How do slot machines work?

In the Wiz' Megabucks thread, I got off on a tangent, and The Wiz suggested I start a new thread. The following quotes are all from that thread.

Quote: DJTeddyBear

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.

Quote: DJTeddyBear

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?

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.

Quote: JB

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.

Programmed / Designed ... Semantics.


JB, you ARE aware we're talking about a reel machine and not video, right?

If so, then I'll accept that the truth is a combination of what you're saying and the Wiz's assertation that I'm wrong.

Since the physical reel has only about 20 symbols, if it has 100, or 368, 'stops' they are probably not evenly distributed. If the physical reels are identical, the design can include a random position of which stop table applies to which reel, this way the 'near miss' doesn't show an inordinate number of hits on any specific reel.

Is any of this close to the truth?

Up here in nanny-state Canada, a placard on each slot machines at the casinos state something to the effect that the appearance of winning symbols close to a winning combination do not equate to being close to a win.

Ya know, sometimes I gotta open my eyes when I read.

Early in the MegaBucks thread, the Wiz referenced his Slot Machines Explained page.

Here's a telling portion:

Quote:

Note how there are clusters of the same symbol in a row. For example, stops 60 to 62 on reel 1 all are mapped to a 1 bar symbol. These will all be directed to the same 1 bar symbol on the actual reel. There are exactly 22 groups of like symbols on each reel, which is the standard number of stops on an electro-mechanical three-reel slot machine, known as a "Stepper Slot."

Also note that only stop 45 on reel 1 is mapped to the red 7 symbol. However the blanks above and below it have five positions each. This causes the often seen near miss effect, where the reel stops directly above or below the highest paying symbol.

So this anwsers all of my questions, except one: Can the table assignment be randomized so a symbol that actually HITS the payline, doesn't always hit on the same reel?

According to John Robinson the odds of hitting Megabucks are 1 in 49,836,032. That is (1/368)^3. So I claim that for each reel the probability it steps on the jackpot symbol is 1/368.

Although stepper slots generally have 22 actual positions on each reel, the jackpot symbol in Megabucks has a lower weighting than the average symbol. As evidence, my slot machine appendix 1 show the results of 3,976 spins on a game in Reno. Notice how the reels stop on the double red 7 about 1/6 as often as the blanks above and below it. As I understand it, there is a law that consecutive positions on a reel strip can not differ in weighting by a factor of more than 6. This is so that the "near miss effect" is not too egregious.

I hope that helps.

I understand the Wiz's explanation now. So the strip could make it easy to look like you were close to a Red 7 (or Jackpot symbol), but if the actual symbol shows up on the payline, you indeed hit the correct stop on that reel, and do have a better chance (with the other stops unknown to you) than you did before you hit the "Spin Reels" button.

On the Wheel Of Fortune slots, they probably do have more stops for the Jackpot symbol on the first reel, because I do see it more often there than the other two reels. I guess that means if you get the WOF Jackpot Symbol on the THIRD reel (and not on the other 2), you really did come closer than ever to winning the Jackpot. You got the "hard" one, but not the "easier" ones.

One question...how is this different on the WOF with 5 Paylines, ($1 Machine, 5 credits/spin).

Quote: DJTeddyBear

WHO do slot machines work? OY. I noticed that typo two seconds too late.....

Fixed.

Quote: DJTeddyBear

JB, you ARE aware we're talking about a reel machine and not video, right?

Yes.

Quote: DJTeddyBear

Since the physical reel has only about 20 symbols, if it has 100, or 368, 'stops' they are probably not evenly distributed.

You have nearly answered your own question...

Quote: DJTeddyBear

If the physical reels are identical, the design can include a random position of which stop table applies to which reel, this way the 'near miss' doesn't show an inordinate number of hits on any specific reel.

Is any of this close to the truth?

