 # Immersive Introduction to Basic Probability

Hey there :)

This is an immersive introduction to probability.

You have been hired by John to design games for his casino. You need to design the games in such a way that can maximize casinos profit and minimize its loss. However, it should also give enough rewards to players, so they are motivated to play.

Let's go with a simple game, predicting a coin toss. Player needs to pay \$10 to play this game, if they get the prediction right, they will be rewarded with \$20. Let's simulate this game and see how well it goes for the casino; if this was played a thousand times. Go ahead and tap on the simulate button.

📟 Coin Toss Simulator

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As you can see, the difference between player wins and casino wins is marginal. This doesn't make sense for the casino. Since they will be paying out more instead of making money. We need to drastically reduce the player's odds of winning.

#### Counting probabilities

So how do we calculate odds or probabilities? It's simple, divide the count of desired outcomes over total possible outcomes. Didn't get it? Try out the probability calculator for different games.

📟 Probability Calculator

Change this to find probabilities for other games.

The player has least odds of winning in predicting the outcome of a 20 sided dice roll. Since the probability is 1/20 or 5%. This game has drastically reduced the player's chance of winning from earlier 50% to 5%.

So what about casino's chance of winning in every game? How do we calculate those odds? Logically, if a player is loosing, then the casino is winning. Since the player's odds of winning is only 5%, the rest 95% of odds are in favour of the casino.

Are you excited to see how much money the casino can make with these new games? Go ahead and try the 'Dice Roll Simulator'.

🎲 Dice Roll Simulator

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As you can see, knowing probabilities pays off well. However, predicting dice rolls is not an appealing game since players know their chance of winning is less.

#### Probabilities of Multiple Events

Good casino games should give hopes to the player they can win. As they play, giving them a feeling they almost won, will motivate them to try more. The slot machine is an example of such a game. Let's learn about calculating probabilities of multiple events with a simulated slot machine.

#### AND Probability

Here's a simple slot machine with three slots. Each slot generates a random number between 1 & 7. The player wins \$100 if all three slots hit 7. So how do we calculate odds of all three slots hitting 7?

Here we need to find the probability of the first slot hitting 7 AND second slot hitting 7 AND third slot hitting 7. To find AND probability of multiple events, we need to multiply probabilities of individual events.

That is, probability of the first slot hitting 7 * probability of second slot hitting 7 * probability of the third slot hitting 7. From counting probabilities, we know that odds of individual slot hitting 7 is 1/7 (Desired Outcome Count/Total Possible Outcomes).

Hence the probability of all three slots hitting 7 is 1/7 * 1/7 * 1/7. Go ahead and try the simulator.

📟 Slot Machine Simulator

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A good game should give hopes to the player that they have a chance in the game. In our slot machine, the player gets hope when two slots hit 7, or at least one slot hits 7. Probability of two slots hitting 7 can be calculated with AND probability. However, let's focus on finding the probability of either one of the slots hitting 7.

#### OR Probability

Here, we need to find the probability of the first slot hitting 7 OR second slot hitting 7 OR third slot hitting 7. This can be calculated by summing up individual slot probabilities and subtracting it with the product of individual slot probabilities.

That is, (Probability of First Slot Hitting 7 + Probability of Second Slot Hitting 7 + Probability of Third Slot Hitting 7) - (Probability of First Slot Hitting 7 * Probability of Second Slot Hitting 7 * Probability of Third Slot Hitting 7).

In our case, (1/7 + 1/7 + 1/7) - (1/7 * 1/7 * 1/7). Go ahead and try the simulator.

📟 Slot Machine Simulator

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Congrats, you have learned to count probability and calculate probabilities of multiple events with logical AND, OR operators. If you are interested in the upcoming chapters on probability, sign up here.