Weighted Outcomes on Mechanical Reel Slots

The way I've always understood things is that every possible stopping position on each reel of mechanical slot machines is mapped to a specific number. A random number generator picks 3 numbers (stopping positions) and the reels stop accordingly.

Where I get confused is that it seems like certain outcomes (or stopping positions) seem to be more prevalent than others.

Lets take the classic Wheel Of Fortunes machines for example. The third real has a 'Spin' icon on it and if the reel lands on spin, the user gets to spin the wheel. Many other mechanical reel machines with bonus rounds use the same idea. The third real lands on a specific icon, you get the bonus round.

Since I don't know the real amount (and if somebody does, please let me know), lets say there are hypothetically 50 possible stopping positions on a reel. Does every position on the reel carry an equal probability of getting landed on? It seems like a very high percentage of the time, the reel stops either just below or just above the bonus round icon as a 'tease'. I don't have any statistical proof, it's just the way it seems at the casinos I've visited.

The real amount is usually between 32 and 64 virtual stops, mapped unequally to 22 physical ones. Here's how most mechanical slot games have worked since the mid-1980s:

Telnaes patent

The tease effect you note is called a "near miss" and it is accomplished by increasing the virtual weight of the blanks above and below the symbol. For example, if a reel strip has a segment with blank/TopAward/blank, and you weight those 6/1/6 (out of 50 total virtual stops), then you have a 26% chance of seeing the TopAward symbol in the viewing window but only 2% chance of actually having it land on the payline. Some jurisdictions have limited the weighting ratios in situations like this.

For more, I highly recommend chapter 4 of "License to Steal, Nevada's Gaming Control System in the Megaresort Age" by Jeff Burbank. All but one page of that chapter is available on Google Books.

Quote: MathExtremist

The real amount is usually between 32 and 64 virtual stops, mapped unequally to 22 physical ones. Here's how most mechanical slot games have worked since the mid-1980s:

Telnaes patent

The tease effect you note is called a "near miss" and it is accomplished by increasing the virtual weight of the blanks above and below the symbol. For example, if a reel strip has a segment with blank/TopAward/blank, and you weight those 6/1/6 (out of 50 total virtual stops), then you have a 26% chance of seeing the TopAward symbol in the viewing window but only 2% chance of actually having it land on the payline. Some jurisdictions have limited the weighting ratios in situations like this.

For more, I highly recommend chapter 4 of "License to Steal, Nevada's Gaming Control System in the Megaresort Age" by Jeff Burbank. All but one page of that chapter is available on Google Books.

Very interesting and informative post. Answered my question perfectly. Much appreciated.

Maybe I'm taking this out of context, but I had read somewhere on WoV (possibly a Wizard post) that most modern 3 reel machines, particularly those with huge jackpots such as Megabucks, have 368 virtual stops for each reel.

368 ^ 3 = 49.8 million. This means the maximum odds are 1 in 49.8 mil which is good since there is a rule that the maximum odds are 1 in 50 mil.

Quote: DJTeddyBear

368 ^ 3 = 49.8 million. This means the maximum odds are 1 in 49.8 mil which is good since there is a rule that the maximum odds are 1 in 50 mil.

Where? In Nevada? The only rule I am aware of is, if the odds of hitting the jackpot are 1 in 100 million or worse, then the odds have to be displayed on the machine.

Not sure where.

Like I said, I was just repeating what I remember reading here somewhere.

I may have some details wrong, but the 368^3 thing was something specific I remembered.

I worked on a wide area progressive in the 1990's and the slot machines had to be modified because they only allocated one byte to each virtual reel. Those 256 stops were not enough for our progressives. I don't recall exactly what we ended up using but i know it was more than 256.

Quote: DJTeddyBear

Maybe I'm taking this out of context, but I had read somewhere on WoV (possibly a Wizard post) that most modern 3 reel machines, particularly those with huge jackpots such as Megabucks, have 368 virtual stops for each reel.

368 ^ 3 = 49.8 million. This means the maximum odds are 1 in 49.8 mil which is good since there is a rule that the maximum odds are 1 in 50 mil.

