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14 results for “game theory”

Formulae (14)

EV = \sum_i p_i x_i

Probability-weighted average outcome of a decision.

f^* = \frac{bp - q}{b}

Optimal fraction of bankroll to bet for long-run growth.

EU = \sum_i p_i u(x_i)

Weighted average of the utility of outcomes, not just their cash value.

a \succ b \iff u(a) > u(b)

One strategy dominates another if its payoff is always higher.

v = \max_a \min_b u(a,b)

Best worst-case payoff a player can guarantee.

p = \frac{d - c}{(a-b)+(d-c)}

Probability that makes an opponent indifferent between their options.

P(A|B) = \frac{P(B|A)P(A)}{P(B)}

Update a belief's probability given new evidence.

VPI = EV_{info} - EV_{no\,info}

How much better decisions become with full information.

R = u^* - u

Difference between the best possible payoff and the one you got.

p = \frac{o}{1 + o}

Convert betting odds into an implied probability.

E = \sum_j q_j u(a, b_j)

Your payoff when the opponent mixes strategies.

EV = \sum_{k=1}^{\infty} \tfrac{1}{2^k} 2^{k-1}

A game with infinite expected value yet little real worth.

\phi_i = \tfrac{1}{2}(v(i) + [v(N) - v(j)])

Fair share of the total from a player's marginal contributions.

p = \frac{L}{L + W}

Win probability needed for a bet to break even.