4 ms·
A good use of Excel particular to users here: dynamic programming. E.g. set up the base cases on the first row and column, and then experiment with the recursiv
by scarmig 4y ago
A good use of Excel particular to users here: dynamic programming. E.g. set up the base cases on the first row and column, and then experiment with the recursive case in the first empty cell, filling out the rest of the table.
Recently did this to solve a particular Brownian bridge. Given a deck of 52 cards, whenever you draw a red, you get $1, and whenever you draw a black, you lose $1. You can stop drawing cards whenever you like. What's the expected value of this game with a full deck? (solution: something like $2.61, don't have the exact number off the top of my head)
- deleted 4y ago[deleted]
- Balgair 4y agoYou can use the Solver GUI to do it in one column maybe: https://www.youtube.com/watch?v=0nbkaYsR94c https://www.youtube.com/watch?v=0nbkaYsR94c (48 min)
- arrow7000 4y agoWhy wouldn't it just be $0 on average?
- scarmig 4y agoHint: a suboptimal but positive EV strategy: You flip the first card. If it's red (50%), you immediately stop and take your winnings (+$1). If it's black (50%), you draw down the entire deck ($26 - $26 = $0). That gives you a guaranteed EV of $0.50/play. Alternatively, consider the case where you have a deck of 1 red and 1 black.