#60 How do Casinos make money?
Saturday, April 16, 2022
Have you ever wondered how do the Casinos make sure that they don’t go broke? If gambling is all about luck, how does Casinos book huge profits and almost never lose money?
The trick is simple - The longer you play, the chances of you losing money increases significantly. The odds are not heavily stacked against you, but the Casinos have done masters in human psychology. They know that "winning" is addictive, hence, the mathematics is structured in such a way that you tend to stay longer in the game and the longer you stay, chances of you going broke increases.
Let's try this out and understand why the house always wins!
Let's play a simple betting game. Consider a circular disk which is divided into 100 equal parts and we assign each part a unique number from 1-100 (both 1 & 100 are inclusive). Now we spin this disk and throw in a paper ball.
Once the disk stops rotating, the paper ball points at a number and that is your RANDOM number for the experiment.
The rules of the game are as follows:
If the number is between 1 and 50 (both inclusive), the House wins.
If the number is between 51 and 99 (both inclusive), You win.
If the number is exactly 100, the House wins again.
The probability of you winning = 49/100.
Probability of The House winning = 51/100.
Clearly the House got a slighter edge. This little advantage is there in all the casino games and this small percentage turns out to be the X - Factor as we will see ahead.
Now consider you have $1000, and you bet $100 in each round. What is the probability that you won't go broke after 10 rounds? What is the probability that you won't go broke after 100 rounds? After 1000 rounds? Or after 10000 rounds? Remember they all are independent events!
For the sake of experiment, I wrote a small program in python to answer the questions stated above, you can do the simulation yourself by running the code attached here. Sharing a few results from the simulation I performed -
NOTE - The x-axis shows the wager count i.e. the number of rounds and y-axis shows the Account value.
RESULT - 1
This graph is for 10 wager rounds. Clearly if we start with 1000$ and bet 100$ in each round, we don't go broke.
RESULT - 2
Change the wager count to 100 and we observe that if we stay longer in the game, say 100 round, there's a good probability that we might go broke. In a number of other scenarios we don't go broke but we lose some money. There's no profit.
RESULT - 3
STUNNED? As we increase the number of betting rounds, the probability of we going broke increases significantly. Infact no one actually books a profit.
RESULT - 4
WOW!!! Increasing the betting rounds further by a factor of 10 results in every person going broke. EACH AND EVERY PERSON IS UNDER DEBT. Clearly the probability of you winning the bet is not the same when you started the game, even though they are independent events.
This is exactly what goes in the favour of Casinos. The amount of money they lose to the winners is significantly less compared to the money they make when people go broke. This is simple mathematics but compounding and human psychology do their job well!
See you next Saturday, until then have a great weekend :)
Cheers!
👾 MY TOP 5 TWEETS OF THE WEEK 👾
Apparently, Elon is buying Titter(yes Twitter without a ‘w’), so this week’s top tweets are obviously gonna be about him!
Some things that you may find interesting-
Video: Elon Musk talks Twitter, Tesla and the future at TED2022
Book I am reading: LifeSpan - Why we age and why we don’t have to?
Song I am listening to: Nasha (The Wildstone advertisement song)
Thought of the week: "Everyone is so smart when it comes to telling others how they should live their lives."