Suppose the physical reel strip contains each paying symbol once, separated by blanks, like so:

Blank #1
Cherry
Blank #2
Single-Bar
Blank #3
Double-Bar
Blank #4
Triple-Bar
Blank #5
Red Seven
Blank #6
Jackpot

(Blank #1 is below the Jackpot symbol because it wraps around)

This doesn't mean each symbol has an equal chance of being stopped upon. Instead, a random number is selected from a larger pool of numbers, such as 368. This random number from 1 to 368 is then "funneled" down to the appropriate symbol, such as:

1 to 44: Blank #1
45 to 79: Cherry
80 to 119: Blank #2
120 to 149: Single Bar
150 to 189: Blank #3
190 to 214: Double Bar
215 to 254: Blank #4
255 to 274: Triple Bar
275 to 314: Blank #5
315 to 324: Red Seven
325 to 367: Blank #6
368: Jackpot

This gives the following probabilities for each symbol:

Blank = 247/368
Cherry = 35/368
Single Bar = 30/368
Double Bar = 25/368
Triple Bar = 20/368
Red Seven = 10/368
Jackpot = 1/368

Using virtual stops like this allows the manufacturer to fine-tune the game's return by adjusting what range of numbers correspond to which symbol. And while this is a theoretical example that I just came up with, notice how all of the blanks have a probability of 40/368, except the two that surround the jackpot symbol: the one above it has a 43/368 probability, and the one below it has a 44/368 probability. Doing this will make the jackpot symbol appear to "miss" more often than the other symbols.

Edit: Man, I take too long reading, re-reading, and revising my posts. Missed the boat again!

Wiz -

I think I understand. This means that it is far more likely to have all three Megabucks symbols appear in the space below the payline, as it is to win it. (Or more likely on the 'wrong' payline, winning a minor prize, for multi-line machines.) And that if only one MB symbol appears, (regardless of position) it is equally likely to appear on any wheel.

Is that right?


When I first mentioned the 'near miss', and the possibility of the machine being designed to screw with a player's head, I was talking about something different.

Based on the sample 45 line reel tables on your slots explained page, I assume the three tables are not identical.

Let's say there is a combination that the designer wants to have hit 100 times as often as that MB jackpot. My pea-brain says to put it once on one reel tables, and ten times on the other reel tables. But that would mean that symbol hits a lot on those two reels.

Do the designers randomize the assignment of the table column to the reel so that in the scenario I just described, a loser hitting one or two of the three symbols is evenly distributed among the three reels?

Quote: JB

Edit: Man, I take too long reading, re-reading, and revising my posts. Missed the boat again!

Me too! I started my above post half an hour ago!

(Now where's that damn laughing emoticon?)

Quote: DJTeddyBear

Do the designers randomize the assignment of the table column to the reel so that in the scenario I just described, a loser hitting one or two of the three symbols is evenly distributed among the three reels?

I would think they can't really "randomize" anything like that, because they have to take into account all the payouts possible with different combinations. Three red 7s may be a big payout, but three ANY 7s also pays, as may 2 Red 7s and a Jackpot of Wild Symbol. I'm sure they have to get all of their ducks in a row exactly how they need to for the payouts they desire.

So now I'd like to know the EXACT chance of spinning the wheel on the Wheel of Fortune Machines ($1/3 credit/1 line). If that third reel has its own RNG and a fixed number of stops, how often do you think the SPIN symbol pops up?

Also, Wizard, do you mind saying how much you made (or lost) during your experiment described in the Slot Appendix?

Sorry to hijack the thread, but since the title doesn't specify reel slots, I will forge ahead.

My wife likes to play a WGM game called Goldfish, an animated video slot.
Every so often you get random Bonus plays. One of them puts about 7 bubbles on the touch screen, and you get to pick one of the bubbles. They range from 5x your bet up to 70x your bet, and then one bubble says you win ALL of the payouts from all of the bubbles.
Another Bonus game puts 3 turtles on the screen, and you pick one of the 3 turtles. Again, you win 3x your bet, 30x your bet, or 300x your bet (The numbers are off as I don't recall the exact multipliers).

