Lately, I've been diving into the fascinating world of online casinos, particularly intrigued by the mathematics and probability that power them. There are three main concepts that keep these platforms running smoothly: the House Edge, Random Number Generators (RNG), and Probability. However, in many ways, probability underpins them all—it's the key principle that enables casinos to remain profitable in the long run. Let's break down these concepts to understand how they work together.
Multiplier
How much money should the player get for the bet? How do we decide if I bet $10, I will get $20 or $30?
It’s very simple. It is all probability. If the probability of an event occurring is 1/5 then you deserve a payout of 2X. If it’s a probability of 1/4, then the payout is 4X.
Payout - 1 / Probability
But, its not so simple in case of casinos as we have another thing to learn their - house edge.
House Edge
House edge is the percentage of money the house will keep from the profit.
Let me give you an example. Let’s say there is a coin toss. You have wagered on heads $10. It it lands heads then you win $10 without house edge but with house edge its slightly less. Coin toss may have a house edge of 2 per cent. Then you will win $9.8. This method helps casinos stay profitable
It may not be intuitive enough. Even the multiplier that casinos decide is dependent on the house edge. Let me give you another example showing how a house remains profitable because of the house edge mathematically.
Consider this game. There are three bombs here so the probability of not choosing a bomb is 1/4. The house edge is 2%. So the multiplier becomes - 4 - 4×4% = 3.92.
Now, mathematically a person can win 1 out of 4 times here. Let’s say a person bets 4 times and wins the fourth one. But still, because of the house edge, the house makes a profit and the person will lose money.
Bets - $100, $100, $100, $100 - $400
Returns on fourth bet - $100 × 3.92 = $392
Loss - $400 - $392 = 8
House edge - $400 × 2% = $8
This way, mathematically, the house always remains profitable. If there was no house edge here then that person will be even and can bet more. But always the house edge is kept very low so that people don’t notice and they slowly give their money to the house.
Random Number Generator (RNG)
How we decide the outcome of the event. if there is a coin toss, how do we decide if it lands Head or Tails?
We make use of a random number generator for this. RNG usually generates a number between 0 and 1 with equal distribution. If the number is less than 0.5, it’s a heads or tails otherwise.
There are other algorithms as well which can give different permutations of an event with equal probability but in a nutshell, RNG is the way to go.
Thanks, Happy Coding 😎