4 ms·

>it’s also about maximising your chances of success — or your expected utility, or whatever your goal is — based on the information you do have (e.g. in poker).

>it’s also about maximising your chances of success — or your expected utility, or whatever your goal is — based on the information you do have (e.g. in poker). Can you explain this with a few examples?

ben_w 6y ago
I’ll try :) Toy example: You are offered the opportunity to play a game of chance. The house draws one card from a standard, fair, deck. Number cards win their face value in $, jack/queen/king/ace wins $20/$25/$30/$100 respectively. Assuming each dollar you win has the same utility to you, what is the largest amount you should be willing to pay to enter the game? Expected value = expected win - cost; anything which makes the EV positive is worth playing Expected win = $(100+2+3+4+5+6+7+8+9+10+20+25+30) * 4 / 52 = $17.61 (and a bit) But most people get more utility from their first dollar than from their 1000th, so: if your net worth is $100k and the utility of money to you is sqrt(dollars), how does this change? I’m still learning this one on brilliant.org right now; I think it works out as: EV = mean of EVs of all possible outcomes, each outcome being sqrt(100000 - cost to play + result of that win) What if you are in a sketchy casino and you’re not confident the game is fair? If there’s a 10% chance the game is rigged and will force you to draw a 2, now what is the fair price to play the game? Same idea, but now weight the results by the chances; 10% chance of a $2 return, 90% chance of previous result. I don’t play poker; what little I do know is that it is a hidden information game where in order to win you have to attempt to infer the other player’s hands relative to your own, and that this is a game of skill rather than pure guesswork.
- passivate 6y ago
  Thanks for the reply! It helps to understand the principle, but I was also curious how you apply Rational thinking to everyday situations. Using math as a tool is great, but that might only work in some situations.

ben_w 6y ago

I’ll try :) Toy example: You are offered the opportunity to play a game of chance. The house draws one card from a standard, fair, deck. Number cards win their face value in $, jack/queen/king/ace wins $20/$25/$30/$100 respectively. Assuming each dollar you win has the same utility to you, what is the largest amount you should be willing to pay to enter the game? Expected value = expected win - cost; anything which makes the EV positive is worth playing Expected win = $(100+2+3+4+5+6+7+8+9+10+20+25+30) * 4 / 52 = $17.61 (and a bit) But most people get more utility from their first dollar than from their 1000th, so: if your net worth is $100k and the utility of money to you is sqrt(dollars), how does this change? I’m still learning this one on brilliant.org right now; I think it works out as: EV = mean of EVs of all possible outcomes, each outcome being sqrt(100000 - cost to play + result of that win) What if you are in a sketchy casino and you’re not confident the game is fair? If there’s a 10% chance the game is rigged and will force you to draw a 2, now what is the fair price to play the game? Same idea, but now weight the results by the chances; 10% chance of a $2 return, 90% chance of previous result. I don’t play poker; what little I do know is that it is a hidden information game where in order to win you have to attempt to infer the other player’s hands relative to your own, and that this is a game of skill rather than pure guesswork.

passivate 6y ago
Thanks for the reply! It helps to understand the principle, but I was also curious how you apply Rational thinking to everyday situations. Using math as a tool is great, but that might only work in some situations.