How to Play Ace-Seven 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 seven the answer never moves off the minimum, whatever the suits do.

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-7 lives there with about a hundred other hands. Being in that band is not a comment on how strong A-7 is. It is a comment on the fact that 1x is the only stake that beats folding without being worth more than folding costs.

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.

Start with the finding, because everything else on this page follows from it. A-7 suited prices at -0.197500 per unit on the Across bet. A-2 suited prices at -0.295969. The gap is 0.098469 per unit in favour of A-7, and A-2 is the hand with the straight draw. A-7’s straight frequency is not small. It is zero. Our engine enumerated all 19,600 three-card boards for the hand and returned exactly 0.0000%.

The push protection from a seven outvalues the straight route from a deuce. That is the whole result in one line, and it is worth sitting with, because it inverts the instinct that a hand with a draw must be ahead of a hand without one.

Why the straight frequency is exactly zero

This is structural, not a quirk of the sample. No five-card straight contains both an ace and a seven. The ace only ever appears in two straights in a standard deck, A-2-3-4-5 at the bottom and 10-J-Q-K-A at the top, and neither of them holds a seven. Since both hole cards must play in Criss Cross Poker, there is no board at all, on any row, that can put your ace and your seven inside the same straight.

Why the seven wins the comparison anyway

Look at what happens when the small card pairs, which is the outcome that actually arrives often. A pair of sevens is a low pair, and on this pay table a low pair pushes: the line bet is returned and the ante is returned. A pair of deuces is below the push band, so the line bet loses and the ante loses with it. Same event, an unremarkable board that pairs your small card, and two completely different settlements.

• Pair the seven and you get your money back. A pair of sixes through tens pushes on the Across, Down and Middle bets and pushes on the ante. Nothing is won, but nothing is lost, and that floor is what A-7 is buying.
• Pair the deuce and you lose. A pair of deuces sits under the floor. The hand improved and the money still went, on the line bet and on the ante both.

Now weigh the two effects against each other. The wheel arrives for A-2 suited on 0.3214% of boards, which is roughly one board in 311, and it pays 5 to 1 when it lands. Pairing the small card happens on a large share of boards by comparison, and it decides between getting your stake back and losing it every single time. A rare 5 to 1 cannot outrun a common push-versus-loss swing. That is the arithmetic behind the 0.098469.

The two hands are otherwise close to identical. Suited, they make a flush at almost the same rate, 0.8418% for A-7 against 0.8367% for A-2, because a flush only cares about suits. Both are 1x opens. Both hold the same ace. Strip out the flush and the ace and what is left is the seven against the deuce, and the seven is the better card because the pay table has a floor and the seven stands on it.

Once you know the Across-bet figure for one ace hand you very nearly know it for all of them, because the ranks in between do not matter. What matters is two things: whether the kicker pairs into a win, a push or a loss, and whether the two cards can sit in a straight together. That produces four tiers, and A-7 is in the third.

A-7 has no special standing inside its tier

A-9, A-8, A-7 and A-6 are identical to six decimal places. Not close, not approximately equal. The same number, -0.197500, for all four. If you have been treating A-9 as a clearly better hand than A-6 because the kicker is three ranks higher, the solve says the distinction does not exist on the Across bet. All four kickers pair into a push, and none of the four can appear in a straight with an ace, so there is nothing left for the rank to change.

Being precise about A-10

A-10 is often described as having limited straight interaction, which is vague enough to be misleading. Be exact instead: A-10 sits in exactly one straight, 10-J-Q-K-A, at a frequency of 0.3214%. That single straight is why it prices at -0.153112 and stays ahead of A-9 through A-6. It is the same 0.3214% that A-2 gets from the wheel, arriving at the same rate, and here it is enough to lift the hand because A-10’s kicker still pushes when it pairs. The straight is a bonus on top of the push floor rather than a replacement for it.

Tier 1 is the only place an ace hand comes close to break-even, and it gets there for a different reason again: a pair of aces, kings, queens or jacks is a high pair, so both cards pair into a paid hand. Nothing below the jack does that. The jack-to-ace hands in full

Hold and you have no made hand yet. What you have is two cards with separate jobs, and the mistake to avoid is expecting the same thing from both of them.

