I got this math problem online: A gambler starts with $\$10$ and plays a game for $20$ rounds. At each round, his wealth either increases by $\$1$ or decreases by $\$1$, but the moment his wealth falls below $\$5$, he is not allowed to play anymore. How many wealth sequences are possible in which he […]

I’m looking at a betting game where I have \$100 and want to double my money by repeatedly betting on a biased coin; it shows heads with probability $p<\frac{1}{2}$ in which case I win even money. I imagine my best strategy is to go all-in, but I also wanted to investigate what happens if I […]

People always like to evaluate the variance, but is there any way for variance to be interesting to the gambling game makers? In another word, what is a pratical gambling game that involving some distributions that is relating to variance other than the normal distribution?

Inspired by this question, I want to know if there is a version of the scenario that actually fits Newb’s intuition about the problem. Scenario template You roll a 6-sided die and add up the cumulative sum of your rolls. The game ends under the following conditions, with the associated payouts: You choose to stop […]

Given odds $o_i$ for $i=1,2,\ldots,n$ and the possibility to bet the amount $b_i\in \mathbb{R}$ on each event such that if event $i$ occurs you receive $b_io_i$ and if it doesn’t you recieve $-b_i$. I am trying to find out the condition for arbitrage. My immediate thoughts are that $1/o_i$ represents probability, and since these events […]

The promotion is like this: Starting credit: 500 dollars Maximum bet: 500 dollars Win up to 10000 dollars and get 10000 dollars free. House edge 52.5%. Is this exploitable?

I am attempting to determine two variables in this game: The optimum strategy: (What number the bettor should stay at) The expected value given perfect play: (The percent return on a bet when using the optimum strategy) Here is how the game works: There are two players. One is the “dealer” and the other is […]

Player A vs Player B. Bookie 1 offers 1.36 odds on player A winning. Bookie 2 offers 5.5 on player B winning. We have $1000 in total to bet. How would you place your bets such that profit is maximized? I have been told that this can be solved using linear programming, but I don’t […]

I want to calculate the Kelly bet for an event with more than two possible outcomes. Suppose the following game: A jar contains $10$ jelly beans. There are $7$ black jelly beans, $2$ blue jelly beans, and $1$ red jelly bean. The player wagers $x$ and grabs a single jelly bean randomly from the bag. […]

Both players start with $\$n$ Each player antes $\$1$ and rolls a private 100-sided die so that they are the only one that sees the result. After the rolls a round of betting occurs (same method as Poker betting which is described below) Player 1 chooses to either check keeping the stakes at $\$1$ or […]

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