Trader Fair-Bet Probability and Number Sequences

Trader and Sneak Peek assessments ask fast probability-to-fair-bet conversions, mental arithmetic, and sequence-recognition questions under tight time limits. Requirements The trader-style OA asks for fast numeric answers, not long explanations. Core fair-bet format: For each event, imagine that you can place a bet that returns 1000 plus your original stake if the event occurs. Enter the dollar amount that makes the bet's expected value exactly zero. Round to the nearest dollar. Representative probability events include: Draw one card and win if it is a face card or an ace. Draw one marble from 20 marbles with 11 green and 9 blue; win if green. Choose a random hour; win if it is between 9 AM and 5 PM. Flip coins two or four times; win on two heads, at least one head, or the exact sequence heads then tails. Roll dice; win if not a 6, odd, or sum of two dice equals 12. Pick a random day in February 2025; win if it is a weekday. Pick a random 4-digit number; win if the last two digits are 00. Sequence questions include geometric progressions, alternating operations, fractional patterns, alphabet sequences, look-and-say style strings, and mixed sign/magnitude series. Notes If the win probability is p and the stake is s, the zero-EV equation is: p * 1000 - (1 - p) * s = 0 s = 1000p / (1 - p) Some candidates phrase the payout differently; in the visible prompt the returned amount is 1000 plus original stake, so the net profit on a win is 1000 and the loss on a miss is the stake. The bottleneck is speed. Pre-memorize common fractions and their fair-bet conversions: 1/2 -> 1000, 1/3 -> 500, 1/4 -> 333, 1/5 -> 250, 2/3 -> 2000, 3/4 -> 3000, 5/6 -> 5000. Preparation Drill 8-minute mental arithmetic sets; standard Zetamac practice helps but may not cover the larger-number style. Convert common card, dice, coin, calendar, and spinner probabilities into fair-bet stake amounts without writing the formula each time. For sequences, classify first: arithmetic/geometric, alternating subsequences, numerator/denominator separately, alphabet index, and recursive digit description.