Introduction

Binomdist() function

So, I got the idea to see if anyone would be interested in selling me copies of par sheets for various machines with progressives, or just the relevant information from them. (Of utmost interest are the jackpot cycles, but meter rates, seed values, and potential payback% settings are also of interest.).

Class II Slots

Oklahoma, and various other Indian casinos, have what are called 'Class II' slots. The outcome is actually determined by the draw of bingo balls. Players at various different slot machines are linked together, each player has different cards but the draw of the balls is common to all players connected via the network. There is generally a 'game ending pattern' in which if some player competes it then balls quit drawing for all the other players. However with most manufacturers these game ending patterns are very hard to achieve so the element of competition is negligible. Unless the game ending pattern is achieved a certain number of balls are drawn, your cards are automatically daubed, and you are paid according the highest paying pattern you cover, and there are hundreds of patterns. A video representation of a slot machine is only to illustrate how much you have won. If done well, and they often are not, the games play almost just like a Vegas slot machine.

Class III Slots

A standard slot machine, like the kind played in Las Vegas, Atlantic City, and major gambling markets. The outcome of modern Class III slots is determined by the draw of random numbers, which are then mapped to particular stops on the reels, at the moment the player spins the reels. This is unlike Class II slots, in which the result is determined by bingo balls and two or more players are required to play.

Combin() function

This is an Excel function that calculates the number of ways to choose x items out of y, without regard to order. For example if a pizza parlor has 10 toppings and you can choose any 3 of them there are combin(10,3) = 120 ways to create a pizza. The mathematical formula for combin(x,y) is x!/(y!*(x-y)!). The combin formula is frequently used in card probabilities, for example number of different 5-card stud hands is combin(52,5)=2,598,960.

Composition Dependent

Used to describe blackjack strategy where the player makes use of not just the total of his cards but the composition as well. The fewer the decks the more beneficial using composition dependent basic strategy is. For example in single-deck blackjack the player should normally stand with 12 against a 4. However if the 12 is composed of a 10 and a 2 the odds favor hitting. This is a composition dependent exception. Also see 'Total Dependent.'

Wizard Of Odds Slot Machines

Element of Risk

The ratio of the expected player loss to the total amount bet. This is a good measure of comparing the value of one bet against another. For games in which there is no raising the element of risk will be the same as the house edge. However for games in which the player may increase his bet the element of risk will be lower. For example in Caribbean Stud Poker the house edge is 5.22%. However the average amount bet per hand is 2.0445 times the initial bet, so the element of risk would be 0.0522/2.0445 = 2.55%.

EPROM

EPROM is an acronym standing for Erasable Programmable Read Only Memory. More importantly EPROMs are a microchip used in slot machines that determine the theoretical return of the game. A slot manager can change the return of a slot machine by simply replacing the EPROM chip, although regulations may require additional paperwork.

Expected Value

Expected value is how much you can expect to lose (negative) or win (positive) from a bet. For example the expected value in American double-zero roulette is -5.26%. That means you can expect to lose 5.26% of every dollar you bet.

Factorial

Factorial is a frequently used math function. For any integer x, factorial(x) is represented as x!, which equals 1*2*3*...*x. For example:

This would be the number of ways you could order x items. For example, if you had a baseball team of 9 players, the number of possible batting orders would be 9!=362,880.

Hold Percentage

The ratio of money a particular game takes in to total chip purchases. For example if player’s purchase $1000 in chips at a blackjack table and walk away with $800 in chips then the table profit (or hold) is $200 and the hold percentage is $200/$1000 = 20% for the sample period. The hold percentage will be much higher than the house edge because players tend to circulate through the same money. The longer the player plays the more the house edge will grind him down, causing the hold to increase. The player does not need to be concerned about the hold percentage but it is of interest to casino management.

House Edge

The ratio of the expected player loss to the initial amount bet. For example if the house edge for blackjack is 0.5% then for every $100 you bet initially you can expect to lose 50 cents. The house edge is a good measure of expected player wins or losses over time but is not a perfect measure of comparing one game to another. The reason is the house edge does not include additional money bet (for example doubling in blackjack or raising in Three Card Poker) as money bet. Two common mistakes in calculating the house edge are not including ties (they should be counted towards money bet) and including additional money bet (like doubling and raising) towards money bet. An exception to the usual definition is in craps, in particular proposition bets that can take multiple rolls to resolve. For place, buy, lay, and hard way bets the house edge is defined as the expected player loss per bet resolved. Another exception is in Let it Ride, in which the house edge is the ratio of the expected loss to a single bet (or 1/3 of the total initial bet).

