Is Seven-Deuce Really Unplayable in Criss Cross Poker?

The Across decision is made with no community card showing, which makes it the one decision in Criss Cross Poker that can be solved outright. We solved it: every one of the 169 starting hands was evaluated against all 19,600 three-card combinations available to it from the remaining 50 cards. Nothing here is sampled, estimated or taken from another source. For 7-2 the solve returns the same instruction both ways, and it is not close enough to argue about.

You will see 7-2 recommended as a 1x opening bet. Our own computation disagrees, and it disagrees by a margin rather than by a rounding. The arithmetic is short enough to check in full.

Folding costs exactly one unit

Both antes are posted before you see a card. Folding the Across decision forfeits that line’s bet and its Ante Across, and since no bet has been made yet, what you give up is the ante alone. That is a fixed, exact −1.000000 unit. It is the number every other action has to beat, and it never moves.

Betting is priced as anteEV + lineEV at 1x, because the ante now has a chance to be paid and the Across bet is settled against the pay table. Both parts are negative with 7-2, and together they are worse than simply handing back the ante.

Read the last column and the decision is made for you. Playing 7-2 suited for the minimum buys you a worse outcome than folding by about three hundredths of a unit per hand, and playing it offsuit costs about twelve hundredths. At a $10 ante that is roughly 30 cents and $1.22 of pure waste every time you take the hand on, which does not sound like much until you notice it is a choice you never had to make.

What raising would cost

There is no case for 3x either, and the reason is worth holding on to for the rest of the page. You raise to the maximum only when the line EV itself is positive, because then every extra unit you put out is worth having. With 7-2 suited the line EV is −0.442398 and with 7-2 offsuit it is −0.518163. Each additional unit staked simply subtracts that amount again. Only fourteen starting hands in the whole game carry a positive Across bet: the thirteen pocket pairs and Q-J suited.

Both hole cards must be used in Criss Cross Poker. Your Across hand is your two cards plus the three cards of the horizontal row, so every hand you can make has to contain the seven and the deuce. Ask which five-card straights contain both and the answer is none. There is no such straight in the deck. Our engine, which counts categories rather than assuming them, measures the straight frequency of 7-2 at 0.0000%.

That is not a small penalty applied to a weak hand. It is the difference between folding and playing, and the cleanest way to see it is to compare 7-2 with the hand one rank across.

7-3 suited beats folding by 0.000765 of a unit. That is less than a thousandth, which is about as thin as a decision gets, and it is still on the right side of the line. It sits there for exactly one reason: 3-4-5-6-7 is a straight, so a 7-3 lands one on 0.3214% of boards and gets paid 5 to 1 for it. Take that away and the hand goes under.

Taking it away is precisely what the deuce does. Every straight that contains a seven and every straight that contains a deuce is listed below, and the two lists never meet.

Nothing appears on both lists. A seven bottoms out at 3-4-5-6-7 and a deuce tops out at 2-3-4-5-6, so the two ranks are one step too far apart to share a run. Five cards span five consecutive ranks, and a seven and a deuce span six.

This is the part the popular framing gets right and then walks past. It is common to see the missing straight named as seven-deuce’s main structural weakness and then to see the hand opened for 1x anyway. Both halves cannot stand. The missing straight is not a colourful detail about a bad hand. It is the exact quantity that drops the hand under the fold line, and the 7-3 comparison prices it: a straight route worth 0.3214% of boards is the difference between a hand that clears folding and a hand that does not.

Why the straight matters more than it looks

A straight pays 5 to 1 on the Across bet, which is the fourth-best row on the pay table and by far the most reachable of the big ones. A hand like 7-2 is never going to win by making a full house. What a low unpaired hand needs is a cheap route to a paying category, and for connected low cards that route is the straight. Deleting it does not leave the hand slightly weaker. It leaves the hand with the flush as its only real upside, and a flush needs three cards of your suit to land in one row.

Line the seven-x hands up in order and the boundary is easy to see. Suitedness carries 7-6, 7-5, 7-4 and 7-3 across the fold line without difficulty. It fails to carry 7-2, because 7-2 is the only one of the five with no straight behind it at all.

Both lists are engine-confirmed against the same exhaustive solve. Read them side by side and the pattern is not about high cards or about suits on their own. It is about reach. 7-6, 7-5, 7-4 and 7-3 all sit inside at least one straight, and their suited versions are all playable. 7-2 sits inside none, and its suited version is the single suited seven in the deck that the solve throws away.

Offsuit, the boundary lands one rank higher. 7-6 offsuit still plays, and 7-5, 7-4, 7-3 and 7-2 offsuit all fold, because losing the flush route costs roughly as much as one step of straight reach. That is why 7-3 has a split verdict, playable suited and a fold offsuit, while 7-2 folds either way.