My question is, Does it really matter which bubble or turtle you pick? Or is that just a sideshow thrown in for the player's amusement, and to make them think they are affecting the outcome of the game? If the player is truly determining the outcome, how would they know what the payout % is, since it can vary greatly based on whether players were picking correctly or not.
My suspicion is that the multiplier has already been decided by the RNG, and it doesn't matter which bubble or turtle you pick, it will be whatever the game has already decided. Then after you decide, the program just throws the remaining values on the screen to show you 'where' they were.
Anyone know for sure?

There are a number of significant portions of the Wizard's explanation of how slot machines work:

(1) The near miss is very much alive and legal as long as it is based on probabilities and not pre-determined. Psychologists point out it is a powerful incentive to the addict.
(2) The virtual stops mapped to the real stops are explained in detail. As the younger generation is less enamored with three wheel mechanical machines, the virtual stops will probably phase out of existence. The video five reel machines have enough combinations that the mapping is no longer necessary. Initially people were used to mechanical machines, and they distrusted the 5 reel video machines. The mapping was necessary for people to have a familiar visual display.
(3) The original method to encourage multiple coins was to pay 2X, 3X, ... the pay for the equivalent number of coins. The least likely outcomes would increase by a higher percentage (or alternatively a progressive payout) to induce the player to bet more than one coin. Much more effective is the Wheel of Fortune or the Blazing 7's method, where the first coin is dedicated to more numerous payouts of very low multiples, and the 2nd or 3rd coin is dedicated to less frequent larger jackpots. An overwhelming number of people who play these games will play multiple coins.
(4) The low tech slots usually pay a higher percentage. The high tech machines with themes (Sex and the City for example) pay much lower percentage since they are often participatory machines, where the slot manufacturer takes a share of the play. Slot companies make the majority of their income from slots on participatory machines.
(5) Penny machines are hot commodity in the slot industry. The average person play 60 cents per play, and they are excited by the multiple times they get a payout. However, the graphics and sound effects obscures the fact that the payout is usually less then what was gambled.
(6) Any brand of slot comes with a package of up to 6 circuit cards that determine the percentage payback. The slot manager is in charge of determining which circuit card goes in which machine. There is no objective way to determine which circuit card is within which machine, so there is no such things as a "hot" brand. One "Blazing 7's" machine may pay much lower than another.

Steve Bourie, writer of the American Casino Guide has a few interesting things about the near miss phenomen, and slots in general.

Quote: Croupier

Steve Bourie, writer of the American Casino Guide has a few interesting things about the near miss phenomen, and slots in general.

Great article! Interesting that NV allows the casinos to alter the chips in the machines, but in NJ, the casinos can't touch anything inside without permission.

This was a little misleading i thought:

Quote:

Did PrimeTime Live mislead its viewers to think that any kind of “near-miss" was legal on Nevada’s slot machines? I believe they did. At no point in the show did they ever actually define what a "near-miss" was and they also implied at the beginning of the program that the "near-misses" were occurring directly on the payline. Additionally, they never mentioned the fact that a “near-miss" on the payline is illegal in Nevada. This was a simple fact they could have easily looked up in the state’s gaming regulations and it’s hard to believe that they didn’t know about it.

Based on today's discussion, "Near misses" are not ILLEGAL in Nevada, but setting up a machine to display near-misses MORE than when the strip says it should is illegal. Basically, a near-miss isn't illegal when it's actually a "near miss". You had to actually hit the symbols on the first two reels, and you did have an actual chance at the big win.

Quote: cclub79

Based on today's discussion, "Near misses" are not ILLEGAL in Nevada, but setting up a machine to display near-misses MORE than when the strip says it should is illegal. Basically, a near-miss isn't illegal when it's actually a "near miss". You had to actually hit the symbols on the first two reels, and you did have an actual chance at the big win.

