Casinos generate numbers for their slot machines based on a normal distribution. So when Probability and Expected Profit/Loss are set up in the house’s favor, they can lose once or twice, but overall the casino will be profitable. All because the casino’s math calculations reflect the set distribution. If there is a digital slot machine with, say, 3 symbol 'wheels' (they are obviously not real wheels, digital) with each having a few (say 2) corresponding states (e.g. Each have a lemon and a lime) where winning means all three states match (e.g. 3 limes), and when a button is pressed the final state of the system is determined, yet the. If there is a slot machine with 4 slots, each with a possibility of being either a cherry, a lemon, or a 7, what is the probability of getting exactly two lemons? My thinking: 4 slot machine, 3 options: 3.3.3.3 = 81 total options. Getting exactly 2 lemons: 1.1.3.3 = 9. P(LL) = 9/81 = 0.1111. What is wrong with this? But machine B’s data doesn’t look like happening by chance. But just in case, you decided to estimate those 2 machines’ winning probabilities by MAP with hyperparameters α=β=2. (Assuming that the results (k wins out of n plays) follow binomial distribution with the slot machine’s winning probability θ as its parameter.).
3-reel slot machines
1. Case A – the same number of stops and symbol distribution on the reels
Slot Machine Probability Distribution Definition
1.7 Event – Any combination of at least one of three specific symbols
Slot Machine Probabilities
The probability of is , where , , and are the distributions of the three symbols on a reel.
For the numerical probabilities, we can use the table and the results of section 1.1 (event -A specific symbol three times) for .
Slot Machine Probability Distribution Rules
Example:
Find the probability of any combination of seven-type symbols (assume for example that there are red, blue, and black sevens) occurring on a payline of a 3-reel slot machine with 48 stops on each reel, having 2 red, 2 blue and 3 black sevens on each reel.
Slot Machines Probability
Take for instance , , and (for any permutation of these values on the denotations, we will reach the same result, as the probability formula is symmetric in these three variables). We take c = 2 + 2 + 3 = 7 and look in the table of section 1.1 at the intersection of row t = 48 with column c = 7, where we find the probability P = 0.00310149 = 0.310149%.