The Arcade · house edge: educational

Games rigged in favor
of the central limit theorem.

Seven games. Convergence, bell curves, market survival, the goat theorem, optimal bet sizing, a chart-reading Turing test against real S&P history, and a correlation-guessing exam. All have been backtested on my own dignity.

random walk · the platformer a market simulator disguised as a video game
You are a portfolio. The ground is a price chart. This is already too realistic. space or tap jump, twice for conviction ● alpha, +100 ◆ dividend, +250 ◍ diversification, one free mistake ▮ candles, swans, and gaps in the chart itself
fair coin, allegedly a live experiment in the law of large numbers
click anywhere on the felt to flip
0
Flips
0
Heads
–
Heads %
0
Max streak

The chart will show your running heads ratio against the 95% confidence funnel. Flip enough times and you will watch certainty emerge from chaos, which is the entire job description of statistics.

the galton board drop balls, receive bell curve, question free will
balls: 0 every ball flips a fair coin at every peg. freedom is involved, the outcome is not.
monty hall · the goat theorem switching is correct. you will not believe this at first.
ROUND 1

0
Switch wins
0
Switch plays
–
Switch win %
0
Stay wins
0
Stay plays
–
Stay win %

expected: switch 66.7% · stay 33.3%

You are a contestant. The car is behind one of three doors. Monty knows where the goat is. So do statisticians.
kelly criterion · the optimal bettor 60% edge, even money, 20 rounds. the math knows what to do. do you.

BANKROLL: 1,000
WIN PROBABILITY: 60%
PAYOUT: 1:1
ROUNDS: 20
KELLY OPTIMAL BET: 20% per round

your edge is known. your sizing is not.

You are a bankroll. The coin is biased in your favor. This does not mean you cannot go broke.
real or random · the turing test for charts one of these charts has feelings. neither will tell you which.
CHART A
CHART B
round 1 · 0/0 correct · streak 0

the tell you cannot see

what GBM gets right: the daily return distribution, the drift, and the volatility level. those three parameters are everything a standard pricing model uses.

what GBM gets wrong: real returns cluster their variance. calm days follow calm days; violent days follow violent days. real returns also have fat tails: extreme moves happen more often than a normal distribution predicts.

why you cannot see it at this scale: 120 days is half a year. vol clustering needs a long run to become visible, and fat tails need a crash to show their face. at this resolution both series are wiggly lines going somewhere. the GBM is not a bad model. it is a sufficient model. those are different things.

You are shown two 120-day charts. One is real SPY history. One is a GBM calibrated to that exact segment. Click the one you believe is real.
guess the correlation a scatter plot walks into a bar. you say rho is about -0.4. you are wrong.
rho = +0.00

You are looking at 80 points from a bivariate normal. Slide to your estimate of rho and lock it. Error over 0.35 costs a life. You have 3.