Mixed Strategies, Bluffing & RPS
Key ideas about randomized play, the indifference principle, and designing RPS triads and bluffs.
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Questions Covered in This Set
11 cards to master
Mixed strategy
A probability distribution over your available options, rather than always picking one action.
Why does Rock-Paper-Scissors have no pure Nash equilibrium?
Any fixed choice can be beaten, so the best response chases in a cycle — no cell where both players stand still.
Indifference principle
At a mixed equilibrium, every option you actually use must give the same expected payoff; otherwise you'd stop mixing.
RPS equilibrium mix and value
Play each of Rock, Paper, Scissors with probability 1/3; expected payoff is 0 (fair, unexploitable).
Why does RPS stay interesting despite trivial math?
Humans are bad random number generators — they over-play Rock first and switch after losses, so reading patterns is the real skill.
Penalty kick equilibrium insight
With payoffs 0.2/0.7 and 0.9/0.2, the goalie dives Left with q = 0.5/1.2 ≈ 0.42.
Whose payoffs determine whose mix?
Your own payoffs determine your OPPONENT's equilibrium mix, not your own.
Design implication of buffing an option
Buffing an option can change how often opponents defend against it, sometimes leaving its own usage rate unchanged.
Why is bluffing an equilibrium, not a trick?
Betting only strong hands makes opponents always fold; always bluffing makes them always call — a mix keeps them indifferent.
Rough bluff-to-value ratio for a pot-sized bet
About one bluff for every two value bets.
Why use RPS triads in game design?
They prevent dominant strategies — each unit/option counters another, keeping choices meaningful.
