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
House edge versus hold
Nevada's measured 12-month hold beside the computed edge of each bet: blackjack 11.91% against 0.51%, and why both are right.
Is the side bet always worse?
Almost everywhere, yes, by 1.6 to 13.6 times on the common tables. 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 0.17% 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. The usual one-line rule is incomplete; the complete one has two exceptions.
Every bet we compute, ranked
149 computed house edges in one table, sorted by what they cost, with the exact fraction beside each decimal where one exists and the open data behind it.
En prison is not la partage
La partage costs exactly 1/74. Single-imprisonment en prison costs 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 repeated. 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”, as the one-line rule prints it, is not a true statement of Let It Ride strategy. Classifying all 22,100 three-card hands in that rule's vocabulary, three categories fall on both sides of the decision. The one-gap holding splits 24 to 48, so the plain rule is wrong on two of every three such hands. The complete rule needs one more axis, the cards ten or above, and has two memorised exceptions, 2-3-4 and A-2-3 suited; the full card Wizard of Odds publishes says the same.
- 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 with single imprisonment, where a second zero loses the stake, costs exactly 19/1369. Almost every published source quotes both as 1.35%.
- Total 10 or 11 in sic bo is exactly a 7-to-1 shot. 27 of 216 ways, and 27 × 8 = 216, so a box paying 7 to 1 would be the one bet in the game with no house edge at all. The common tables pay 6 to 1, which costs 12.50%.
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.