption in your original post:
Quote: ThatDonGuyIf, instead, the 50,000,000 plays ignored the jackpot and played just two coins each, the income would be $100,000,000, but the non-jackpot payouts would remain the same at $120,000,000 - so the machines have a player advantage of 20%
The non-jackpot payouts would NOT remain $120,000,000. You forgot to take into account that payouts are multiple of the bet. So at 2 coins, using your logic, the payout would be $80,000,000.
EDIT: Here's the paytable:
March 21st, 2012 at 9:33:16 PM
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Quote: ThatDonGuyif you're willing to risk the chance of making a major fool of yourself if you happen to get the three jackpot symbols.
There's a different way to think about that. The machine's RNG is constantly cycling game results. When you push the button to spin the machine asks the RNG for the current result and sets the reels accordingly. That may be a bit over simplified but is good enough for my point which is: If it took you even a few milliseconds to bet 3 credits instead of 2 credits you would have never had that result. Therefore if you're betting only two credits and hit the three MegaBucks you're most likely WAY better off than if you had played all three credits.
Long ago when I was a dealer we got one of the first set of shuffle machines for Caribbean Stud. When a player was complaining about how crappy his luck was with the machines I'd explain that the shuffler uses a random number generator based on time (a half-truth but whatever). I'd hold the deck over machine and tell the customer to say "NOW!" when he wanted me to insert them. The following hand I'd tell him to get ready, because this was HIS hand. If he ended up winning the hand I was almost guaranteed a tip, and it was something fun to do either way.
March 21st, 2012 at 9:37:40 PM
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Quote: PopCanBut seriously, you made a very bad assumption in your original post[/q
Based on that picture, you're right in that my assumption (d) - that the third coin does nothing more than activate the progressive - may not be as accurate as I thought.
However, let me ask you: how old is that photo? The last time I was in Vegas (in mid-2009, admittedly), I couldn't find a Megabucks machine where the third coin payouts were different from the two-coin ones (other than the progressive, of course). Then again, maybe I just didn't look hard enough?
March 21st, 2012 at 10:31:59 PM
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I have no idea how old that photo is. Every photo I found had different payouts for the third coin but I believe you when you say you've seen the third coin only enable the jackpot. This is a great logic puzzle in that case; sorry for jumping to conclusions.
I'm going to take an educated guess and say that although you're not eligible for the jackpot when betting 2 coins, the same portion of your coin-in goes into the meter and reserve (the reserve is used reseed the jackpot at $10 million after it's hit). I'll have to think for a while before I can actually write out any sort of formula as to why that works out.
I'm going to take an educated guess and say that although you're not eligible for the jackpot when betting 2 coins, the same portion of your coin-in goes into the meter and reserve (the reserve is used reseed the jackpot at $10 million after it's hit). I'll have to think for a while before I can actually write out any sort of formula as to why that works out.
March 22nd, 2012 at 10:09:08 AM
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Here are some numbers I got from the Nevada Gaming commission site for Megabucks statewide:
"2-coin in" is 2/3 of the "coin in" value (i.e. the assumption of what the coin in would be if everybody put in 2 coins instead of 3)
Note that there were no jackpots in these months (March and May 2009 were chosen because the $33 million hit was in April 2009).
Based on this, you would think the 2-coin strategy would work.
However, there are a couple of other things I didn't take into account:
First, I am making the assumption that numbers reported as "Megabucks" are strictly dollar Megabucks machines. If it includes Quarter Megabucks and Penny Megabucks, this would skew the numbers.
