You will be shown payout tables or odds for three independent games. Your task is to quickly evaluate value, risk, and trading opportunities. If exact odds are not provided, answer generically (in terms of probabilities p and decimal odds o) and illustrate with a small numeric example of your choice.
(a) For the quoted odds/payouts, quickly estimate for each available bet:
(b) Determine whether a risk-free arbitrage exists across the available bets. If so, construct a stake allocation guaranteeing nonnegative payoff in all outcomes, with strictly positive payoff in at least one.
(c) Suppose at least one positive-EV bet exists. Propose a bankroll-sizing strategy for bankroll B over T rounds, comparing full Kelly, fractional Kelly, and fixed-fraction sizing. Choose and justify a fraction given the estimated edge and variance.
(d) Under your chosen sizing strategy, compute or approximate the probability that cumulative profit after T rounds is positive. State assumptions (e.g., independence, identical odds) and use appropriate approximations (binomial or normal/CLT). Briefly discuss accuracy vs. speed for mental estimation.
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