HypGeomDist() function

This is an Excel function (short for 'Hypergeometric Distribution') that calculates the probability of matching W of X numbers, given that Y numbers are selected from Z numbers. A popular application of this function is calculating Keno probabilities. If you selected 10 numbers, the probability of matching 6 of them would be hypgeomdist(6,10,20,80): The 6 is how many numbers you matched; the 10 is how many numbers you selected; the 20 is how many numbers the house selected; and the 80 is how many numbers the house can choose from. The formula for hypgeomdist(W,X,Y,Z) is combin(Y,W) * combin(Z-Y,X-W) / combin(Z,X).

Martingale

A betting system in which the player starts with a small wager on an even money game. If he wins he stops playing. If he loses he doubles his bet. If he wins the second bet he walks with a profit of his original wager. If he loses the second bet he doubles his wager again. The player will keep doubling his wager as long as he keeps losing. The ultimate result will either be a net win equal to his original wager or a loss of his entire bankroll.

The Martingale is one of the oldest and certainly the most famous betting system. I personally I have seen players using it at Internet casinos numerous times. It is deceptive in the short run because it usually does win. However in the long term it loses, as all betting systems do. The big losses eventually add up to more than all the small wins.

Wizard Of Odds Slot Machine Par Sheet Shackelford

Match Play

Often found in fun books a match play is a chip or coupon the player may use in connection with a bet in most table games. The rules generally state that the player must bet an amount equal to the face value of the match play. Then if the player wins he is paid on both his bet and the match play. Win or lose the match play is taken after the bet is resolved. In the event of a push it is not removed.

Every match play I have ever seen is restricted to 'even money bets.' This generally includes qualifying bets in roulette, craps, big six, baccarat, and blackjack. For more about Match Plays please visit my page on promotional chips.

Non-cashable Bonus

Often seen at Internet casinos a Non-Cashable Bonus is a bonus which may never be cashed out. It always sticks to the player's account until lost gambling. A good strategy to get rid of a non-cashable bonus is to withdraw all cashable money in the account, leaving on the non-cashable bonus. Then gamble with the non-cashable bonus with the goal of either doubling your balance or go bust trying. If you double then cash out the winnings and play the sticky bonus again. Keep repeating until you lose. The value of a non-cashable bonus is almost 100% of face value, just deduct two times the house edge of the game you are playing. For example if the house edge in blackjack is 0.5% and you have a $100 sticky bonus then the value of it is $100*(1-2*0.005) = $99.

Par Sheet

Slot Machine Percentage Sheet

A par sheet is a document that details how a particular slot machine is designed, including the pay table, reel strips, and any other pertinent information to rules of the game. I've hard various theories where the 'par' comes from the most plausible, in my opinion, are:

• An Acronym for Pay table And Reel Strips.
• An Acronym for Probability Accounting Report.
• It just means par, as in the expected outcome of the game.

Penalty Card

Wizard Of Odds Slot Machine

Sometimes in video poker the correct play in a borderline hand is determined by the value of the discards. Let’s look at an example in 9/6 Jacks or Better with K♣ 10♣ 9♠ 6♣ 3♦. The best options are to either keep the suited 10 and king or the king only. The suited 10 and king is usually the better option. However in this scenario two potentially useful cards would be discarded, the 9 of spades (lowering the odds of forming a straight), and the 6 of clubs (lowering the odds of forming a flush). These two cards are called penalty cards because they degrade the value of the best play, the suited 10 and king. In this case they degrade the value to below that of keeping the king only. Penalty cards are also applicable in Hold ’em Challenge.

Penetration

For blackjack purposes, 'penetration' refers to how deeply into the cards the dealer deals before shuffling. For example, if the dealer deals 5 decks before shuffling in a 6-deck game then the penetration would be 5/6 or 83%. Penetration is extremely important to card counters, the greater the penetration the greater the advantage.

Permut() function

This is an Excel function for the number of ways to pick x items out of y, with regard to order. For example if you form a new country and wish to create a 3-color flag from 10 colors available then there would be permut(10,3)=720 possible color arrangements. This assumes that color position does matter, for example the flag of the Netherlands is different from the flag of the Russian Federation. The mathematical formula for permut(x,y) is x!/max(y,x-y)!.

Phantom Bonus

Wizard Of Odds Slot Machine Par Sheet Template

What I used to call a Phantom Bonus I know refer to as a Sticky Bonus, to be consistent with the general terminology.

Probability

The probability of an event is the number of ways that event can occur, divided by the total number of possible events that could occur. For example, there are 4 ways to be dealt a Royal Flush in a 5-card hand (one for each suit), and there are combin(52,5)=2,598,960 possible 5-card hands that could be dealt, therefore the probability of being dealt a Royal Flush in 5 cards from a 52-card deck is 4/2598960 = 0.00000154.