Second, for all I know, the "coin out" value includes how much is paid out to past jackpot winners who didn't take the 60% lump sum option (with annual values spread out over the entire year).
| Month | Casino Profit | Casino % | Coin In | 2-Coin In | Coin Out |
|---|---|---|---|---|---|
| March 2011 | 5,754,000 | 13,70 | 42,000,000 | 28,000,000 | 36,246,000 |
| May 2011 | 6,279,000 | 14.23 | 44,125,000 | 29,417,000 | 37,846,000 |
| March 2009 | 7,383,000 | 13.05 | 56,575,000 | 37,717,000 | 49,192,000 |
| May 2009 | 3,897,000 | 9.63 | 40,467,000 | 26,978,000 | 36,570,000 |
Note that there were no jackpots in these months (March and May 2009 were chosen because the $33 million hit was in April 2009).
Based on this, you would think the 2-coin strategy would work.
However, there are a couple of other things I didn't take into account:
First, I am making the assumption that numbers reported as "Megabucks" are strictly dollar Megabucks machines. If it includes Quarter Megabucks and Penny Megabucks, this would skew the numbers.
Second, for all I know, the "coin out" value includes how much is paid out to past jackpot winners who didn't take the 60% lump sum option (with annual values spread out over the entire year).
March 22nd, 2012 at 11:03:39 AM
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Coin out should not include any of the mega-jackpot prizes. These games are on a revenue share, where IGT gets about half of the hold and pays the big winners. The casino never pays the prizes, even if the player might settle for a lump sum.
If you can provide a picture of glass which shows what you are describing, I'll be able to explain why there's no advantage.
I also guarantee that if there were an advantage, players would have found it and exploited it, then the games would be shut down.
If you can provide a picture of glass which shows what you are describing, I'll be able to explain why there's no advantage.
I also guarantee that if there were an advantage, players would have found it and exploited it, then the games would be shut down.
I heart Crystal Math.
March 22nd, 2012 at 12:06:44 PM
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Quote: CrystalMathCoin out should not include any of the mega-jackpot prizes. These games are on a revenue share, where IGT gets about half of the hold and pays the big winners. The casino never pays the prizes, even if the player might settle for a lump sum.
The same reports show a coin-in of $53,275,000 and a coin-out of $54,804,000 for April 2009 (when the $33 million was won), so I am assuming that the coin-out includes at least part of the jackpot.
March 22nd, 2012 at 1:03:42 PM
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Quote: ThatDonGuyThe same reports show a coin-in of $53,275,000 and a coin-out of $54,804,000 for April 2009 (when the $33 million was won), so I am assuming that the coin-out includes at least part of the jackpot.
Well, maybe it does. I wonder how they do the accounting, though. For players who choose to get paid over 20 years, it seems like the book value would be the net present value of the annual payment and not the jackpot amount.
I heart Crystal Math.
March 22nd, 2012 at 1:11:25 PM
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It appears that my assumption that Megabucks machines don't increase the non-jackpot payouts on the third coin may not be as accurate as I thought. The Harrah's slot machine database says that all of its Strip properties have Megabucks Double 3x 4x 5x machines, and, according to the IGT website, those do pay extra on all pay lines on the third coin.
(It's possible that, if those machines that I thought didn't pay extra for the third coin really were Megabucks machines, then they were ones where there was an additional feature activated besides the progressive - for example, the Spin on WoF dollar slots.) Guess I'll have to pay a little more attention next time I'm in town.
(It's possible that, if those machines that I thought didn't pay extra for the third coin really were Megabucks machines, then they were ones where there was an additional feature activated besides the progressive - for example, the Spin on WoF dollar slots.) Guess I'll have to pay a little more attention next time I'm in town.
August 28th, 2012 at 12:05:12 PM
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Bump...I finally got around to getting back to Vegas, and yes, there were dollar Megabucks machines where the third coin in increased all of the payouts accordingly. My bad...
August 28th, 2012 at 5:33:06 PM
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I'm late to the party!!!
But, yes, the only MegaBucks machines I have ever seen have had a prefectly graduated payout with exception to the Progressive on the third coin.
But, yes, the only MegaBucks machines I have ever seen have had a prefectly graduated payout with exception to the Progressive on the third coin.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
