← Back to Home
Lab
Interactive Demonstrators
Self-contained analytical tools demonstrating mathematical concepts. Each module is interactive (experiment with the parameters).
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]
Posterior Mean
Monte Carlo π Estimation
Estimate π by sampling random points in a unit square.
Monte Carlo Estimation
Stochastic Convergence Analysis
N = 0
ESTIMATE
0.000000
TRUE VALUE
3.141593
ABSOLUTE ERROR
3.141593
EXPECTED ERROR O(1/√N)
—
Pre-Flop Range Analysis
Visualize starting hand ranges for Texas Hold'em.
Pre-Flop Range Analysis
GTO-Approximated Opening Ranges
AA
AK
AQ
AJ
AT
A9
A8
A7
A6
A5
A4
A3
A2
AK
KK
KQ
KJ
KT
K9
K8
K7
K6
K5
K4
K3
K2
AQ
KQ
QQ
QJ
QT
Q9
Q8
Q7
Q6
Q5
Q4
Q3
Q2
AJ
KJ
QJ
JJ
JT
J9
J8
J7
J6
J5
J4
J3
J2
AT
KT
QT
JT
TT
T9
T8
T7
T6
T5
T4
T3
T2
A9
K9
Q9
J9
T9
99
98
97
96
95
94
93
92
A8
K8
Q8
J8
T8
98
88
87
86
85
84
83
82
A7
K7
Q7
J7
T7
97
87
77
76
75
74
73
72
A6
K6
Q6
J6
T6
96
86
76
66
65
64
63
62
A5
K5
Q5
J5
T5
95
85
75
65
55
54
53
52
A4
K4
Q4
J4
T4
94
84
74
64
54
44
43
42
A3
K3
Q3
J3
T3
93
83
73
63
53
43
33
32
A2
K2
Q2
J2
T2
92
82
72
62
52
42
32
22
Raise
Call
Fold
VPIP (Voluntarily Put $ In Pot)
23.7%
PFR (Pre-Flop Raise)
23.7%
Knight's Tour Heuristics
Warnsdorff's algorithm for solving the knight's tour problem.
Knight's Tour
Warnsdorff's Heuristic
0 / 64 squares
Click a square to set the starting position
VISITED
0
BACKTRACKS
0
TIME (ms)
0
Warnsdorff's Rule: Move to the square with the fewest onward moves. This greedy heuristic typically finds a solution without backtracking.
Response Latency Analysis
Measure your reaction time distribution.
Latency Calibration
Response Time Analysis
0 / 20
20 arithmetic problems. Measure your response latency.
24 Game Solver
Combinatorial search to make 24 from 4 numbers.
The 24 Game
Combinatorial Search & Expression Trees
8
4
8
5
Algorithm: Recursive backtracking over all operator/operand permutations. Prunes invalid paths (division by zero). Explores O(n! × 4^(n-1)) expressions.