lab

Interactive workbench

Small browser native tools for intuition and sanity checks. Filtering and simulation lead; older mathematical play modules sit lower on the page.

lead modulefiltering

Watch a Kalman filter track a noisy signal

A one dimensional filter, a hidden synthetic price, noisy observations, and sliders for Q and R.

open demo

module index

open lead demo

lead moduleKalman filter tracking

A live one dimensional filter with adjustable process and measurement noise.

restored moduleBayesian belief updating

Beta Binomial conjugacy with posterior mean and interval updates.

restored moduleMonte Carlo option pricing

GBM option pricing and pi estimation by repeated random sampling.

restored module24 game solver

Combinatorial expression search over four numbers.

math playPreflop range analysis

Starting hand range visualization by position and action.

math playKnights tour heuristics

Warnsdorffs rule as an interactive graph traversal demo.

math playResponse latency analysis

Reaction time calibration over small arithmetic tasks.

Bayesian belief updating

Watch priors become posteriors as evidence accumulates.

Bayesian Belief Updating

Beta Binomial Conjugacy

n = 0

POSTERIOR PARAMS

α = 1, β = 1

OBSERVATIONS

H = 0, T = 0

E[p]

0.5000

95% CI

[0.000, 1.000]

BIASED_COIN

Posterior Mean

Monte Carlo option pricing

Estimate option prices and pi by repeated random sampling.

Monte Carlo Estimation

Stochastic Convergence Analysis

N = 0

π ESTIMATIONGBM OPTION PRICING

ESTIMATE

0.000000

TRUE VALUE

3.141593

ABSOLUTE ERROR

3.141593

EXPECTED ERROR O(1/√N)

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24 game solver

Search expression trees to make 24 from four numbers.

The 24 Game

Combinatorial search and expression trees

SOLVER MODETEST MODE

Algorithm: Recursive backtracking over all operator/operand permutations. Prunes invalid paths (division by zero). Explores O(n! × 4^(n − 1)) expressions.

math play

Older interactive modules kept because combinatorics, graph traversal, and measurement are still useful ways to test reasoning.

Preflop range analysis

Visualize starting hand ranges for Texas Holdem.

Preflop Range Analysis

GTO approximated opening ranges

Raise

Call

Fold

VPIP (Voluntarily Put $ In Pot)

23.7%

PFR (Preflop Raise)

23.7%

Knights tour heuristics

Use Warnsdorffs rule for graph traversal on a chessboard.

Knights Tour

Warnsdorffs Heuristic

0 / 64 squares

Click a square to set the starting position

VISITED

BACKTRACKS

TIME (ms)

Warnsdorffs Rule: Move to the square with the fewest onward moves. This greedy heuristic typically finds a solution without backtracking.

Response latency analysis

Measure response time distribution under small arithmetic tasks.

Latency Calibration

Response Time Analysis

0 / 20

20 arithmetic problems. Measure your response latency.