Articles of gambling

How many ways does the gambler break even?

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 […]

Betting a constant fraction on a biased coin

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 […]

Does variance do any good to gambling game makers?

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?

Should you ever stop rolling, THE SEQUEL

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 […]

Arbitrage opportunity

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 […]

Is this casino promotion exploitable?

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?

100-Sided Dice “Blackjack” Game

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 […]

Arbitrage sports betting

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 […]

Kelly criterion with more than two outcomes

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. […]

Game Theory Optimal Solution to 2 Player Betting Game

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 […]