• 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 seven and you push. A pair of sevens is a low pair. The line bet comes back and the ante comes back. You are level on that row, not ahead. The seven is defensive and it is never profitable on its own.

That is the honest description of a seven in this game. It is insurance, not a source of profit, and the insurance is real: three of the four sevens are still in the deck, and any one of them landing on your row turns a losing row into a returned bet. Three of the four aces are still there too, and those are the ones that actually pay. Six cards can pair you. Three of them win money and three of them save it.

Two rows in that table are closed to A-7 in a way that is worth naming. The straight row is closed permanently, on every board, because no five-card straight holds both an ace and a seven. The 1 to 1 pair row is closed to your seven, because a pair of sevens is a low pair and lands on the push line instead. Everything the hand is worth comes from the ace, from pairing the board rather than your own cards, or from the flush when you are suited.

What an exposed ace means, and what an exposed seven means

Both antes are already posted, so by the time community cards appear you are reading, not deciding whether to be in the hand. The two ranks tell you very different things.

The Across bet is made blind, on your two hole cards alone. Once it is down, the dealer turns over the left and right cards of the horizontal row and leaves the centre card face down. That is the first information you get in the hand, and it arrives after the money it grades is already committed. Reading it well is not about the Across bet at all. It is about the Down decision that comes next.

There is one row that will never appear on that table. No reveal can put A-7 on a straight draw, because no five-card straight contains both an ace and a seven. The ace reaches only A-2-3-4-5 or 10-J-Q-K-A, and neither of them holds a seven. A-7’s straight frequency is exactly 0.0000%. Two connected cards in the middle of the row look encouraging and are worth nothing to you.

That is why the Down bet is a fresh decision rather than a follow-up. All three cards of the column are still face down when you make it, exactly as all three cards of the row were face down when you made the Across bet. You are answering the same question with the same two hole cards, with two more cards known to be gone. Nothing in the reveal can turn A-7 into a hand with a positive line, so the answer stays the same: back the column for the minimum, and do not fold it.

The one thing worth genuinely tracking is removal. If both an ace and a seven appear on the reveal, your best two outcomes in the column have each lost a third of their outs before you commit a chip. That does not change a 1x into a fold, since A-7 is nowhere near the fold line, but it is the difference between a column you would like to see and one you are simply obliged to pay for. The full order of play

A-7 has no straight in it, suited or not. That leaves pairing and one other route, and only the suited version has the other one. Both of your hole cards are always part of the five-card hand, so a flush needs your two cards plus three matching community cards on one row. Three of the three. The row has no spare seat for a card of another suit.

Sharing a suit is worth 0.075765 per unit on the Across bet, from the exhaustive solve over all 19,600 three-card line combinations. The ante improves slightly as well. That is a real edge and it is not rounding noise, which is why offsuit A-7 is the weaker of the two hands by a clear margin even though the two versions look almost identical on the felt.

There is a useful cross-check here. Suited A-2 has a flush frequency of 0.8367%, which is a hair under the 0.8418% of suited A-7. The two hands have effectively the same flush route. So none of the 0.098469 that separates them comes from flushes, and none of it comes from straights, since A-2 is the hand with the wheel draw and A-7 has none. All of it comes from what happens when the kicker pairs. Counting the ways a hand can improve tells you very little. Weighing what each of them pays tells you everything.

One practical consequence: the flush only starts to matter after the reveal. Before any card is face up, a suited A-7 is a minimum bet made for the same reason as an offsuit one. After the reveal, two cards of your suit in a row with the centre card still face down is a live one-card draw and worth counting. Two cards of your suit scattered across the layout are scenery. The full hand ranking ladder

When the Middle bet is offered, four community cards are face up and only the shared centre card remains hidden. You can see six of the seven cards in play: your two hole cards and the four exposed community cards. That leaves 46 cards unaccounted for, and exactly one of them decides both of your hands at once, because the centre card belongs to the row and to the column.

Every one of those 46 cards falls into one of a small number of groups. For A-7 the groups are unusually easy to name, because there are only two ways this hand improves on its own and one of them needs help that is already visible.