Correction: setting up a machine to display near-misses MORE than when the virtual strip says it should is illegal.

But the slot designer can design the virtual strip how he chooses. He can greatly increase the number of virtual stops that land just above and below the critical number to create the near miss phenomena. So he is using a true random selection for the virtual strip, but he designs the way the virtual strip is mapped to the physical strip. So what the player sees on the display is decidedly not uniformly random.

The Wizard uses an actual IGT machine (an old version of Red White and Blue) to actually show you the programming . There are a large clusters in virtual stops 38 to 48 of his table.

Yes, the corporate spokesman for the article you cited was being very mealy mouthed. Everyone knows that the near miss phenomena is a major feature of slot machines.

Research, funded by the Economic and Social Research Council and the Responsibility in Gambling Trust, found brain activity to near-misses in the striatum and insula cortex of the brain. These areas are thought to be involved in drug addiction, and receive input from the brain chemical dopamine (a neurotransmitter which plays a role in 'reward').

The study, was published in the journal Neuron, where they scanned the brains of 15 people while they gambled on a computerised slot machine.

SIDE ISSUE
Some readers may get the mistaken impression that virtual stops were created to cause the near miss phenomena. They were actually created to allow a larger range of probabilities, allowing the machine to have larger and larger jackpots to make them more competitive with state lotteries who increased the publics appetite for jackpots. The older jackpots on mechanical slot machines usually did not pay much more than 100:1 since the most remote probability was 1:22^3 or 1:10648 . To have a 1000:1 payout used almost a tenth of the design space leaving much less room for smaller payouts. The public resisted 4 and 5 wheel machines, and mechanically they were less reliable. The virtual stops allowed much larger jackpots. The near miss programming was a just a byproduct.

I don't know if this helps, but think of a craps game.

Suppose you throw two virtual six sided dice with even probabilities of getting 1 to 6. There is a mapping to the visual device which may be a computer graphic image of two dice. The mapping is one to one, so there is still a house advantage of 7/495=1.41% .

Now change the virtual device so the for one die we randomly select a number from 1 to 7. The mapping to the computer graphic image of this dice is 2 of the 7 numbers go to a 1 on the image of the dice, and the other five numbers go to their respective number on the dice. The second dice is random number from 1 to 6 and functions normally.

This mapping will slightly decrease the odds of winning on a come out roll, it will also increase the probability of you making your point on a 4,5 or 6. But it will decrease the probability of you making your point on a 8,9, or 10.

Overall it will change your probabilities so the house edge is now 5.98%.

Because the player will not visually know which is the skewed dice, he may never notice the difference, but the house edge has been dramatically changed.

If my virtual dice were 256 sided, I could design a mapping to very subtly change the overall statistics of the pass line bet. A gaming commission would immediately make this game illegal because they generally follow the principal that things that look like dice, roulette wheels, or cards must behave exactly like their physical counterparts. But since spinning wheels are more complex, the gaming commission gives the manufacturers carte blanche to invent their own mapping.

Quote: RaleighCraps

My question is, Does it really matter which bubble or turtle you pick? Or is that just a sideshow thrown in for the player's amusement, and to make them think they are affecting the outcome of the game?

Raleigh,
It is my understanding that if the machine shows other possible values after you make your selection that the outcome was not predetermined. For example if you picked a bubble and the bubble was 5x and then the other bubbles revealed other values such as 3x, 20x, 70x etc then your selection did determine the outcome. If the other values are not displayed then it might be predetermined. It doesn't mean that it was but it could be.

Mark

Quote: Wizard

As I understand it, there is a law that consecutive positions on a reel strip can not differ in weighting by a factor of more than 6. This is so that the "near miss effect" is not too egregious.

That is my understanding also. I'm sure I've seen it written but I don't remember where.

