ExSpade Start With the Math ↗

A Closer Look at Gambling Math

Know What
the Odds Mean.

Take a price apart. Compare the rules. See what the numbers can—and can’t—tell you.

01 / Interactive Workbench

Decode the Odds.

Change either number.
The math updates as you type.

Implied ProbabilityBreak-Even Point
52.38%

The win rate needed to break even.

0%50%100%

A price does not tell you the true chance of winning.

Decimal Odds1.91
Profit if You Win$9.09
Return if You Win$19.09

Return includes the stake. Losing means losing the stake. No fees included.

Understand Expected Value ↗

02 / Understand the Game

Same Money. Different Math.

Compare All Games ↗
01

Blackjack

See the cost of changing a table rule.

02

Baccarat

Banker, player and tie, with the rules attached.

03

Craps

One table. Very different bets.

04

Poker

Learn the hand, the action and the decisions.

The Cost of One Extra Zero

What Does
the House Keep?

Single-Zero Roulette~$27.03
Double-Zero Roulette~$52.63

Expected loss at $10 × 100 spins. Standard payouts; no special rules. Actual outcomes vary.

Change the Numbers ↗

Build Your Understanding

Give the Numbers Some Structure.

Four Practical Lessons

Learn the Math.

Read a price, trace a payout, count repeated bets and compare outcomes.

Start the Learning Path →Twelve Worked Terms

Find the Meaning.

Definitions with an example, a common mix-up and a tool to try.

Open the Glossary →Three Matched Comparisons

Change One Rule.

Compare the same initial stakes under different rules and payouts.

Compare the Rules →

03 / Put the Numbers to Work

Try It. Then Look Closer.

All Tools ↗
Understand

Expected Value

See how your assumed win probability changes a bet’s average result.

Explore

Roulette Outcomes

Same average cost, different swings. See the full distribution of outcomes.

Compare

Payouts After Fees

The existing equal-risk calculator for contract fees and sportsbook odds.

04 / What an Average Hides

A 2.70% Edge Isn’t
a 2.70% Loss Every Time.

A single number and red/black have the same expected cost on a single-zero wheel. Their range of outcomes is very different.

Explore Roulette Outcomes ↗
Red / Black18 of 37winning pockets · pays 1 to 1
Single Number1 of 37winning pockets · pays 35 to 1

05 / The Reading Room

Find Your Next Answer.

All 26 Guides ↗
Dice GamesYour First Craps Round, Explained Roll by RollUse one Pass Line bet and the dealer’s puck: OFF means come-out rules; ON means the point must repeat before 7 for the bet to win.Card GamesLearn Texas Hold’em One Hand at a TimeFollow a worked No-Limit Hold’em hand from the blinds through betting order, pot growth and hand comparison, with no raises or side pots.Sports BettingA Transparent Look at the Week 1 Picks We Can Actually VerifySix public selections span three matchups, with analyst names, markets, captured lines, game times, and verification limits.Sports BettingThe Tax Rose, Then Bettors’ Effective Return FellJuly’s betting ledger shows how an 11.2% hold and weaker promotional spending changed the economics for North Carolina sportsbook customers.
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