luck, lucky number, 17

How Do Casinos make money !!

How the casino roulette is rigged to always win.

luck, lucky number, 17

At least once in your life, you must have thought about visiting a Casino, Spin the roulette and bag all the cash that’s in there and live the life of the multimillionaire you have always wanted to. But after reading this post, you will want to reconsider your thoughts.

So, the basis of this post would be the American roulette- which consists of 38 numbers 18 red, 18 black, and 2 green numbers.
There are 3 types of bets you can place in the roulette and I will explain why the casino is always at an advantage. Interestingly all this boils down to two simple concepts -:

1) Basic Probability
2) Expected value

Let’s start with the first type of bet.

1) Bet on a single color – This is a simple bet where you choose one color either red or black. This is an even bet and for every dollar placed you get an extra dollar back.
So as there are 18 numbers each, the probability that you win will be
P ( win ) = 18/38 = 0.4736 , P ( not win ) = 20 / 38 = 0.5263

play, card game, poker
Casino chips

Now, I hope you noticed that it’s not a fair game. you are always at a disadvantage, why? just read on, you will know.

At this point, I want to tell you about one very important concept. the concept of expected value, believe me, this is a very significant part of the whole roulette concept,

Expected Value is nothing but the weighted average of how much you can win while you place your bet.

Expected value = ( Winning amount ) [ P ( win ) ] – ( losing amount )[ P ( lose ) ]

Thus in the first type of bet,
Expected value = ( 1 $ ) ( 0.4736 ) – (1 $ ) ( 0.5263 )
= – 0.052 $

Don’t, worry about the maths here, for now just observe that there is a negative sign before the amount that you can win.

2) Bet on numbers from 1 to 12 – This is the bet where you choose all the numbers from 1 to 12, if the ball rolls on any of the number selected, you win. In this bet, you get 2 extra dollars for every dollar placed.

Again, let’s see the maths-:
P ( win ) = 12/ 38 = 0.3157 P ( Lose )= 26/38 = 0.6842

Clearly, you have an even lesser chance to win now !!

Let’s see the expected value,

Expected value = ( 2 $ ) ( 0.3157 ) – ( 1 $ ) ( 0.6842 )
= -0.052 $

Strange, Same expected value, why do you think this keeps happening. There is got to be a reason for this. Yes, there is, Stay with me.

3) Bet on a single number – This bet is the riskiest of all the bets and thus has got greater returns. For every 1$ placed you get 35$ as a reward.

Luring right !!

luck, lucky number, 13

Probability has the answer :
P ( win )= 1/38 = 0.0263 P ( lose )= 37/38 =0.9737

Whoa, such low chances of winning !!

Let’s see what the expected value holds for us :

Expected value = ( 35 ) ( 0.0263 ) – ( 1 ) ( .9737 )
= – 0.052 $

Now, if you have been alert, you would have noticed that the expected value has been the same in all the cases. The prize money is decided based on the probability theory.
The reason behind your continuous loss, those 2 green numbers. These Green numbers have been placed in order to create an imbalance in the fair chance of winning and losing. Due to these extra two numbers the casino always wins.

So, the next time you walk into one of these wheels, you know these are not the fortune wheels.

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3 thoughts on “How Do Casinos make money !!”


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