Low-Card Starting Hands in Criss Cross Poker

This page covers one narrow group of starting hands: unpaired holdings made of two cards from two through five. That is 2-3, 2-4, 2-5, 3-4, 3-5 and 4-5, in every suit combination. There are only six rank pairings in the whole category, and our exhaustive calculation folds all twelve of the suited and offsuit versions on the Across decision.

Pocket pairs are a completely separate category and nothing on this page applies to them. A pair of deuces is not a low unpaired hand; it is a pocket pair, and pocket pairs are raised to the maximum. That looks like a contradiction, so section 6 works through why.

The suited row and the offsuit row give the same instruction. They do not give the same number, and section 3 shows the gap.

The reason is the pay table rather than anything about the cards themselves. On the Across, Down and Middle bets a pair of jacks or better pays, a pair of sixes through tens pushes, and anything below that loses. Two unpaired low cards start with nothing, and the best thing that can happen to them cheaply, pairing one of them, still makes a losing hand. Everything they can profitably become sits further up the ranking ladder, and the board does not get there often enough.

The method

Each of these hands was evaluated with this site’s own engine against all 19,600 three-card combinations that can be dealt from the 50 cards left in the deck. Nothing is sampled and nothing is estimated. That gives an exact expected value for the Across ante and an exact expected value for the Across bet, per unit staked.

The comparison

Folding forfeits the Across ante, so it is worth exactly −1.000000 units. It is a fixed, known cost. Playing on at the minimum stakes one more unit on the line, so its value is anteEV + lineEV. If that total is worse than −1.000000, folding is the better of the two, and the difference between them is the price of playing on.

Read the last column and the case is closed. Every row is worse than folding, suited rows included, and the smallest margin in the table is 0.152908 units. The worst case, an offsuit 3-2, costs 0.314898 units more than simply letting the Across ante go. Add the ante EV to the line EV in any row and you will land on the total in the fourth column; subtract 1.000000 from that total and you have the fifth.

Six rank pairings, twelve hands, twelve folds. The three ranks in each row share a figure because they share a straight count and a gap size.

Notice how orderly the table is. The ranks themselves barely matter: what moves the number is how many straights the two cards can appear in and whether they are suited. 5-3 and 4-3 are identical to six decimal places, and so are 5-2, 4-2 and 3-2, because in this range the engine is pricing the same shape twice. The one hand that comes closest to a bet, 5-4 suited, is the connector in this group with the most straights available and the flush still live, and it is still 0.152908 units short.

It is worth being precise here, because suitedness matters more for these hands than it does for a pocket pair. A pocket pair holds two different suits by definition, so it can never make a flush at all. Two suited low cards genuinely can: they can reach a flush, and they can reach a straight, and either one would be paid. That extra upside is real and the engine prices it.

Suitedness is worth roughly 0.085 to 0.093 units for these holdings, just under a tenth of a unit. You can see it in section 2 by reading a suited row against its offsuit twin: 5-4 improves from a line EV of −0.562245 to −0.468929, and 3-2 improves from −0.601429 to −0.516888. Real money, on every board where the flush or the straight lands.

Now put that beside what it has to overcome. The suited hands trail folding by 0.152908 to 0.213724 units. Being suited is not a bonus applied on top of a break-even hand; it is a discount applied to a hand that is already losing by more than the discount is worth. Give 3-2 offsuit its flush equity and it moves from 0.314898 behind folding to 0.213724 behind folding. It is still behind. That is the whole argument, and it is the reason this page treats the suited and offsuit versions the same way even though it does not pretend they are the same hand.

A flush draw improves a losing hand. It does not turn one into a bet.

Plenty of players carry a habit from other games: pair either hole card and you have something. In Criss Cross Poker that reasoning breaks down completely for this category, because of where the pay table splits. On the Across, Down and Middle bets a pair of jacks or better pays 1 to 1, a pair of sixes through tens pushes, and a pair of fives or lower loses outright. Pairing a two, three, four or five makes a pair below sixes, which is the losing band. The board hit you and you still lose the bet.

Worked example: 3-5

Say you hold and the three horizontal community cards bring another five. In a lot of games that is a result. Here it makes a pair of fives, which sits in the losing band, so the Across bet loses and the Across ante loses with it. The same is true of catching another three. Both of the obvious ways to improve this hand land on a payout of nothing.

