Ever tried a card game and lost your money playing? It pains to be the loser but you keep coming back for more even though you know it's a game of luck. I have smashed pillows, punched walls, and almost broken my knuckles after a rummy game, and still went back the next day hoping to win.
Behind all of this, there is a mysterious host who silently knows that you're suffering while you still manage to keep a poker face. What do they get? Pleasure? Nope. They stack bags of money from your loss. They smile at you politely knowing that they just made 4X the money since the last game while you sat there and strategized your response to every outcome of the game.
Consider the game of Roullete. The rules are simple. There is a spinning wheel and a ball is dropped in it. You bet on where the ball is going to land when the wheel stops spinning. If you're right with your prediction, good job, you just got lucky. Wrong prediction? It's about time to pack up and do something else or say goodbye to this month's rent.
Oh, so you're an optimist? Consider this:
There are 38 places the ball can land. Assuming that the wheel is evenly built, the ball can land in any of the 38 slots. Say, you predict it's going to land on 30. The chance of landing on 30 is 1/38.
For every turn you try, you give them 20 coins. If you win, you get 100 coins back and if you lose, well, you just lost your 20 coins. Sounds fair right? What an investment that is! 100 coins for every 20 coins I spend. Let's see a real example.
Here is a game I simulated in python. I created a list of random numbers that take values between 1 and 38. I simulated 100 games and checked whether the ball ever landed on 30. It landed...twice!
import random
random_list = [random.randint(0,38) for i in range(100)]
print(random_list)
By the rules of the game, I add 100 to my wallet if it lands on 30 and subtract 20 if it doesn't
for i in random_list:
if i==30:
money.append(100)
else:
money.append(-20)
print(sum(money))
[out]: -1760
I lost 1760 coins! Now, the obvious learning is that don't play games you can't win but was there a way I could have known that before I tried playing?
Expected Value
If there is a way to prevent the damage, take it! Now, there is no constant winning in anything but there is something called a net payoff. You lose small but you win big.
Since we know that the probability of landing on any number is the same which is 1/38, each time it lands on 30, we make 100, or else we lose 20.
So, consider a list of 38 numbers from 0 to 38.
Now calculating the expected value or the average money made possible using this formula, we get:
ev_money=[]
for i in nums:
if i==30:
ev_money.append((1/38)*100)
else:
ev_money.append((1/38)*-20)
print(sum(ev_money))= -16.31
That's the 'average' money you would make per roll. Now if you were to play 100 games, that would be -16.31*100 = -1631
Now, that's the money you would "probably" lose or the best-case scenario. Even though the theoretical average ( 1631) and the real value ( 1760) differ by 129 coins, it is safe to say that the best case scenario is you losing 1631, and if you ask me that is not the best case scenario at all!
This is why it's important to know the risk-to-reward ratio to play any game. Some games aren't worth playing but we don't play to satisfy our rational brains. We play because it is fun. We are stupid but that's what makes it great!
If we can make smarter decisions based on data, we can be more confident in our predictions and wins. A probabilistic thinking approach makes us more rational and prepared.
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