I think that's accurate for Megabucks specifically. Modern stepper games can, of course, have virtual reels of almost any length. It's usually not necessary to get that high for non-progressive games because the top awards don't call for it. I never dealt with single-byte restrictions on reel stops the way DRich did, but regardless I don't recall doing a one-line game with virtual strips anywhere close to 256 symbols. I've only done a handful of single-line games in any event; mostly it's some variation of 5-reel multiline + many bonuses/free spins and the occasional mini-reel grid-style game, and because there are more reels in those games, the individual reels don't need to be nearly as long in order to get very long odds. 5 reels with 64 stops each is about a billion-to-one longshot for an award with one stop per reel.

Quote: DJTeddyBear

Like I said, I was just repeating what I remember reading here somewhere.

I may have some details wrong, but the 368^3 thing was something specific I remembered.

I read that somewhere as well, and I think it was somebody saying that Megabucks slot machines have reels with 368 virtual stops, but he didn't say what his source was.

Quote: DRich

I worked on a wide area progressive in the 1990's and the slot machines had to be modified because they only allocated one byte to each virtual reel. Those 256 stops were not enough for our progressives. I don't recall exactly what we ended up using but i know it was more than 256.

I recall testing games at GLI with 512 stops. Of course, there must be more than 1 top award symbol per reel to bring down the top award odds. In most jurisdictions, the top award odds are limited to 1:17 million, but not in NV.

Quote: CrystalMath

I recall testing games at GLI with 512 stops. Of course, there must be more than 1 top award symbol per reel to bring down the top award odds. In most jurisdictions, the top award odds are limited to 1:17 million, but not in NV.

I felt like burning off some of my time this afternoon/evening and double checked this for several states (not an exhaustive list):

Actually many states require only a hit frequency of greater than 1 in 50M, which has been GLI standard since at least 2000 (v. 1.3). The fact GLI suggested greater than 1 in 50M makes me believe Megabucks is likely 1 in (368)^3 = 1 in 49.8M. I've never seen the parsheet obviously, but this is what John Robison has claimed a few times.

Hit frequency of less than 1 in 100M allowed with explicit payglass display of odds (effectively a 1 in 100M requirement):
Nevada

Hit frequency always greater than 1 in 100M:
Arkansas (racinos)
New Jersey
Mississippi

Hit frequency always greater than 1 in 50M:
Arizona
Indiana
Iowa
Kansas (state-run casinos) (ripped off most technical standards by referencing GLI-11 v. 2.0 except bumping minimum payout to 87%)
Maine (large ripoff of GLI-11 v. 1.3)
Maryland
Missouri
Pennsylvania

Hit frequency always greater than 1 in 50M for linked progressives; 1 in 17M for non-linked progressives:
Colorado

Hit frequency greater than 1 in 17M:
Connecticut

I generally restricted myself to mostly non-tribal states though.

Well, I did leave GLI 6 years ago. Most of the games that were submitted were limited to 1:17M to comply with the odds regulations from most, if not all, jurisdictions. I just checked Colorado, and theirs states that the odds must be 1:17M or better unless it is a "multi-link" progressive, in which case, it can be 1:50M. That definitely changed in the last 6 years.

I remember one game was submitted which had exactly 1:17M odds, and it created an enormous problem because the regulations in most states say something to the effect of "better than." I recall that CT refused to accept the game, among other jurisdictions.

Quote: CrystalMath

I remember one game was submitted which had exactly 1:17M odds, and it created an enormous problem because the regulations in most states say something to the effect of "better than." I recall that CT refused to accept the game, among other jurisdictions.

Silliness. And you're right, many states when I looked them up are "hit frequency greater than 1 in 50M, etc." It sounds like they really didn't let combinatorics naturally do its thing for that payout either. I'd assume that 1:17M is the strictest that ANY state requires, so it behooves slot/video poker manufacturers to abide by this, barring linked-progressive games a la Megabucks. And yeah, I forgot to look at Colorado, whoops. Post updated.