Pull Tab

The original form of a pull tab was a piece of paper with a tab the player lifts to reveal a win. This piece of paper the player may take to the cashier for redemption. In addition there are electronic pull tab games, in which the player presses a button to reveal his win. As a visual aid the game may show how much the player won in the form of a slot machine of video poker game. However don’t be fooled, there is never any skill in a pull tab game. Even if the game looks like a five card draw video poker game your outcome is predestined. For example if you get a royal flush on the deal and throw all of it away you would get another royal flush on the draw. If you kept only one card to a royal you would get four wild cards on the draw. Pull tabs are most likely to be found in Indian casinos that do not allow normal slots or video poker games.

Soft 17

In blackjack a hand that can be counted as 7 or 17 poins, for example A♣ and 6♦, is called a soft 17. A frequent rule variation is whether the dealer hits or stands on a soft 17. It is to the player’s advantage if the dealer stands on a soft 17.

Sticky Bonus

Often seen at Internet casinos a Sticky Bonus is a bonus which may never be cashed out and disappears from the player's balance when any withdrawal is made. It is called a sticky bonus because it just sticks to the player's bonus temporarily, until a withdrawal is made, and then falls off. A good strategy to get rid of a sticky bonus is to set a high winning goal. Then play aggressively until you either meet your goal or go bust trying. An aggressive strategy, and one casinos don't like, is to bet everything on a single number in single-zero roulette.

The greater your winning goal the greater the value of the Phantom Bonus, up to a point. For example if you have a $100 Phantom Bonus and $200 in cashable chips if you bet everything on a single number in single-zero roulette your available balance to withdraw is $300*36-$100 = $10700 if you win. In this case the expected value of the Phantom Bonus is $10700/37 - $200 = $89.19, or 89.19% of face value.

Sticky Chip

A gambling chip which may wagered but not be cashed out. Winnings from a sticky chip are paid in real chips. Sticky chips are often given to a player as part of a junket, or as compensation for an entrance fee. The value of a sticky chip is almost 100% of face value, just deduct two times the house edge of the game you are playing. For example if the house edge in blackjack is 0.5% and you have $100 in sticky chips then the value of the chips are $100*(1-2*0.005) = $99.

Total Dependent

Most blackjack basic strategy charts are said to be 'total dependent.' That means the total of the player’s cards are considered, but not the specific composition. Total dependent basic strategy also considers whether the hand is soft or hard, and whether doubling, splitting, or surrender is possible. Also see 'composition dependent.'

True Odds

The necessary payoff for a bet to have zero house advantage. For example the any seven bet (next roll will total seven) in craps has true odds of 5 to 1. If the true odds are t, then the probability of winning is 1/(1+t). If the probability of winning is p, then the true odds are (1-p)/p. For bets which can only win or lose, if the actuall payoff is w, and the true odds are t, then the house edge is (t-w)/(t+1). In the case of the any seven bet in craps the true odds are 5 to 1, and the payoff is 4 to 1, so the house edge is (5-4)/(5+1) = 1/6 = 16.67%.

• Appendices
• Slots Analysis
• Miscellaneous

Introduction

Slot Machine Par Sheet

Henderson/Lake Mead Nickel Slot Return Percentages

The following table ranks the casinos of Henderson according to the looseness of their video display reeled nickel slot machines. Henderson spans a large area just south and east of Las Vegas. All the casinos listed are within Henderson except the Hacienda, which according to my map is in the Lake Mead Recreation Area. An explanation of the methodology of this survey can be found in Appendix 3A ranking the Las Vegas casinos.

Henderson/Lake Mead 5 cent machines

Voluntary exclusion: The Fiesta Henderson did not allow my associate to take notes while playing their slots. I can not include any casino that is not cooperative with the survey. I will honor any requests for exclusion.

Insufficient sample: The Hacienda only had one kind of machine that I test for, which I consider to be too small a sample. Based on the one game they did have the return was 93.50%.

Acknowledgements

I would like to thank Par Sheet Pete (not his real name) for providing the par sheets, without which this project would not have been possible. I would also like to thank Rob Feldheim for his help collecting data.

Internal Links

• Appendix 1 shows the details and analysis of almost 4000 actual spins on a Reno slot machine.
  
• Appendix 2 shows an example of the virtual reels behind a hypothetical slot machine and how the average return is calculated.
  
• Appendix 3A: 2003 Las Vegas slot machine rankings.
  
• Appendix 3B: 2002 Jean/Primm slot machine rankings.
  
• Appendix 3C: 2002 Tunica slot machine rankings.
  
• Appendix 3D: 2002 Henderson/Lake Mead slot machine rankings.
  
• Appendix 3E: 2002 Quarter and dollar returns for Las Vegas slots
  
• Appendix 4 shows how the return is calculated for my Wizard's Fruit Slot Machine.
  
• Appendix 5 analysis of the 21 Bell Slot Machine.
  
• Appendix 6 Analysis of Red, White, & Blue Slot Machine.
  
• Lock and Roll analysis of the skill-based slot machine found in North Carolina.
  
• Deconstructing Megabucks.
• Baltimore Sun article, in which I am quoted.