Wizard
Joined: Oct 14, 2009
• Posts: 16341
March 16th, 2010 at 9:56:42 AM permalink
I'm in the early stages of some analysis of the Megabucks slot machine. Two questions I'd like to address are the return and probability of winning the jackpot.

It is pretty easy to get a good estimate of the return. Nevada Gaming Control Board annual reports have a specific line item for Megabucks from their web site. Here is a summary from 1996 to 2009.

Year Profit (\$) Profit (%) Handle
2009 53,352,000 10.43% 511,524,449
2008 83,981,000 11.85% 708,700,422
2007 88,858,000 12.72% 698,569,182
2006 100,923,000 12.39% 814,552,058
2005 100,923,000 12.39% 814,552,058
2004 67,326,000 10.54% 638,766,603
2003 83,069,000 10.41% 797,973,103
2002 76,842,000 11.98% 641,419,032
2001 69,821,000 11.50% 607,139,130
2000 69,103,000 9.75% 708,748,718
1999 74,921,000 12.28% 610,105,863
1998 134,943,000 12.25% 1,101,575,510
1997 66,166,000 12.18% 543,234,811
1996 57,619,000 10.03% 574,466,600
Total 1,127,847,000 11.54% 9,771,327,540

The handle column was derived by dividing the second column by the third column. So we see a profit, or house edge, of 11.54%.

According to www.a2zlasvegas.com, Megabucks has been hit 34 times between 1996 and 2009. I start at 1996, because they start on Oct. 18, 1995, and I don't know if anybody hit in 1995 before Oct. 18.

It costs \$3 a pop to qualify for the progressive. Dividing the handle by \$3, that would be 3,257,109,180 plays. Dividing that by 34 jackpots yields a probability of winning of 1 in 95,797,329. However, probabilities of winning often bandied around are 1 in 15 million to 1 in 50 million. I tend to believe the 1 in 50 million. The Las Vegas Sun quotes John Robinson, who puts it at 1 in 49,836,032.

There are a lot of bright people who participate in my forum (thank you), so I'm putting this out there for peer review. Here are some possible comments, and counter-comments:

Perhaps the handle is inflated by players betting \$1 or \$2 (who wouldn't qualify for the jackpot), this would lower my estimate of the probability of winning. Somewhere in the back of my mind I recall hearing of a woman who only bet \$1 and got the three Megabucks symbols, but only won \$5,000 because of the small bet. However, I tend to think the vast majority of bets are at \$3. This alone I don't think should cause me to be off by a factor of 2.

Another thing to confuse the issue is the Megabucks penny machine. A \$3 bet is still required to win the jackpot, but perhaps the probability of hitting is different from the 3-reel game.

Another issue may be that jackpots are paid in an annuity. If the win in the Gaming reports is based on amounts actually paid, not including future payments, that would mess things up. I sent a letter to the Gaming Control Board asking for an answer to that question.

It is also possible the probability of hitting has changed at some point since 1996. Somewhere I heard the jackpot seed changed from 8 million to 10 million at some point, but can't remember when, or the source.

I plan to actually go out there and play it about 2,000 times, so see how often the jackpot symbols come up. However, for now, any comments or criticisms of the above?
It's not whether you win or lose; it's whether or not you had a good bet.
cclub79
Joined: Dec 16, 2009
• Posts: 1147
March 16th, 2010 at 10:13:09 AM permalink
Quote: Wizard

I plan to actually go out there and play it about 2,000 times, so see how often the jackpot symbols come up. However, for now, any comments or criticisms of the above?

My comment goes back to something we were discussing a few weeks ago, and I apologize if it was already answered: Can you tell something substantive from how often the symbols come up? I thought the RNG determined whether or not you won and then displayed the 3 reels in any combination. So a losing RNG could show three blanks, or 2 Jackpot symbols and a blank. When I get 2 Wheel Of Fortune symbols in a row, and then nothing, does it mean that I was closer to winning than a different time, or if I get 2 WOF and a cherry, did it just want to find a different way to give me 40 credits instead of paying me 40 credits with 3 Double Bars?

Once on a Double Diamond \$1 WOF (5 line), I got 3 Double Diamonds Diagonally (\$800), and due to the position, I also got a diagonal Double Bar with the Double Diamond in the middle position, giving me something like an extra 40 bucks. Is there a position on the RNG for a pay of \$840 that has to be paid in that manner? And other 3 Double Diamonds that don't pay that way? I'm just trying to find the link between the RNG and the way the win (or loss) is displayed.
Wizard
Joined: Oct 14, 2009
• Posts: 16341
March 16th, 2010 at 10:20:48 AM permalink
Single-line slot machines work by randomly stopping each reel according to probabilities established by the slot maker. Each reel is independent, so the win is determined by the reels, not the other way. My page on slot machines tries to explain it.
It's not whether you win or lose; it's whether or not you had a good bet.
DJTeddyBear

Joined: Nov 2, 2009
• Posts: 9594
March 16th, 2010 at 10:36:11 AM permalink
I'm afraid to say this, but I think you're thinking like a typical gambler, and not the math wiz your nickname portrays you to be.

First, I believe you're underestimating the amount of coin-in that doesn't qualify.