The fold rule, stated exactly

You will often see the simplified version: fold only unpaired, unsuited hands with nothing above a five. That rule does not fold 7-2, and it does not match our solve, which folds 42 starting hands and was checked against all 169 with zero mismatches. The rule that is exactly right runs the other way round:

It is worth being precise about what you are holding, because the two cards do different jobs and neither job is winning. Criss Cross Poker has no dealer hand and no qualifying requirement, so your hand is settled against a fixed pay table. What matters is which row you land on, and a bare seven or a bare deuce lands below every paying row.

Put those together and the picture is bleak in a specific way. The best cheap outcome available to 7-2 is a push, and it needs the seven to pair for it. Everything that actually pays has to come from three community cards doing the work, and the deuce contributes to none of the routes that a low unpaired hand normally relies on.

The high-pair row, jacks through aces, is not reachable at all: neither of your cards can pair into it. So 7-2 is playing for two pair or better on a hand where the single most accessible route to that, the straight, has been removed by the rank gap. The complete pay tables

Sharing a suit is the one genuine improvement available to seven-deuce, and it should not be waved away. Unlike a pocket pair, which cannot make a flush at all because its two cards sit in different suits, a suited 7-2 has a live route to the 8 to 1 row. Our engine measures the flush frequency of 72s at 0.8418%. That is a real number attached to a real payout, and it is the entire reason the suited version is worth more than the offsuit version.

On the Across bet itself the flush route is worth about 0.076 per unit, with a little more coming from the ante. It is a meaningful edge and it is not noise. It is also aimed at the wrong target. Suited 7-2 has to close a gap of 0.029643 against folding, and it starts from an offsuit version that is 0.122245 adrift. Roughly three quarters of the deficit is removed by the matching suit, and the remaining quarter is exactly what makes this a fold rather than a 1x.

Compare that with what one rank of straight reach is worth. 7-3 suited is the same hand with the same flush route and it clears folding, at a margin of 0.000765. The flush route alone does not get 7-2 there. It needs the straight it cannot have.

The flush frequency is also worth keeping in proportion. At 0.8418% it arrives on fewer than one board in a hundred, and it needs all three cards of a row to match your suit, since both hole cards must be used. Two cards of your suit in a row is scenery. That is why a route paying 8 to 1 still amounts to less than a tenth of a unit once you weight it by how rarely it lands.

Seven-deuce arrives at the Criss Cross Poker table carrying a reputation, and the honest answer is that the reputation happens to be right for reasons that do not apply here. It is worth separating the two, because a habit imported from the wrong game will be right about 7-2 and wrong about the next hand.

So the common line that 7-2’s Hold’em reputation does not carry over is half right, and the half it gets wrong is the interesting one. The reason does not carry over at all. The verdict happens to agree exactly. It is the worst starting hand in both games, arrived at by two completely unrelated routes: relative weakness against other players in one, and a structural hole in the pay-table routes in the other.

The clearest way to keep the two apart is to remember what you are actually being paid for. In a game with opponents you are paid for being ahead of them. In Criss Cross Poker you are paid for landing on a row. Two pair pays 2 to 1 whether every other seat folds or every other seat makes quads, and a hand that cannot reach the rows is worth exactly what it is worth on its own. The hand ranking ladder

Folding the Across bet does not end the hand. The Down decision and the optional Middle decision are still in front of you, and they are made with community cards showing rather than blind. For 7-2 that makes them largely moot, since the correct Across action is a fold and the correct Down action with the same two cards and no help on the board is the same one. The guidance below is for the two cases where it still matters: a table where you played the hand anyway, and a neighbouring hand such as 7-3 suited that is genuinely live.

• The Down decision is the same question with more information. By then the left and right cards of the Across row are face up, so you know four of the seven cards in play. The Down bet has its own ante, so folding it forfeits that ante the same way. Bet it when the vertical cards have given you something, and treat a bare 7-2 with no improvement in sight the way you treated it at the Across decision.
• Passing the Middle bet forfeits nothing. The Middle carries no ante of its own, so declining it costs you zero rather than one unit. That makes it the easiest of the three decisions: there is no fold penalty to weigh, so you make it only when the better of your two lines is genuinely worth backing. Fold both the Across and the Down and the Middle is not offered at all, and only the Five Card Bonus can still be paid.
• 2x is never uniquely optimal. Expected value is linear in the stake: betting N units returns N times the per-unit figure. So the best stake is always at one end of the range. If the per-unit value is positive you want the maximum, and if it is negative you want the minimum or a fold. A middle size is only ever tied with something at the edge, never better than both.
• The commitment if you had played it. At a $10 table, opening 7-2 for 1x puts $30 on the felt: the $10 Ante Across, the $10 Ante Down and the $10 Across bet. Two of those three chips were posted before you saw a card and were never yours to withhold. The third is the one this page is about, and the whole of the argument is that it should stay in your stack.

None of this makes the game beatable. The overall house edge is 4.33% on the ante, or 1.48% as element of risk, and both antes are posted on every hand, so you cannot sit and wait for a good starting hand. Maximum exposure in a single hand is 11 units, which is $110 at a $10 ante. Folding 7-2 does not turn a losing game into a winning one. It removes an avoidable leak from a game that already has an edge built into it. The full order of play