TATITIC CALCULATOR
Parrondo Paradox
A precise tool.
What is the Parrondo Paradox & How does it work?
Parrondo’s paradox demonstrates that two losing stochastic games can be combined to produce a winning expectation.
Game A is a simple biased coin toss with winning probability p_A < 0.5, while Game B switches between two coins depending on the player's capital parity, each also losing when played alone.
When the games are alternated with mixing proportion Ξ±, the overall winning probability can exceed 0.5, defying intuition.
P_{win}=\alpha\,p_A+(1-\alpha)\left[\frac{p_{B,even}+p_{B,odd}}{2}\right]
P_{win} = overall winning probability of the mixed game
Parameters
Result
β
Frequently Asked Questions
What is Parrondo’s paradox?
Parrondo’s paradox demonstrates that two losing stochastic games can be combined to produce a winning expectation.
How do I input the probabilities for Game A and Game B?
Enter the probability of winning for Game A (p_A) and the probabilities for the two coins in Game B (p_B,even and p_B,odd).
What does the mixing proportion Ξ± represent?
The mixing proportion Ξ± represents the fraction of time Game A is played; the rest of the time, Game B is played.
Can I use this calculator to determine if my games will always win?
No, while Parrondo’s paradox shows that two losing games can be combined to win, specific probabilities are needed for accurate results.
What is the formula used in the calculator?
The formula used is P_win = Ξ± * p_A + (1 – Ξ±) * [(p_B,even + p_B,odd) / 2].
Results are for informational purposes only and do not constitute professional advice.