Ace-Low Starting Hands in Criss Cross Poker

The Across bet is the first of the three betting decisions, and it is the only one you make with no community card showing. That makes it the one decision in Criss Cross Poker that can be solved outright, and we have solved it: every one of the 169 starting hands was evaluated against all 19,600 three-card boards available to it. For an ace with a low kicker the answer never moves off the minimum.

Only fourteen starting hands are raised to 3x: the thirteen pocket pairs and Q-J suited. Everything between the folds and the raises is a 1x, and A-2 lives there with about a hundred other hands. The full grid is on the printable strategy chart.

What you have committed at that point

At a $10 table the Across decision leaves $30 on the felt: the $10 Ante Across, the $10 Ante Down and the $10 Across bet. Both antes are posted before you see a card, so two of those three chips were never yours to withhold. The Down bet and the optional Middle bet are later decisions, made with community cards showing, and they are not part of the opening commitment.

Hold and you have no made hand. An unpaired ace is a high card, and a high card is paid nothing on any of the three lines. What you have is two ways to improve, and they are not worth the same.

• Pair the ace and you are paid. A pair of aces is a high pair, so the Across, Down and Middle bets pay 1 to 1 and each ante pays 1 to 1 as well. This is the outcome the hand is played for.
• Pair the deuce and you lose. A pair of deuces sits below the push band, so the line bet loses and the ante loses with it. Improving your hand and losing your money are the same event here.

That second row is the one people underrate. In most poker games any pair is progress. On this pay table a pair of deuces is a dead hand that has cost you a bet, and half of your starting cards can only ever make one.

Two pair counts, and aces and deuces is two pair. A paired deuce is only dead while the ace stays unpaired.

Everything above 1 to 1 needs the board to do the work. A flush needs three more cards of your suit in one direction, which is only available to you if the two hole cards are suited, and a straight needs the board to bring exactly the three ranks that fill it. Those outcomes are real, and section 3 prices how little they add. The complete pay tables

The usual case for A-2 is that the deuce is connected: A-2-3-4-5 is a straight, and A-7 can never make one at all. That is true and it is the wrong emphasis. We evaluated every suited ace-x hand against all 19,600 three-card boards, and the results sort into four tiers. The tier is set by what happens when the kicker pairs, not by straight potential.

Read the table down the middle two columns and the point is unavoidable. A-7 has no straight available to it and beats A-2, which has one. The tiers track the last column, not the second: the hands whose kicker pairs into a winner are at the top, the hands whose kicker pairs into a push are in the middle, and the four hands whose kicker pairs into a loser are at the bottom on their own.

Both of the smaller figures come straight out of the same table. The straight route is worth about 0.044 per unit, which is the gap between A-10, with one straight and a kicker that pushes, and A-9, with no straight and a kicker that pushes. Being a dead card when it pairs costs about 0.143 per unit, which is the push-versus-lose penalty once that straight bonus has been accounted for. The straight is genuine, and it is roughly a third the size of the penalty it is being asked to offset.

How often the wheel actually arrives

A straight is possible with A-2, which is more than a pocket pair can say. The board has to bring exactly 3-4-5 in one direction, and it does that on 0.32% of boards. Three hands in a thousand.

Offsuit the picture is worse in the same shape. A-2 offsuit returns −0.376122 per unit on the Across bet, against −0.273265 for A-7 offsuit and −0.131224 for A-K offsuit. The ante is negative throughout as well: −0.458367 holding A-2 suited and −0.475102 holding A-2 offsuit, because the bare ace does not qualify and the paired deuce does not either.

The conclusion, without softening it: A-2 is in the bottom tier of ace hands. It is the worst kind of ace you can be dealt, its wheel draw does not rescue it, and it is behind a hand that cannot make a straight at all. You still play it, because 1x beats folding, but you play it knowing what it is.

After the Across bet the dealer turns the left and right cards of the horizontal row and leaves the centre face down. The Down bet is then made on the vertical column. Your two hole cards play in both directions, so those two exposed cards do not belong to the column, but they have already removed two ranks from the deck and they may have hit your hand.

The practical version is short. Your hole cards have not changed and the column is still three unknown cards, so the same reasoning that made the Across bet a 1x makes the Down bet a 1x. What the reveal changes is what you now know about the row you have already backed, and that matters most at the Middle decision, where a single unknown card settles both hands at once.

