I am a big fan of MMORPGs, and this one, Cabal Online, has a particularly punishing upgrade system. Items can be upgraded to increase their stats, ranging from level 0 to level 15 (for simplicity). Upgrading costs cores (can be interpreted as currency). Attempting an upgrade can result can result in the item’s level going … Read more
Context So I’m doing some research regarding the Kelly Criterion. By considering a coin tossing game in which you have even money odds where there is a probability p > 1/2 of winning, a probability q < 1/2 of losing and you bet the fraction \ell of your capital in each bet. Then, your capital … Read more
In the novel Spaceland by Rudy Rucker, the protagonist Joe Cube is grafted with an eyestalk that sticks vout into the fourth dimension. This lets him see under and inside three-dimensional objects the way we could see inside the bodies of Flatlanders. His wife encourages him to take advantage of his new ability by going … Read more
This is a very interesting word problem that I came across in an old textbook of mine. So I know its got something to do with probability, which perhaps yields the shortest, simplest proofs, but other than that, the textbook gave no hints really and I’m really not sure about how to approach it. Any … Read more
I’ll start off by saying that this is probably not deemed an adequately advanced question for this site, and I’ll probably phrase this poorly, I apologise if I do. Suppose there is a 5×5 grid [∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗] On this grid, coins will be placed on some of the squares, and bombs will be placed on the … Read more
Imagine you play a game where you can set a certain amount of money, and you have a 50% chance of doubling your bet and 50 % of losing your bet. (To make the game interesting to play you can also give a chance of winning higher than 50%). You can play the game multiple … Read more
I am trying to a solve a variant on the Gambler’s Ruin problem, in which two gamblers A and B make a series of bets until one of the gamblers goes bankrupt. A starts out with i dollars, B with N−i dollars. The probability of A winning a bet is given by p, with 0<p<1. … Read more
The St Petersburg paradox is a hypothetical game. The pot starts at $1. A fair coin is flipped and if it is heads, the pot doubles, if it’s tails, the player takes the pot. The game has a certain cost to enter, c and we assume that the house has unlimited funds. The probability of … Read more
Imagine you have a machine that you pay 1$, push a button, and it will randomly give you 2$ (you win) or keep your money (you lose) Now, the probability for you to win changes every week at the same daytime, and it’s chosen randomly as well between 0% and 100% using a uniform distribution … Read more
Imagine someone claims they win significantly more than they lose when betting on roulette. Presuming that it were possible to have a winning system how could you calculate the statistical significance of their claim? The roulette table has no “edge” (i.e. no zero/double zero…). The issue comes with the fact that they are able to … Read more
