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For Students · Gambler's Ruin

Gambler's Ruin for a regression forecast

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a regression forecast live below — adjust the inputs and watch it respond, right in your browser.

Gambler's RuinLive

the house always wins in the end

Controls

Presets

Starting stake ($)

Target ($)

Win probability

A gambler betting against a rich casino faces gambler's ruin: even a nearly fair game (49% odds) almost always ends in bankruptcy before hitting a big target, because the house has effectively unlimited funds. The tiny edge compounds relentlessly over many bets — which is exactly how casinos stay in business.

▶ Run in Python

Data Inspector

P(ruin) theory80.8%

Ruined (this run)0 / 30

Edge per bet-1%

Governing equation

P_{ruin} = \frac{( q / p ) ^{i} - ( q / p ) ^{N}}{1 - ( q / p ) ^{N}}, p = 0.49, i = 20, N = 50

Reading this result: The house edge (p<0.5) makes ruin nearly certain — P(ruin) rises exponentially with the target, so aiming for $50 from $20 all but guarantees going broke first.

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Frequently asked questions

Is this good for students?: Yes — this version of "Gambler's Ruin for a regression forecast" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.