There are plenty of players that play less then the full coin-in - as long as the basic game is fun and entertaining, they play at low stakes because they know they aren't going to hit the jackpot anyway.

Many players that do play max-bet, will play whatever odd amount is left over on the last spin when they bust out.

Second: Strange as it may seem, I think 14 years is still not enough time to get the true 'law of large numbers' large number.

For instance, I don't recall any sudden national prosperity that enabled the handle to double in 1998, and return to the norm in 1999. That alone should tell you that in 1998 there were far fewer jackpots paid out than normal. Is that because there were other 'winners' that decided to keep quiet rather than suffer the shame of betting cheap and winning a cheap prize? Or does that suggest that the randomness has enough variance that you can't do the kind of analysis you're suggesting?

---

Edit: See my followup post below.

I don't know if your 2,000 spin test will prove anything other than if the casino's comp system correctly records your play.

Does the RNG select the stop point of the three wheels indepentently, and then the computer calculate if the resulting symbols is a winner? I think not.

I may be completely out of my mind here, but this is how I think modern slot machines work: You hit the button which fetches a number from the RNG. That number indicates a win or a loss. If it's a win, it also dictates what type of win and for how much (Or a second RNG number dictates that). The computer then stops the wheels on the symbols that match the type and value selected.

Here's the tricky part:

If it's a loser, I REALLY think the computer does NOT have 'random' results displayed. I think the losing wheels will occasionally deliberately show a 'near win'. Not necessarily a near jackpot, but something, anything, that would screw with a player's head and encourage additional play.
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? Note that the same could be said for Religion. I.E. Religion is nothing more than organized superstition.
DJTeddyBear

Joined: Nov 2, 2009
• Posts: 9594
March 16th, 2010 at 10:39:33 AM permalink
Quote: Wizard

Single-line slot machines work by randomly stopping each reel according to probabilities established by the slot maker. Each reel is independent, so the win is determined by the reels, not the other way. My page on slot machines tries to explain it.

OK. You wrote this while I was composing my prior email.

Does this mean the RNG stops the wheels WHEN it wants to (i.e. a duration of spin thing), or on a specific symbol?

I.E. Couldn't the jackpot symbol on two wheels be programmed to come up often, but on the third wheel to almost never come up?
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? Note that the same could be said for Religion. I.E. Religion is nothing more than organized superstition.
Wizard
Joined: Oct 14, 2009
• Posts: 16341
March 16th, 2010 at 10:51:22 AM permalink
DJTeddyBear, I'm afraid you are dead wrong about how slot machines work. I would lay 1000 to 1 on that. I have a box of PAR sheets showing how they are designed. However, I don't want to sidetrack this into another discussion about how slot machines really work. If you want to do that, please start up another thread.

I could be wrong about most plays being \$3 bets. That is based on observing players playing for long period of time, consistently betting \$3. Much like video poker players usually bet the full 5 coins to qualify for the full pay on a royal flush.

The standard deviation over that time period should be about 5.8 jackpots. So I doubt it is far off from expectations.

Regarding the large handle in 1998, a jackpot was hit for \$27,580,878 at the Palace Station on 11/15/98. The seven jackpots before that ranged from 6.3 to 12.5 million. So perhaps the large jackpot induced a lot of play. I've heard of players lining up to play when the jackpot gets big.
It's not whether you win or lose; it's whether or not you had a good bet.
JB
Joined: Oct 14, 2009
• Posts: 2053
March 16th, 2010 at 10:53:34 AM permalink
Quote: DJTeddyBear

OK. You wrote this while I was composing my prior email.

Does this mean the RNG stops the wheels WHEN it wants to (i.e. a duration of spin thing), or on a specific symbol?

I.E. Couldn't the jackpot symbol on two wheels be programmed to come up often, but on the third wheel to almost never come up?

It could be designed to do that, but not programmed.

For an overly simplified example, suppose each reel has 100 stop positions. Reels 1 and 2 both have 10 stops that correspond to the jackpot symbol, but reel 3 only has 1 stop that corresponds to the jackpot symbol. If the reels were designed this way, you would naturally see more near misses where the 1st and 2nd reels have the jackpot symbol, and not the third.

I wouldn't call that "programmed" though, because it is still random, it's just that the probability of a near miss would be greater with that kind of reel stripping.

However, based on John Robison's figure, I would guess that each reel has 368 stops, with only 1 stop per reel corresponding to the jackpot symbol.
cclub79
Joined: Dec 16, 2009
• Posts: 1147
March 16th, 2010 at 11:00:46 AM permalink
It wasn't my intent to hijack the thread, so thank you both for your response!
DJTeddyBear

Joined: Nov 2, 2009
• Posts: 9594
March 16th, 2010 at 11:45:16 AM permalink
Quote: Wizard

DJTeddyBear, I'm afraid you are dead wrong about how slot machines work. I would lay 1000 to 1 on that. I have a box of PAR sheets showing how they are designed. However, I don't want to sidetrack this into another discussion about how slot machines really work. If you want to do that, please start up another thread.

Understood.

I created a new thread: How do slot machines work.
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? Note that the same could be said for Religion. I.E. Religion is nothing more than organized superstition.
thlf
Joined: Feb 24, 2010