BETKYO JOURNAL

The mathematics of luck, told from Tokyo

Exact odds pulled from our own game engines, the history of Japan’s games of chance, and how to verify every result yourself. No hype — numbers first.

証 FAIRNESS STUDIESLATEST

How the Journal verifies a number: the method behind every figure on this site

Every probability, multiplier and return printed in the Journal is read from the code that settles real rounds, and the article says where. This page is the procedure: what counts as a source, what a “verified” block means, what we do when the engine and the marketing copy disagree, and the two times the process found a bug in our own games.

BETKYO RESEARCH · 2026-09-12 · 7 MIN READ

数 MATH OF LUCK

瓦版The mathematics of luck, told from Tokyo

How the Journal verifies a number: the method behind every figure on this site

Glossary: casino math and provably fair terms, defined in two sentences each

Dust: the balance you cannot withdraw, and why it exists

Dealer bust odds by upcard, on an infinite shoe

A roulette bet is a string: self-describing keys and the ×36 table

The machine zone: what a slot floor is designed to do to time

Mahjong in Japan: the 1924 boom and a century in the grey zone

Tommy Carmichael and the light wand: what a slot sensor could not see

What the withdraw window checks before it sends

One rounding, not many: why the verifier matches the server bit for bit

Designing Fukubukuro: the lucky bag that always pays something

Casino Hold’em priced: the qualifying rule and the ante bonus

Designing Koban Flip: every face is fixed when you buy the coin

Address poisoning: the wrong address is already in your history

The house money effect: why a win changes the next bet

Takarakuji: Japan’s lottery, from temple tomikuji to a billion yen

The Ritz laser scanner: £1.3 million in two nights, and why it was not a crime

One nonce, many numbers: what the cursor counts

The hot hand: thirty years a fallacy, then the fallacy was the mistake

Wheel bias: the two men who beat roulette by writing numbers down, and why a court said it was legal

Ban-sugoroku: the dice game Japan banned in 689, and the master who said play not to lose

Designing Bingo: 38 balls, 12 lines, and why the centre star is worth a whole ball

What a hash commitment proves, and the three things it cannot

The illusion of control: why choosing your own client seed feels like it matters, and what it actually does

When a stablecoin loses the peg: what a casino balance is actually made of

Plinko, priced: why the middle bucket pays ×0.2 and the edge pays ×1,000

Designing Hanabi: a slot whose free spins build ×1, ×2, ×3, ×5 — and what its source file admits

Edge sorting: how Phil Ivey read the backs of the cards, and why two courts called it cheating

Sic Bo’s cheapest bet and its dearest: Big, Small and the triple tax

Right coin, wrong network: how a deposit goes missing

What a confirmation is, and why your deposit waits for several

Why ten mines pays the same as fifteen: the ×3,236,072 full clear

3:2 or 6:5: the one number that decides a blackjack table

The price of one more flip: how a 2% fee becomes 18%

Two rides, two curves: what Limbo and Crash actually charge

The superuser: when the house could see your cards

The near-miss effect: why almost winning feels like information

9/6 Jacks or Better: the one game here you can play wrong

Chō or han: the fairest game Japan ever ran

What a keno risk level actually changes — and what it does not

The auditor was the attack: Ronald Harris and the slot machine he was paid to check

Risk of ruin: why a 99% game still empties a bankroll

The Kelly criterion: the formula that tells most gamblers to bet nothing

Pachinko: how Japan built a gambling industry in a country where gambling is illegal

Designing Tairyō: what a slot’s paytable is actually promising you

Where the money sits: hot wallets, cold storage and what “proof of reserves” proves

The room is the game: how casino floors are built to keep you in them

What ×1000 leverage actually means: the one number that decides everything

Why our fee rises with leverage — and why we show you the curve

When the price feed goes dark: the fairest thing a desk can do is nothing

Where a crypto price comes from: there is no such thing as “the” price

Oicho-Kabu: the card game that gave the yakuza their name

The night black came up twenty-six times: Monte Carlo, 1913

Chinchiro: the real rules of Japan’s street dice game — with exact payouts

Andar Bahar’s random ×5 boosts don’t change the house edge — here’s the proof

Verify a casino round yourself: a step-by-step walkthrough

Before Mario: Nintendo spent 66 years as a gambling-card company

Omikuji: the shrine lottery that predates every casino

The gambler’s fallacy: why streaks feel like signals (and why the dice don’t care)

A short history of trusting randomness: from knucklebones to hash commitments

Four ways to prove a random number: commit-reveal, beacons, VRF, certified hardware

The honest house: an essay on the ethics of the edge

Playing like it matters: a practical responsible-play toolkit

The Run: how Archie Karas turned $50 into $40 million — and why he had to lose it

Designing Pagoda’s ladder: a game with no bad button

Paying the network, not the house: a player’s guide to crypto fees

Inside drand: the internet’s public dice

The students who beat the house: how the MIT Blackjack Team ran counting as a business

The mathematics of luck, told from Tokyo