Basically all slot machines you'll encounter follows the same principal: MDA (Mechanics, Dynamics and Aesthetics). Mechanics: A mathematician will crunch the numbers for how the results will be, their probability and distributions. For example, assuming an uniform distribution of probabilities (i.e. Every symbol on a reel has the same probability), if 77777 and 55555 are the winning combinations and you have 5 reels with 10 symbols, of which one is 7 and two are 5's, the number of combinations is 10^5 = 100000 and the number of winning combinations is 1^5 (for 77777). Keywords: problem gambling, slot machines, video slots, PAR Sheets, structural characteristics, reinforcement schedules Introduction Slot machines are a very popular form of gambling in North America. For example, Ontario, Canada, has approximately 23,000 slot machines, which in the fiscal year 2002.
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The probability of winning on a slot machine is 5%. If a person plays the machine 500 times, find the probability of winning 30 times. Use the normal approximation to the binomial distribution. Find the area under the normal curve over the interval (29.5,30.5). The probability of getting a lemon on each reel is 1/10. If you get 3 lemons, you win 900 coins. The probability of getting 3 lemons is 1/10 X 1/10 X 1/10, or 1/1000. In odds terms, that's 999 to 1. (Remember, to calculate probability when the question includes the word 'and', you multiply.
In Pokémon Red, Blue, and Yellow, there are playable slot machines in the Celadon Game Corner. The rules are apparently simple: The player needs to line up the same symbols on horizontal or diagonal lines (the set of available lines depends on the number of coins betted), and the player can stop the reels, one at a time, using the A button. In reality, the game may cause the reels to 'slip' after the A button press either to hinder or to help the player, and the rules for doing so are actually complicated, with many oddities that may or may not be glitches. (Together with the separate building for prize claims, this is comparable to how real life Japanese pachi-slots are played.)Thanks to the disassembly, the actual behaviors of the slot machines in Generation I are completely understood, although at some places it may still be unclear whether they match the intended behaviors.
Overview
For each individual spin, the slot machine can be in one of three modes:Mode bad, which guarantees that the player cannot get any match in the available lines.Mode good, which allows the player to get matches of symbols other than sevens or bars.Mode super, which allows and actively helps the player to get matches of sevens and bars. Mode super is the only mode of the three that will persist between spins. It will only end when the player wins a reward of 100 coins (bars) or 300 coins (sevens), and in the latter case only with a probability of 50% (i.e. it still have a 50% chance to persist).In general, for each spin, the mode is set to mode good or mode super with probability 45/256 (~17.6%), with the probability of mode super further depending on which slot machine the player is playing on (see below). It is set to mode bad with probability 210/256 (~82.0%). There is also a chance of 1/256 (~0.4%) to enter a lucky streak which allows the player to play on mode good (but never mode super) for all the spins after this one, until the player wins 60 times.The function to set the mode, called before each spinThe lucky slot machine
Whenever the player enters the Game Corner, a random number between 0 ~ 31 is generated, and if it is 0, it has a 7/8 chance of becoming 1.More precisely, a random number between 0 ~ 255 is generated, it becomes 8 if it is less than 7, then it is divided by 8, discarding the remainder. See the function to generate the index of the lucky slot machine in the disassembly. Then, whenever the player plays on a slot machine, the number is compared with the index of that slot machine (0 ~ 35) plus one. If it matches, the chance of playing in mode super is set to 5/256 (~2.0%), and otherwise it is set to 2/256 (~0.8%).The function to set the chance of mode superEffectively, this means that every time the player enters the game corner, there is usually a 'lucky slot machine' among the machines with index 0 ~ 30. The lucky slot machine is most likely (15/256, ~5.9%) to be the one with index 0 (the rightmost, bottommost one), and cannot be the ones with index 31 ~ 35 (the bottom five in the leftmost column). The other ones all have a probability of 1/32 (~3.1%) to be lucky, including the ones occupied by an NPC, or otherwise unplayable ('Out of order', 'Out to lunch', or 'Someone's keys'). Finally, there is a tiny chance (1/256, ~0.4%) that the lucky slot machine is the nonexistent slot machine -1.
