Why a strategy card is computable at all
In Let It Ride the three bets pay on the same final hand and pay independently, so a bet should ride exactly when its own expectation is positive at the moment of the decision. There is no judgement in it. Sweep the 22,100 three-card hands, take the mean payout over the 1,176 boards that could follow each one, and the set of hands you keep money on falls out.
That set has 1,608 hands in it, which is 7.28% of the deal. The rest of the time correct play takes the money back, in a game named for doing the opposite.
Where the published wording is wrong
The rule every guide prints is "let it ride on a paying hand, three to a royal, or three to a straight flush". The first two are exact. The third is not, and the failure is not marginal.
| Three-card holding | Ride | Pull back |
|---|---|---|
| paying pair | 1,440 | 0 |
| three of a kind | 52 | 0 |
| three to a royal | 4 | 0 |
| 3 straight flush, consecutive | 36 | 4 |
| 3 straight flush, one gap | 40 | 40 |
| 3 straight flush, two gaps | 36 | 72 |
| three suited, no straight | 0 | 912 |
| low pair | 0 | 2,304 |
| nothing | 0 | 17,160 |
Three of those categories sit on both sides. A one-gap three-card straight flush splits 40 to 40, which is to say the plain rule is right about half the time on that holding. Told this way, "three to a straight flush" is not a strategy, it is a coin flip with a justification attached.
The rule that is complete
Adding one axis fixes it: how many of the three cards are ten or above. That resolves every bucket but one.
| Straight flush shape | Cards ten or above | Decision |
|---|---|---|
| Consecutive, no gap | 0 | Ride, with one exception |
| Consecutive, no gap | 1 | Ride |
| Consecutive, no gap | 2 | Ride |
| Consecutive, no gap | 3 | Ride |
| One gap | 0 | Pull back |
| One gap | 1 | Ride |
| One gap | 2 | Ride |
| One gap | 3 | Ride |
| Two gaps | 0 | Pull back |
| Two gaps | 1 | Pull back |
| Two gaps | 2 | Ride |
| Two gaps | 3 | Ride |
And the single bucket it does not resolve contains exactly one rank set. Among consecutive three-card straight flushes with no high card, five of the six are ridden and one is not: 2-3-4 suited is the exception, and it is the only hand on either card that has to be memorised on its own.
So the complete opening decision, derived, is four lines:
- Ride any paying hand: a pair of tens or better, or three of a kind.
- Ride three to a royal.
- Ride a three-card straight flush if it is consecutive, or has one gap and a card ten or above, or has two gaps and two cards ten or above.
- Except 2-3-4 suited, which is a pull back. Everything else is a pull back too.
Mississippi Stud, where one button is decoration
Mississippi Stud offers 1x, 2x and 3x on every raise. On the opening decision, across all 1,326 two-card hands:
| Decision | Hands | Share |
|---|---|---|
| Raise 3x | 78 | 5.88% |
| Raise 2x | 0 | 0.00% |
| Raise 1x | 836 | 63.05% |
| Fold | 412 | 31.07% |
The 2x raise is optimal on none of them. That is not a quirk of this pay table; 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 wants the minimum. The middle option answers neither question, and a game offering three buttons is really offering two.
The other two results are as clean. The 3x raise is correct on exactly the 78 pocket pairs, and on nothing else. And no folded hand contains a card above a ten: holding a jack, queen, king or ace means playing on, every time. Between them the opening decision fits in three lines, for a game with a house edge near five per cent.
What this is worth, and what it is not
None of this makes these games good. Let It Ride costs 3.5057% of the initial bet and Mississippi Stud 4.9149% of the ante, against blackjack at 0.5153%. Perfect play in an expensive game is still expensive, and no strategy on this page moves a house edge to zero or anywhere near it.
What it is worth is the method. A published strategy card is a claim about a deck, and a claim about a deck can be checked. When we checked one, it was incomplete in a way that a reader following it would never detect, because losing a bet you should have pulled back looks exactly like ordinary bad luck.
How the incompleteness was found
Not by suspecting it. The first pass classified each three-card hand in the vocabulary the published cards use and then asked whether any category appeared on both sides of the decision, on the principle that a description you cannot state cleanly is a description that is wrong somewhere. Three categories did. The code prints that as a failure rather than a result, which is why it was noticed at all.
Every figure on this page comes from
let_it_ride_strategy.py and mississippi_math.py
at build time. Both sit on a five-card evaluator that is checked against
the exact hand frequencies before anything is computed, and both refuse to
publish a house edge outside the band published analyses occupy. The
figures are also in the open dataset under CC-BY.
Last computed August 2026.