Why the House Always Wins

The Dream of the Red Chamber Chapter 2



That zero means millions of dollars in profit!
When Jia Yucun (賈雨村) was going out for a walk, he encounters a dilapidated temple.  The two columns at the front of the door has a couplet:

身後有餘忘縮手

When there's plenty behind, one forgets to hold back

眼前無路想回頭

When one there's nothing ahead, one thinks of turning back

There's something called the sunk costs fallacy.   It says one makes decisions about current conditions based on how one invested in the past.

Here's an example I used for my niece that simplifies gambling.

Let's say we bet on a coin toss game and I'm the house.  If it's heads, I win a dollar.  If tails, you win a dollar.  If we decide to play one round, one dollar is at stake.  If we decide to play 100 rounds, 100 dollars at stake.

If we assume the coin is fair, most likely you and I will win 50 dollars.  There might be a chance that I win 49, and you win 51, or visa versa.  There's also the possibility that I win 1 dollar, and you win 99.  But the probability of getting a 49-51 state is much higher than 1-99.

Here's a cute website about binomial probability.  You do the math.

But let's simplify things for the math inept.

Let's go back to the coin toss.  If you win, I give you a dollar.  But if I win, you have to give me 1.01.  After 100 rounds, most likely you WIN 50 dollars, and I WIN 55 dollars.  No big deal, right?

Ah, but let's look at this way, I LOST 50 dollars to pay your winnings, but you LOST 55 to pay my winnings!  If we just take the difference between what was lost and won for each person, I WON five bucks, you LOST 5 bucks.

But if you're a little sunk in the hole, you can win it back right?  SUNK COSTS FALLACY!!!!

1000 rounds?  I win $50.

10,000 rounds?  I win $500.

What if I lived in a world where many people agreed to play against much more than their odds for 24 hours a day?  It would be like some sort of cash gathering machine!

It's called a casino!

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