Mark

Quote: pacomartin

I don't know if this helps, but think of a craps game.

Suppose you throw two virtual six sided dice with even probabilities of getting 1 to 6. There is a mapping to the visual device which may be a computer graphic image of two dice. The mapping is one to one, so there is still a house advantage of 7/495=1.41%.

Although I've never played, based on the descriptions on the Wiz's main site, this is kinda how some California Card Craps work.

Wizard,
I think you would find this paper interesting. In particular it would be nice if you show us how to determine which setting of Money Storm a machine is set at (like you did in your 2001/2002 slot survey ). Paytable And Reel Strips (PARS) sheets are included for 96.2%, 95.0%, 94.0%, 92.5% , 90.0%, 87.5%, and 85.5%

There is an article by two Canadians PAR Sheets, probabilities, and slot machine play: Implications for problem and non-problem gambling where they obtain through the Freedom of Information and Protection of Privacy Act, PAR Sheets, for slot machine games that are in use in Ontario, Canada.

They obtain 23 PAR sheets:
• One version of Double Diamond Deluxe
• Eight versions of The Phantom of the Opera
• Seven versions of Lucky Larry’s Lobstermania
• Seven versions of Money Storm

The paper is lengthy (30 pages), but it includes a detailed analysis of the near miss programming as well as the other operant conditioning built into the machine.

I would recommend going through the example of the Red White and Blue slot machine on the Wizard of Odds site first, and making sure you understand that before you do the slots in this paper.

NEAR MISSES ARE LEGAL

Awesome, awesome find, Frank.

I believe that the casinos in Ontario are forced to put on the machine that the appearance of jackpot symbols in the layout close to the payline do not indicate that a jackpot is about to be won. I'll get you the exact wording when I'm in Niagara this weekend.

For those of you who are unfamiliar with how the Wizard did his 2001/2002 survey of Las Vegas casinos I will quote him:

An anonymous source provided me with PAR sheets for the games in question. Each of the different PAR sheets has five sets of distinct reels. There are various three-symbol combinations that appear in at least one but not all PAR sheets. So if one of these combinations occurs on an actual machine it narrows down the possible PAR sheets. By playing enough the player can narrow down the possible PAR sheets to just one. To help identify the unique combinations I wrote a computer program for each game, which had the exact reel order of all 5 reels of all the PAR sheets. The program then counted the number of PAR sheets with each possible three-symbol combination. If the number was greater than 0 and less than the maximum then that combination was identified along with the associated PAR sheets it belonged to. It is then a matter of simply playing the game and comparing the outcomes to the list of partially unique combinations. It only takes about 5-10 plays per machine to narrow down the possibilities to just one PAR sheet.

The results of his survey were based on how many machines in each casino were set at a given percentage. It was not necessary for him to reveal the PARS sheets (which are proprietary) to the general public by which he did his calculations.

In this paper we have the PARS sheets revealed by Freedom of Information Act, so they are no longer a secret. Although you can find PARS sheets on the web on occasion, they are almost always for archaic machines. Within 5-10 plays you would be able to determine what the setting is for one of the given games.

Then again he may tell us to figure it out for ourselves.

Thanks for the link to that paper, which was outstanding. I wish I could get PAR sheets via the FOIA here. Mine were given to me by an anonymous casino employee. It would probably violate intellectual property law for me to post them. However, if any reader would like to see them while in Vegas, let me know and perhaps I'll show them to you over coffee.

That article unfortunately didn't post the order of the symbols in the video slots, so I wouldn't be able to tell which chip was in the machine. Even if they did, it is very time consuming to program all the reel strips into my pattern-finding program.

