Articles of gambling

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 […]

Would you ever stop rolling the die?

This question already has an answer here: Toss a fair die until the cumulative sum is a perfect square-Expected Value 1 answer

Can you make money on coin tosses when the odds are against you?

The strategy Given an initial investment $n$ dollars and a “bet buffer” $b$. Calculate the bet size $x=\left\lfloor\frac{n}{2^b-1}\right\rfloor$ dollars. Wager $x$ dollars on random variable $C$ that $C=1$ with $P\left\{C=0\right\}=p>.5$ and $P\left\{C=1\right\}=1-p<.5$ and payout x$2$. If the bet is won, update $n:=n+x$ and go to step 1. If the bet is lost, update $n:=n-x$, $x:=2x$, […]

Prove a thm on stopped processes given fundamental principle 'you can't beat the system'?

How does the principle below imply the thm below? From Williams’ Probability w/ Martingales: Principle: Thm: What I tried: $$E[X_{T \wedge n} – X_0 | \mathscr{F_m}] =/ \le X_{T \wedge m} – X_0 \ \forall m < n$$ $$\to E[X_{T \wedge n} | \mathscr{F_m}] =/ \le X_{T \wedge m}$$ $$\to E[X_{T \wedge n} | \mathscr{F_0}] […]