Reel stopping
The mode of the slot machine comes into play when the player presses the A button to stop a reel, as the reel may 'slip' after the A press depending on its position. The exact logic for stopping the reel also depends on which reel the player is stopping. Internally, the first two reels are programmed to slip 4 times unless a condition is met earlier, while the third reel can either slip up to 4 times to help the player get a match, or slip any number of times to prevent a match.First reel
In mode bad or mode good, the condition for the first reel to stop early is that the middle symbol is not a cherry. Since there are no two consecutive cherry symbols (in fact, there are no consecutive same symbols on any reel), that means the first reel will slip at most once.In mode super, the condition for the first reel to stop early is that any of the three symbols showing is a symbol with an internal value less than that of the seven symbol. Since the seven symbol has the lowest internal value of all symbols, this condition is in fact never satisfied, and the first reel will always slip by 4 positions.The condition for the first reel to stop early
Second reel
In mode bad or mode good, the condition for the second reel to stop early is that there must be a 'potential match' on the first two reels, i.e. two of the same symbols that may form a line if the third reel stops in a good position. The player's bet is not considered; for example, a diagonal potential match counts even if the player only betted 1 or 2 coins.In mode super, the condition for the second reel to stop early is that the potential match
![Distribution Distribution](https://s2.studylib.net/store/data/014523200_1-59bfbb9b89d999827a09640b110873f4.png)
![Slot Slot](https://media.wired.com/photos/5a9f45843ea6d47cc8934024/4:3/w_312,h_234,c_limit/ff_scammingslotsb_f.jpg)
Third reel
In mode bad or mode good, the third reel will always slip to prevent a disallowed match, i.e. any match in mode bad, or a match of sevens or bars in mode good. There is no upper limit for the distance the reel has to advance this way; as an extreme example, hacking the game so that the reels contain all sevens will likely cause the game to softlock.The piece of code run after finding a matchIn addition, in mode good or mode super, the reel will slip up to 4 times if no match is found. This is not counting the number of slips done to skip disallowed seven or bar matches in mode good, so the total number of slips may exceed 4.The piece of code run after not finding a match
Notice that, due to the design of the reels, there can never be more than one match at any time.
Oddities
On the spin where the player enters the lucky streak, the actual mode stays as it is on the previous spin, which can be either mode bad or mode good (the mode is initialized to mode bad at the beginning of a sessionAll the memory addresses from $CD3D (wStoppingWhichSlotMachineWheel) to $CD50 (wSlotMachineBet) are zeroed, which included the mode flag at $CD4C.). If the mode happens to be mode good and the player wins, it will still count towards the 60 wins to end the lucky streak. There is a line of code to immediately end the lucky streak if the player wins a reward of 300 coins, but this seems to be impossible, because the lucky streak is mutually exclusive with mode super, and mode good doesn't allow matches of sevens. The probability distribution of the lucky slot machine is weird in multiple aspects. The fact that one machine is more likely to be lucky and some others have no chance might be intended, but the fact that it can be the nonexistent slot machine -1 seems certainly an off-by-one error. The fact that the first reel's early stop condition in mode super is never satisfied is most likely a bug. Presumably, the intention is that the reel should stop if a seven symbol is showing, but the developers mistakenly wrotejr c
instead of jr z
. The second reel's early stop condition in mode super is weird in two aspects. The 'bottom symbol on the second reel' condition seems like an accidental use of leftover variable, although it may also be intended since there are two instructions specifically making it the bottom symbolThese two dec de
instructions make de
point to the bottom symbol of the second reel instead of the top symbol, and they seem to serve no other purpose.. The 'sevens or bars' check is only for the first potential match found, in the order of 'bottom-bottom, bottom-middle, middle-middle, top-middle, top-top' (i.e. from bottom to top), which means a potential match of bars may be rerolled if it appears above a potential match of another symbol.External links
Analysis of how the slot machines in Pokémon Red, Blue, Yellow work by Crystal_:REDIRECT Template:YouTube![Distribution Distribution](https://medias.unifrance.org/medias/235/34/8939/format_page/geminis.jpg)
Third reel
In mode bad or mode good, the third reel will always slip to prevent a disallowed match, i.e. any match in mode bad, or a match of sevens or bars in mode good. There is no upper limit for the distance the reel has to advance this way; as an extreme example, hacking the game so that the reels contain all sevens will likely cause the game to softlock.The piece of code run after finding a matchIn addition, in mode good or mode super, the reel will slip up to 4 times if no match is found. This is not counting the number of slips done to skip disallowed seven or bar matches in mode good, so the total number of slips may exceed 4.The piece of code run after not finding a match
Notice that, due to the design of the reels, there can never be more than one match at any time.
Oddities
On the spin where the player enters the lucky streak, the actual mode stays as it is on the previous spin, which can be either mode bad or mode good (the mode is initialized to mode bad at the beginning of a sessionAll the memory addresses from $CD3D (wStoppingWhichSlotMachineWheel) to $CD50 (wSlotMachineBet) are zeroed, which included the mode flag at $CD4C.). If the mode happens to be mode good and the player wins, it will still count towards the 60 wins to end the lucky streak. There is a line of code to immediately end the lucky streak if the player wins a reward of 300 coins, but this seems to be impossible, because the lucky streak is mutually exclusive with mode super, and mode good doesn't allow matches of sevens. The probability distribution of the lucky slot machine is weird in multiple aspects. The fact that one machine is more likely to be lucky and some others have no chance might be intended, but the fact that it can be the nonexistent slot machine -1 seems certainly an off-by-one error. The fact that the first reel's early stop condition in mode super is never satisfied is most likely a bug. Presumably, the intention is that the reel should stop if a seven symbol is showing, but the developers mistakenly wrotejr c
instead of jr z
. The second reel's early stop condition in mode super is weird in two aspects. The 'bottom symbol on the second reel' condition seems like an accidental use of leftover variable, although it may also be intended since there are two instructions specifically making it the bottom symbolThese two dec de
instructions make de
point to the bottom symbol of the second reel instead of the top symbol, and they seem to serve no other purpose.. The 'sevens or bars' check is only for the first potential match found, in the order of 'bottom-bottom, bottom-middle, middle-middle, top-middle, top-top' (i.e. from bottom to top), which means a potential match of bars may be rerolled if it appears above a potential match of another symbol.External links
Analysis of how the slot machines in Pokémon Red, Blue, Yellow work by Crystal_:REDIRECT Template:YouTubeReferences
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Remember the movie National Lampoon's Vegas Vacation, when gambling fever consumes Chevy Chase's character, Clark W. Griswold? He goes on a losing streak to beat all losing streaks while his son, Rusty, wins four cars by playing the slot machines. Maybe Clark would have done better if he had read Probability For Dummies! In this article, you discover the basic ideas behind slot machines and how they work, so that you can get past the myths and develop a strategy based on sound probability.