I don't think they obtained every PAR sheet anyway. For example, they indicate only the total reel weights in Lobstermania for the 85.0% and the 96.2% versions. Notice how on the 85.0% version there are 3 buoys on reel 1, and 4 of them on reel 1 of the 96.2% version. Somewhere they would have had to add a buoy, changing the order of the symbols. Identifying certain orders of symbols on the screen can narrow down the machine you looking at. For example a boat-tuna-star fish in a row might appear only on the 85%, 87%, and 89% PAR sheets. Some other pattern I observe might only appear on the 89%, 91%, and 93%, which would mark the game as the 89% version, because it is the only return common to both patterns.

Quote: Wizard

Identifying certain orders of symbols on the screen can narrow down the machine you looking at. For example a boat-tuna-star fish in a row might appear only on the 85%, 87%, and 89% PAR sheets. Some other pattern I observe might only appear on the 89%, 91%, and 93%, which would mark the game as the 89% version, because it is the only return common to both patterns.

Hmmm...

I always assumed that a video slot with the typical 5 columns and 3 rows arrangement was 15 independent reels.

Your comment of looking for three symbol patterns seems to indicate that they are only 5 reels.

Now that I think about it, the math for 15 reels would be horribly complex. And unnecessary since there aren't any vertical paylines.

But wouldn't it be easy to design the machine to use indepently selected stop points, on the same PAR table for the three positions of each column? My pea-brain suggests that the math is identical, while eliminating the near-miss phenomenon, as well as preventing someone from doing what you're suggesting.

---

While I was typing I think I came up with my own answer. Using independent stop points, eliminating the near-miss, means that the jackpot symbols have an equal chance of lining up on any payline. Maybe that's acceptable. But since most often, it only pays the big jackpot when they line up on the last payline, I suspect that indepentent stop points are not used.

But I think they can use non-consectutive stop points. By pre-determining the ofset when designing the machine and the PARs table, they can easily thwart anyone that is trying to observe the symbols as you're suggesting.

I just came up with my own answer.

Doing it any way that I've suggested means that a symbol can appear twice in a column. That never happens.

So forget what I said.

One quote about Lobstermania in the paper was when wagering on all 15 lines, the player wins something on 33.52% of the spins and of these wins, 60.73% are less than the wager.

Although this constant illusion of winning while actually losing part of your wager seems to be addictive, I wonder if the slot companies are cutting their own throat. Obviously the revenue on penny slots is constantly increasing, and the house edge is much higher on penny slots. However, slot revenue is a fraction of what it was two years ago in Nevada. I have to wonder if addicting people to the constant noise of winning is actually meaning that they are now losing much less overall on a trip.

Another comment that I found interesting was that one researcher showed in a laboratory setting that a subset of his participants were sensitive to payback percentage after sampling two machines for 40 spins each, 80% of this subsample chose to gamble on the machine with the higher payback percentage.

For me I see three trends:

(1) the decrease of slot revenue overall over time
(2) the increase of penny slot revenue over time despite the number of machines being the same.
(3) the flatline of multi-denomination slots over time

Here's what I would interpret from this data:

Less slot gamblers overall are gambling with less money. The ones who are left are deserting the quarter, dollar, and nickel machines for the cheaper penny slots and multi-denominational machines (which is gaining ground as a proportion of slot revenue). They perceive these games as more entertaining and a better value than the more expensive machines. They believe that they are parting with their money more slowly.

Quote: DJTeddyBear

I always assumed that a video slot with the typical 5 columns and 3 rows arrangement was 15 independent reels.

Your comment of looking for three symbol patterns seems to indicate that they are only 5 reels.

In general, this is true. There are a couple possible exceptions to this, though:

1) DaVinci Diamonds/All That Glitters. These machines give you a pattern that drops in from the top. Any winners are paid, then disappear, and everything above drops down, and new symbols drop in from the top. Repeat until there are no more winners. I haven't bothered to try to figure out if there's really a pattern to the symbols, or if symbols pop up randomly according to some lookup table.

