Research
What computing the mathematics turns up that copying it does not. Every finding here shows its derivation, so you can check the claim rather than trust it.
Findings
Is the side bet always worse?
Almost everywhere, yes, by two to thirteen times. Two exceptions: one side bet is cheaper than its own game, and one costs exactly nothing.
The jackpot line pays for the sign
Across four pay tables we price, the biggest number on the felt supplies between 0.20% and 14.94% of what the bet returns.
Two strategy cards, derived
The Let It Ride and Mississippi Stud opening decisions computed from the deck. One published rule is incomplete, and one exception is a single hand.
Every bet we compute, ranked
128 computed house edges in one table, sorted by what they cost, with the exact fraction beside each decimal and the open data behind it.
En prison is not 1.35%
La partage costs exactly 1/74. En prison costs exactly 19/1369. Almost every published source quotes both as the same number. The derivation takes two lines.
Open data
Every house edge this site computes is published as edges.json and edges.csv: exact fractions, the deriving page for each figure, CC-BY. Reuse it; link the page the number comes from. The methodology page explains what is derived, what is attributed, and what we refuse to guess at.
What has actually been found here
Three of these are corrections to figures or rules that are widely published. That is the point of doing the arithmetic rather than repeating it: most gambling reference material is copied from other gambling reference material, and errors propagate because nobody recomputes.
- “Three to a straight flush” is not a true statement of Let It Ride strategy. Classifying all 22,100 three-card hands in the vocabulary the published cards use, three categories fall on both sides of the decision. The one-gap holding splits 40 to 40, so the plain rule is right about half the time on it. The complete rule needs one more axis and has exactly one memorised exception, 2-3-4 suited.
- Mississippi Stud offers a button that is never the right answer. The 2x raise is optimal on none of the 1,326 starting hands. It follows from the structure: the pay table multiplies the total staked, so a positive expectation wants the maximum on the table and a negative one the minimum, and the middle option answers neither question.
- En prison and la partage are not the same number. La partage costs exactly 1/74. En prison costs exactly 19/1369. Almost every published source quotes both as 1.35%.
- A sic bo box that pays 7 to 1 on Total 10 or 11 has a house edge of exactly zero. 27 of 216 ways, and 27 × 8 = 216. It is the only true even-money proposition in the game, and it is rare enough that most tables do not offer that pay table.
How to check any of it
Every figure on this site is produced by a program that verifies itself before it writes anything. The five-card engine has to reproduce the exact hand frequencies every poker text prints, all nine categories, or the build stops. Each solved game has to land inside the band published analyses occupy, or the result is refused rather than published.
Those checks are not decoration. The first Let It Ride solve returned 1.1686% and the band rejected it: the total loss was right, but divided by three bets instead of by the one initial bet the published figure uses. That error is now written into the page it affected, because a site that hides its corrections is asking to be trusted rather than checked.
If you think a number here is wrong, that is the most useful message this site can receive. Every value can be recomputed. Say which bet and which figure, and if you are right the correction goes into the engine rather than quietly into the page.