So the hand has to travel further than a pair before any of it is worth anything. Every one of these is available to two low cards, and every one of them needs the board to do more than brush you:

• Two pair, which needs the board to pair both of your cards or to pair one of them alongside a pair of its own.
• Three of a kind, which needs two board cards to match the same hole card.
• A straight, which is genuinely available down here: the wheel, A-2-3-4-5, and the runs just above it.
• A flush, but only if your two cards are suited, and only if all three board cards in that line share the suit.
• A full house or four of a kind, which are the rare ends of the same pairing route.

Two pair is the first result on this list that pays anything at all. A pair of fives is not a small win; it is a loss.

That is the whole reason these hands price out the way they do in section 2. It is not that low cards rarely connect with the board. It is that the most common way they connect, pairing one hole card, is worth nothing here, so all of the value has to come from the outcomes further up the ladder, and those are not frequent enough to pay for the bet. The split that causes it is set out in full on the pay tables, and the ladder itself is on hand rankings

Folding here means folding the Across bet. You make no Across bet at all, and you forfeit the Across ante, which at a $10 table is $10. That is the entire cost, it is fixed, and you know it before you decide. What it is not is the end of the round. You still have your two hole cards, you still see the community cards, and the Down decision is still in front of you, followed by the Middle decision. The order of play is set out on how to play.

Those dollar figures are the per-unit numbers from section 2 multiplied by a $10 unit, nothing more. Folding is not free and this page is not claiming it is. It is simply the cheapest of the choices you are offered, by between $1.53 and $3.15 a hand.

About the figure that circulates

A figure of $30.75 expected loss per hand gets quoted for this category, and it is worth saying what it does and does not describe. It treats the suited and offsuit versions as one group, and section 3 has just shown that they do not behave the same way: at a $10 ante playing on with a suited 5-4 costs $11.53 on average while playing on with an offsuit 3-2 costs $13.15. It also prices the hand as though it is played on rather than folded, which is not the recommendation on this page.

We can give you the Across decision exactly, and that is what the table above is. We have not solved the full three-decision game for these hands, because the Down and Middle choices depend on community cards you have not seen when the Across decision is made, and their value moves with what those cards are. So there is no single fixed total for the whole round to offer you here, and we are not going to invent one. What we will say is the part we computed: fold the Across bet and the cost is exactly one ante, $10 at a $10 table, and every alternative on the table costs more.

This is the part that looks like a contradiction, so it is worth doing slowly. Hold and the pair you start with is a pair of fives, which is in the losing band of the pay table, exactly like the pair of fives you would make by pairing a hole card in section 4. And yet the correct Across decision is to raise 3x.

The ante is a bad bet on this holding and there is nothing to be done about it: at −0.436735 per unit it is already posted before you see a card. The line bet is the part you control, and it returns +0.143673 per unit. That is positive, so each extra unit you are allowed to put on it adds 0.143673 to the hand, and you want all three of them. Fold and you take −1.000000; bet 1x and you take −0.293062; bet 3x and you take −0.005716, which is close enough to break even to make this one of the best Across decisions in the whole game.

The ante is fixed and bad. The line bet is chosen and good. Maximising the good one is the whole decision.

Why the line bet is positive when the pair loses

Because the pair is a floor, not a forecast. Across all 19,600 boards a line finishes as just the pair 71.8367% of the time, and on those boards the low pair loses. But the other 28.1633% of boards convert it into something that pays: two pair on 16.1633%, three of a kind on 10.7755%, a full house on 0.9796% and four of a kind on 0.2449%. Three of a kind pays 3 to 1, a full house 12 to 1 and quads 40 to 1. A start that is already halfway to trips, on a bet where trips and better pay multiples, is worth backing even though the starting hand itself is a loser.

Note what is not on that list. A pocket pair can never make a straight or a flush in this game: two cards of the same rank leave at most four distinct ranks in five cards, and a straight needs five, while two cards of different suits leave at most four cards of any one suit, and a flush needs five. That is the one place where an unpaired suited low hand is genuinely ahead of a pocket pair, and section 3 is where it still does not save it.

Every pocket pair in the game is a 3x on the Across bet, for the same reason, all the way up. Where the pairs differ is how far above break even they land. See medium pocket pairs, 6-6 to 10-10 high pocket pairs, J-J and better