2) White Orchid. It's a four position, five reel video slot, but it looks like each of the positions is arrived at independently. I doubt that there's twenty independent reel patterns, but there might be one pattern for each of the five verticals, each of which is "spun" four times to arrive at the pattern shown. Again, I haven't tried finding patterns, but it appears that way to me because the spinning stops in a cascade effect, where the top symbol stops while the bottom symbol keeps spinning for a second. It's hard to describe in text without tl;dr, but it's easy to see if you play it.

This was a great article and had a lot of bearing on my speculations about multi-line slots in another thread. In particular, Table 6 confirms that the % of spins that pay something does not increase linearly with number of lines bet, due to the non-independence of the different lines. So, simply increasing the number of lines you are betting on may not increase your frequency of getting "hits" as much as you might think. Even more interesting is their analysis on the percentage of "wins" that are really losses or pushes. With 1 line played, all wins are really wins. With 6-15 lines, about 60% of "wins" are actually losses! But, at 5 lines only about 30% of "wins" are losses and another 30% are pushes. Betting on 2 lines is interesting: "wins" are either really wins or they are pushes.

So, I am left feeling like there are real trade-offs and strategies for players with these games. If you just want to maximize the number of bonus rounds and "wins" in a given amount of time then, sure, just bet on all lines. But there are some good arguments to be made for betting on far fewer lines, say 1-5.

Quote: boymimbo

Fewer slot gamblers overall are gambling with less money. ... They perceive these games as more entertaining. They believe that they are parting with their money more slowly.

I'd agree with the less money and perhaps the fewer gamblers. I'd agree with the more entertaining but don't know if the coinage-terminology plays a role. As to parting with their money more slowly, I have heard considerable anecdotal commentary to the contrary, but then again I've heard considerable anecdotal commentary about secret switches to change the odds.

Quote: FleaStiff

As to parting with their money more slowly, I have heard considerable anecdotal commentary to the contrary, but then again I've heard considerable anecdotal commentary about secret switches to change the odds.

Well, your EV may be dropping faster in a slot machine, but you don't have the variance to deal with. People are much more afraid of variance. I was talking to a young couple where he was in the military and she was his foreign born bride. I offered to show him how to play craps. He was playing pass lines with 0X or 1X free odds. His wife literally looked panic stricken the entire time. If he hadn't won early I think that she would have let him play for one roll of the dice.

Then she shifted to wheel of money with it's HA of 11% to 22%. The look on her face was pure bliss. She said she would be happy to play there for four hours straight. Even though I enjoyed talking to them I had to leave because I was bored out of my mind.

People are very afraid of variance. Gambler's like variance and think it's a bargain if you can get it at reasonable HA.

That was a fascinating paper.

But there's more.

The url for the paper referenced is http://www.camh.net/egambling/issue23/pdfs/06harrigan.pdf

But just back up in the url to get to a page with an index, and it has a link for ARCHIVES of the older issues. TONS of interesting stuff there: http://www.camh.net/egambling/archive/index.html Check it out.

I would question whether the woman's fears were due to variance or to perceived complexity of the process. Complexity implies the unknown which enhances the sense of fear whereas that very simple Money Wheel is re-assuring in its simplicity since it is instantly understandable despite language or mathematical barriers. Therefore, the woman who instantly knows the very simple process, is re-assured despite the whopping House Edge but that woman is terrified of the 1.414 percent house edge, mainly because she has no idea what is going on amidst all that complex layout, shouting and chip-flying and therefore has an irrational fear of high losses.

Its not the actual variance but her fear of variance that applies. You are able to recite variance statistics and able to print out various images of charts and simulations, she has but one image in her mind: total ruin.

The technology of slot machines has changed a lot over the years. The classic mechanical designs have been almost completely replaced by computer-controlled machines. But the game has remained the same. The player pulls a handle to rotate a series of reels that have pictures printed on them. Winning or losing is determined by which pictures line up with the pay line, a line in the middle of a viewing window. If each reel shows the same winning picture along the pay line, you win.