Tag: expected-value
Interview Questions
- Tying rope ends in a bag
- Estimate e by summing uniforms past 1
- How many good trades undo one bad fill?
- Sizing a market maker's daily take
- Spin a dial with two re-spins, price the game
- One re-roll, but the re-roll costs you
- Roll three times, keep the best, price it
- Two dice, one re-roll of both, price the sum
- Die with up to two re-rolls, price the game
- Roll a die with two re-rolls allowed, price it
- Re-roll the die, but it costs you a dollar
- Roll a 20-sided die, keep it or re-roll once
- Two dice, keep the sum or re-roll both once
- Roll a die, keep it or re-roll once, what's it worth?
- Ten-sided die, pay two dollars to re-roll
- Spin for a uniform payout, pay to re-spin
- Roll a die with at most two free re-rolls
- How pricey must a re-roll be before you never bother?
- Roll a die, keep it or pay to re-roll, what's it worth?
- What does it mean to "earn the spread"?
- Is this quote actually making money?
- You win two dollars raised to your die roll
- You win the square of two dice summed
- You win the product of two dice
- You win thirty-six over your die roll
- Pay to play, you win the square of a die roll
- The Kelly fraction for uneven odds
- The break-even spread when some traders know the answer
- Backing out the spread from your return target
- From your probability to fair odds
- Is it worth improving the price by one tick?
- Make a market on the sum of ten dice
- Make a market on reds in 100 roulette spins
- Make me a market on the number of heads in 100 flips
- Make a market on the product of two dice
- Make a market on the higher of two dice
- Make a market on heads in ten flips
- Make a market on the sum of three dice
- Make me a market on the sum of two dice
- Make me a market on the min of two dice
- Make me a market on the max of three dice
- Make me a market on the absolute difference of two dice
- Make me a market on the product of two dice
- Make me a market on the max of two dice
- What your overnight book is really risking
- Three draws, keep the most value
- Aggregating a day of fills into a P&L
- What is a good spot in the queue worth?
- Quoting a two-way market on two dice
- Quoting when one fill in three runs you over
- Two faces bust you now
- The fixed-jackpot slot, press your luck
- Double or nothing, when do you walk away?
- When the biggest face is the trap
- Keep rolling or bank it, the greedy pig game
- When the tick won't let you quote your fair price
- The game that stays huge even with a cap
- A positive-EV lottery you'd barely touch
- The martingale that "can't lose"
- How much of the book on a 55/45 coin?
- The St. Petersburg game, what would you pay?
- Symmetric or skewed? Compare the two books
- How long does skewing take to flatten your book?
- A sharper signal on a bigger bet
- A noisy signal when the odds are lopsided
- A signal that cries "high" too often
- The signal is worth double if you can short
- How much is a noisy signal worth?
- Your edge at decimal odds of 2.10
- Your edge at American odds of +150
- From edge to bet size with Kelly
- Your edge at decimal odds of 1.65
- Roll three dice, keep the highest, fair price?
- Expected absolute difference of two dice
- Roll two ten-sided dice, keep the higher
- Roll two dice, keep the lower, fair price?
- Roll two dice, keep the higher, fair price?
- Expected product of two four-sided dice
- Expected value of a die times a coin
- Expected product of two mismatched spinners
- Expected product of three dice
- Expected product of two dice
- Banach's matchbox with a favored pocket
- Banach's matchbox problem
- Betting a dollar on a seven
- How long does a losing streak at the casino last?
- Reaching the finish square by coin flips
- Cashing in a single card draw
- A die game where rolling a 1 wipes you out
- A die game with two rerolls
- Reroll on a twenty-sided die
- A reroll that costs a dollar
- Paid the square of your die roll
- Fair value of a die game with one reroll
- Eight-sided die with two rerolls
- Ten-sided die with one reroll
- Unlimited rerolls, but each one costs you
- Two rerolls, but each reroll costs a dollar
- Die game with two rerolls
- Expected distance between two random points on a rope
- The drunkard who wants to climb one step uphill
- How many aces sit in the top five cards?
- How far from home after n random steps?
- How many boxes stay empty?
- Expected rolls of a die until the first six
- Expected flips of a biased coin until the first tail
- Expected draws until you pull an ace
- Expected quotes until your order fills
- Expected number of coin flips until the first head
- Expected value of the minimum of dice
- Expected maximum of two four-sided dice
- Expected maximum of uniform random numbers
- Expected spread between the two dice
- Expected value of the maximum of dice
- Where does the k-th smallest uniform land?
- Expected maximum of n exponentials
- Expected range of n uniforms
- Expected maximum of uniform random variables
- The smaller of two dice
- How deep is the first heart in the deck?
- Getting paid the product of two dice
- Expected boxes to collect all five toys
- Expected rolls to see five of six faces
- Expected draws to collect all ten coupons
- How many distinct faces after ten rolls
- Expected rolls to see all six faces
- Fumbling with a ring of keys
- The die that explodes on a six
- Taking turns to flip the first head
- How many flips to collect three heads (not in a row)?
- Flipping until you've seen both heads and tails
- The coin has no memory of your bad luck
- Where does the third-smallest random number land?
- The miner and the three tunnels
- Expected number of shared-birthday pairs
- Chasing the one toy your kid actually wants
- The spider stalking a fly on a line of leaves
- When the paradox quietly disappears
- The paradox against a real casino's bankroll
- A biased coin tames the paradox
- Infinite mean, but what's the typical win?
- The St. Petersburg paradox
- Three coins, a dollar a head, and a matching bonus
- The necktie paradox
- The two-envelope paradox
- Expected flips to get three heads in a row
- Expected flips to see the pattern HTH
- Expected flips to two heads in a row with a biased coin
- Expected rolls to see two sixes in a row
- Expected flips to get two heads in a row
- Expected flips until three heads in a row
- Why does HT come faster than HH?
- Expected rolls until a five is followed by a six
- Expected flips until the pattern HTH
- Expected rolls until two sixes in a row
- Expected total once the uniforms first pass one
- How many uniforms to exceed one half?
- How long until a draw is smaller than the last?
- How many uniforms to exceed one?
- How many random numbers to push the sum past one?