mathematics

Decision Theory

Rational choice under uncertainty — Kelly criterion betting, portfolio optimization, multi-armed bandits, and the mathematics of making optimal decisions.

decision theoryKelly criterionportfolioriskmulti-armed banditutilityoptimal stopping

Every day we make thousands of decisions under uncertainty. Should you take the risky job or the safe one? How much should you bet when you have an edge? When should you stop searching and commit? Decision theory provides mathematical frameworks for answering these questions optimally.

These simulations explore the key models of rational decision-making. Watch the Kelly criterion optimize long-term wealth growth, see how diversification reduces portfolio risk, discover the explore-exploit tradeoff in the multi-armed bandit, and understand why our intuitive decisions about risk are systematically biased.

5 interactive simulations

simulator

Kelly Criterion Betting

Visualize optimal bet sizing with the Kelly criterion — compare wealth trajectories for Kelly, over-betting, under-betting, and all-in strategies

simulator

Multi-Armed Bandit (Explore vs Exploit)

Compare exploration strategies in the multi-armed bandit problem — random, epsilon-greedy, UCB1, and Thompson sampling

simulator

Auction Theory Simulator

Compare English, Dutch, first-price sealed, and Vickrey auctions — see revenue equivalence, bidding strategies, and efficiency in action

simulator

Markowitz Portfolio Frontier

Explore mean-variance portfolio optimization — visualize the efficient frontier, tangency portfolio, and diversification benefits

simulator

Prospect Theory & Loss Aversion

Visualize the S-shaped value function of prospect theory — see how loss aversion, diminishing sensitivity, and reference dependence distort rational decision-making