Imagine you and a friend are playing a video game. You both put in $10 to win a $20 prize. The goal is to reach 10 wins, but the power goes out when you are winning 9 to 8.
How do you split the $20?
Most people would say, "I’m winning, so give me more!" or "Let's just split it $10 each." But Fermat and Pascal realized there is a mathematical "fair" answer based on what could have happened.
1. Stop Guessing, Start Counting (Permutations)
Fermat said: "Let’s look at every possible way the next two rounds could go." Since someone has to win 10 points within the next two rounds, the possible outcomes are:
- You win, then You win (You win the prize)
- You win, then Friend wins (You win the prize) **
- Friend wins, then You win (You win the prize)
- Friend wins, then Friend wins (Friend wins the prize)
Out of 4 possible futures, you win in 3 of them. Your friend only wins in 1.
2. The Decision Tree (Pascal’s Way)
Pascal visualized this like a branching path. At the 9-8 score:
- Path A: You win the next point (50% chance). Game over. You get 100% of the money.
- Path B: Your friend wins the next point (50% chance). Now the score is 9-9.
- From 9-9, it’s a coin flip. You have a 50% chance to win from here.
Instead of looking for a "certain" winner, you calculate the Expected Value. You own 75% of the "possible futures," so you should get 75% of the money ($15).
Why this matters for life:
This isn't just about gambling. It’s a way to think about risk:
- Think in Odds: Don't ask "Will this work?" Ask "What are the 10 ways this could go, and how many of them are good?"
- Avoid "Results Oriented" Thinking: If you make a bet where you have a 90% chance to win but you happen to lose, it doesn't mean it was a bad bet. It just means you hit the 10% "branch" of the tree.
The takeaway: Smart people don't try to predict the future; they try to figure out which "branches" are worth the cost of the ticket.
Would you like to try calculating the odds for a different scenario, like a sports series or a business move?
**If you are doubtful on 2nd Probability click on the related article link below.