The Middle bet is offered once the left, right, top and bottom cards are all face up. It carries no ante of its own, so passing forfeits nothing you have already committed, and it is graded on the better of your two hands. The whole decision is about one card: the centre, which belongs to the row and the column at the same time.

At that point you have seen six cards, your two hole cards and four community cards, so 46 cards could be the centre. Every one of them falls into one of four groups. Look at what is already on the felt and count them.

• Premium

  Cards that finish a straight, a flush, three of a kind or a full house in either direction. Holding A-2 suited with both exposed cards of one line in your suit, the nine remaining cards of that suit are all in this group. With 3, 4 or 5 showing twice in one line, the four cards of the missing rank fill the wheel. So is any card that gives you two pair or better.

  Back it, up to 3x
• Pairs the ace

  Three aces are unaccounted for at the start of the hand. Subtract any that are already face up. Each one that is left makes a pair of aces in both directions at once, which is 1 to 1 on the Middle bet and turns both antes into winners.

  Back it
• Pushes

  Cards that pair a six, seven, eight, nine or ten already on the board and give you nothing better. A low pair returns the stake on the Middle bet, so these cards are neither an argument for the bet nor against it. Count them and set them aside.

  Neutral
• Loses

  A deuce, which pairs your dead card and gives you nothing better. A card that pairs a five or lower already on the board. And every blank that leaves your best hand as ace-high. With an unimproved ace-low holding this is usually the biggest group by a distance.

  Reason to pass

Two rules survive the counting. If you have raised to 3x on an earlier decision because the hand warranted it, do not then fold the Middle: the same hand strength that justified the raise applies to a bet graded on the better of your two lines. And if both the Across and the Down bets were folded, the Middle is not offered at all. How the Middle bet is graded

Every one of these wagers pays the same multiple of whatever you stake on it. A straight returns 5 to 1 on one unit and 5 to 1 on three units. That single fact settles the sizing question before you look at a card, because it means the expected value of the bet moves in a straight line with the amount you put out.

Sizing is a yes or no question, not a dial. Decide whether the bet is worth making, then make it at the size that answer implies.

This is why the whole strategy for this game reduces to so few instructions. You are never asked how much to bet, only whether to bet. With A-2 the answer at the Across decision is always the minimum, because the hand runs at a loss of 0.295969 per unit suited and 0.376122 offsuit. Those are negative, so you keep the stake small; they are not negative enough to beat giving up the ante, so you do not fold. The printable chart resolves every other starting hand the same way.

1. 1

   Treating the ace as a made hand

   An unpaired ace is a high card and nothing more. It pays nothing on its own. The hand has to reach a pair of jacks or better before the pay table has any interest in it, and an ace sitting alone in your hand does not get you there.

2. 2

   Valuing an ace pair and a deuce pair the same

   They are not close. A pair of aces pays 1 to 1. A pair of deuces loses outright, because the pay table only starts returning money at a pair of sixes. Half of this starting hand can improve into a winner and half of it cannot, and that asymmetry is the single most important thing about A-2.

3. 3

   Betting off what other players do

   This is a house-banked game. Every wager is settled against a fixed pay table, there is no dealer hand to beat and no opponent to pressure. What the player beside you does with their chips cannot change what yours are paid. Read the board, not the table.

4. 4

   Using a fixed percentage after the reveal

   Once four community cards are face up, the hand is a counting problem, not a statistical one. Exactly one card is unknown and there are 46 candidates for it. Count how many of those finish you a winner, how many push and how many leave you short. A number memorised for "A-2 generally" cannot tell you that.

5. 5

   Maxing out on any pair at all

   Pairing the ace is worth pressing. Pairing the deuce is worth nothing by itself, and a board that pairs your deuce has handed you a losing hand that still needs rescuing. Check which card actually paired, and check both lines, before the stake goes up.

Every one of these comes back to the same thing: an ace with a low kicker is two very different cards pretending to be a strong hand. Play it for the ace and treat the deuce as a card that mostly needs to stay out of the way. The low-card guide covers what happens when there is no ace at all, and unpaired high cards covers the hands where both cards can pair into a winner.