Understanding average payout
Slot Machine Probabilities
When casinos advertise that their slot machines pay out an average of 90 percent, the fine print they don't want you to read says that you lose 10 cents from each dollar you put into the machines in the long term. (In probability terms, this advertisement means that your expected winnings are minus 10 cents on every dollar you spend every time the money goes through the machines.)
Suppose you start with $100 and bet a dollar at a time, for example. After inserting all $100 into the slot, 100 pulls later you'll end up on average with $90, because you lose 10 percent of your money. If you run the $90 back through the machine, you'll end up with 90 percent of it back, which is 0.90 x 90 = $81. If you run that amount through in 81 pulls, you'll have $72.90 afterward (0.90 x 81 = 72.90). If you keep going for 44 rounds, on average, the money will be gone, unless you have the luck of Rusty Griswold!
Slot Machine Probability Distribution Formula
How many pulls on the machine does your $100 give you at this rate? Paragon casino marketplace buffet menu. Each time you have less money to run through the machine, so you have fewer pulls left. If you insert $1 at a time, you can expect 972 total pulls in the long term with these average payouts (that's the total pulls in 44 rounds). But keep in mind that casinos are designing slot machines to go faster and faster between spins. Some are even doing away with the handles and tokens by using digital readouts on gaming cards that you put into the machines. The faster machines can play up to 25 spins per hour, and 972 spins divided by 25 spins per minute is 38.88 minutes. You don't have a very long time to enjoy your $100 before it's gone!
The worst part? Casinos often advertise that their 'average payouts' are even as high as 95 percent. But beware: That number applies only to certain machines, and the casinos don't rush to tell you which ones. You really need to read or ask about the fine print before playing. You can also try to check the information on the machine to see if it lists its payouts. (Don't expect this information to be front and center.)
Implementing a simple strategy for slots
Advice varies regarding whether you should play nickel, quarter, or dollar slot machines and whether you should max out the number of coins you bet or not (you usually get to choose between one and five coins to bet on a standard slot machine). In this section, you'll find a few tips for getting the most bang for your buck (or nickel) when playing slot machines.
Basically, when it comes to slot machines, strategy boils down to this: Know the rules, your probability of winning, and the expected payouts; dispel any myths; and quit while you're ahead. If you win $100, cash out $50 and play with the rest, for example. After you lose a certain amount (determined by you in advance), don't hesitate to quit. Go to the all-you-can-eat buffet and try your luck with the casino food; odds are it's pretty good!
Choosing among nickel, quarter, and dollar machines
The machines that have the higher denominations usually give the best payouts. So, between the nickel and quarter slots, for example, the quarter slots generally give better payouts. However, you run the risk of getting in way over your head in a hurry, so don't bet more than you can afford to lose. The bottom line: Always choose a level that you have fun playing at and that allows you to play for your full set time limit.
Deciding how many coins to play at a time
When deciding on the number of coins you should play per spin, keep in mind that more is sometimes better. If the slot machine gives you more than two times the payout when you put in two times the number of coins, for example, you should max it out instead of playing single coins because you increase your chances of winning a bigger pot, and the expected value is higher. If the machine just gives you k times the payout for k coins, it doesn't matter if you use the maximum number of coins. You may as well play one at a time until you can make some money and leave so your money lasts a little longer.
For example, say a quarter machine pays 10 credits for the outcome 777 when you play only a single quarter, but if you play two quarters, it gives you 25 credits for the same outcome. And if you play the maximum number of quarters (say, four), a 777 results in 1,000 credits. You can see that playing four quarters at a time gives you a better chance of winning a bigger pot in the long run (if you win, that is) compared to playing a single quarter at a time for four consecutive tries.
Slot Machines Probability
The latest slot machine sweeping the nation is the so-called 'penny slot machine.' Although it professes to require only a penny for a spin, you get this rate only if you want to bet one penny at a time. The machines entice you to bet way more than one penny at a time; in fact, on some machines, you can bet more than 1,000 coins (called lines) on each spin — $10 a shot here, folks. Because these machines take any denomination of paper bill, as well as credit cards, your money can go faster on penny machines than on dollar machines because you can quickly lose track of your spendings. Pinching pennies may not be worth it after all!