Betting & Casino Guides: Odds, EV, Bankroll, actfap

The reading path: 8 guides, in order

6 min read1. Betting Odds Explained How decimal, fractional and American odds work, how to read the implied probability behind any price, and how to spot a bookmaker's margin eating your value.
7 min read2. Expected Value in Betting What +EV means in practice, how to work out expected value from your probability and the price on offer, and why closing line value is the honest scoreboard.
7 min read3. House Edge, RTP and What Casino Games Actually Cost You What house edge means, how it differs from RTP and hold, why turnover matters more than your buy-in, and which casino games are cheapest and priciest to play.
7 min read4. DFS Pick'em Entries The per-leg hit rate an all-or-nothing DFS pick'em entry needs to break even, what a boosted pick really changes, and where the format is legally contested.
8 min read5. Bankroll Management How to set a bankroll, size a betting unit or poker buy-in, pick flat or percentage staking, and survive the losing runs a real edge still goes through.
6 min read6. The Kelly Criterion Explained (and Why Most People Use Half) What the Kelly criterion is, the formula for the optimal bet fraction, why full Kelly punishes hard, and how fractional Kelly trades growth for smaller swings.
6 min read7. Do Betting Systems Work? Martingale, D'Alembert and the Rest How the popular staking systems, Martingale, D'Alembert and Labouchere, work, why none of them changes the house edge, and what they do to your results.
7 min read8. Turn $1,000 Into $5,000? Here's What the Odds Actually Say The real odds of turning $1,000 into $5,000 gambling, computed from this site's own risk-of-ruin math, and why grinding it out in small bets makes them worse.

Read the price

Assumes nothing. Everything else on this page assumes this one, so it is where to start if you read only one of them.

Part 1, 6 min
Betting Odds Explained: Decimal, Fractional, American and Implied Probability How decimal, fractional and American odds work, how to read the implied probability behind any price, and how to spot a bookmaker's margin eating your value.

Work out what it is worth

Assumes a price. The same question asked of three different products: what a bookmaker's line is worth to you, what a casino game costs you to play, and what a DFS pick'em entry's multiplier is actually pricing.

Decide what to stake

Assumes an edge. How much to put behind a price you have judged good, how long a bankroll survives it, and why the staking systems sold as a shortcut are not one.

The 27 calculators these guides hand off to

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Numbers we found ourselves

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0 of 10price buckets where the mispricing was bigger than what it cost to reach it
Oct 2026 · 11 min read
The longshot gap, and the spread that swallows it The academic literature reports that prediction-market longshots are mispriced. We checked it on 12,755 settled Kalshi contracts, priced a day before they closed, and then did the part nobody had done: measured what reaching the mispricing would have cost at the same price, at the same moment, out of the same rows. In 10 price buckets out of 10, the cost was larger than the gap.
+1.35 pointsof the +1.38 points rise in Nevada's slot hold is the same machines getting more expensive, not players moving to worse ones
Sep 2026 · 12 min read
Hold is not the house edge Nevada publishes what its casinos actually keep, every month, and has since 2004. We read all 269 reports as one dataset. Two of the numbers in them look alike and measure different things, and almost everything people get wrong about this data starts there.
9.9cmedian two-way cost per dollar of payout across 78,119 quotable Kalshi markets
Sep 2026 · 9 min read
What a prediction market actually charges Prediction markets are sold on not charging vig. We snapshotted every quotable contract on Kalshi and priced the two-way cost the way a sportsbook's hold is priced. On 78,119 markets the median came to 9.9c per dollar of payout, against 4.8c at a standard sportsbook line. On the markets people actually trade, the answer flips.
4.2 timesmore per dollar staked at a title's lowest published setting than at its advertised one, at the median
Sep 2026 · 10 min read
The number on the box One of the two studios in our reference publishes five return settings for almost every game it ships. The other publishes one number. The numbers themselves look identical, and that is the problem.
4.80%how often the tightest spread middle landed over 26 seasons, against the 4.76% it has to clear to break even
Sep 2026 · 12 min read
The number the market hung How often an NFL middle actually landed, measured against the closing price that created it, across 6,719 regular-season games.
125 of 180scenarios in which the median attempt, not the unlucky one, lost the entire deposit
Sep 2026 · 11 min read
The mean is not the outcome What actually happens when you try to clear a casino bonus, 10.8 million simulated attempts at six wagering requirements published by US-regulated casinos.

Guides to the maths behind the bet

The reading path: 8 guides, in order

Read the price

Work out what it is worth

Decide what to stake

The 27 calculators these guides hand off to

Numbers we found ourselves

The maths is the easy half. Putting a number on it is the point.

All tools

Original research

Slot RTP reference