• 3 aces A pair of aces, in both hands. A high pair pays 1 to 1 on the Across bet, on the Down bet and on the Middle bet, and it pays both antes even money. This is the best routine outcome the hand has. Subtract one for every ace already showing.
• 3 sevens A pair of sevens, in both hands. A low pair pushes on every line bet and on both antes. Nothing is won and nothing is lost. This is the group that makes A-7 what it is, and it is the group A-2 does not have. Subtract one for every seven already showing.
• Board pairs A card matching one already face up. That makes a pair inside the line the matched card sits in, and the centre card is in both lines, so a card matching the top or bottom helps the column while a card matching the left or right helps the row. It only pays if the pair is jacks or better. A pair of sixes through tens pushes, and anything lower loses.
• Your suit Only when a line already shows two of it. With suited A-7, a line whose two exposed cards match your suit becomes a flush if the centre card matches as well, and a flush pays 8 to 1. Count the suit cards left in the deck, not the ones in your hand. If no line shows two of your suit, this group is empty.
• Everything else Ace-high, and ace-high loses. There is no dealer to out-draw and no qualifying hand to beat, so a hand that makes nothing is simply paid nothing. Both line bets and both antes go.

Notice what is absent. There is no straight group, and there never will be one, because no five-card straight contains both an ace and a seven. Whatever the four exposed cards look like, and however neatly they seem to line up, A-7’s straight frequency stays at exactly 0.0000%. A row showing 8-9 alongside your seven is not a draw. It is two dead cards.

This is also where the difference between A-7 and A-2 becomes something you can see rather than something you read off a table. Both hands have up to three aces in the deck and both pair the ace for a win. A-7 then has up to three sevens that push, so up to six of the 46 cards pair one of your hole cards without costing you anything. A-2 has up to three deuces, and a pair of deuces is below the low-pair band, so those three cards pair your hand and lose anyway. Same number of pairing cards, half as many that are any use.

Keep the size of all this in proportion. Six useful centre cards out of 46 is not a good hand, it is a hand with a floor. A-7 is a minimum bet because the count is thin, not because the count is promising, and the push group is protection rather than profit. How the Middle bet is graded

Each betting decision offers you 1x, 2x or 3x your ante, or a fold on the two lines that carry one. Three sizes and a fold looks like a lot of room. It is not, and the reason is the shape of the expected value rather than anything about the cards.

That is a straight line in N. The ante is already posted and does not move, so every extra unit you stake is worth exactly the same as the unit before it. Expected value is linear in the stake: nothing about a bigger bet changes the per-unit figure, and nothing about a smaller one improves it. A quantity that moves in a straight line takes its best value at one end of the range or the other, never in between.

So there are only ever two candidate sizes. If the line EV is positive you want as many units of it as the game will sell you, which is 3x. If the line EV is negative you want as few as the game will accept, which is 1x, unless the hand is so poor that even one unit is worse than surrendering the ante. 2x is never uniquely optimal. It can tie with an end point when the line EV is exactly zero, and it can never beat both ends. Any time you reach for it, one of the other two buttons is at least as good.

Put A-7 through that. Suited, the Across-bet EV is −0.197500 and the ante EV is −0.342347. Offsuit, they are −0.273265 and −0.359184. The line is negative in both versions, so 3x is out immediately. Neither piece is remotely large enough for the pair of them to reach the −1.000 that folding costs, so the fold is out too. That leaves one button, and it is the same button suited or offsuit.

One more thing the sizing decision is not: a message. Criss Cross Poker is house-banked. There is no dealer hand, no qualifying requirement and no opponent on the other side of your bet, so there is nobody to bluff and nothing to disguise. A 3x with a weak hand does not buy you anything except three times the loss. The size of the bet is the only thing it is: a multiplier on a number that has already been computed.

• Passing the Middle bet forfeits nothing. The Middle carries no ante of its own, so declining it costs you zero rather than one unit, and your Across and Down bets stay live and settle normally against the pay table. Verified in this site’s own game engine. That makes it the easiest of the three decisions, because there is no fold penalty sitting on the other side of it. Make it when the better of your two lines is genuinely worth backing, and let it go when it is not.
• After a 3x, do not pass the Middle. A 3x on the Across or the Down bet means that line was worth the maximum, and the Middle is graded on the better of your two hands. It inherits whatever made the earlier decision worth three units, at no extra ante. Passing it there is the one version of the pass that actually gives something up.
• Fold both lines and the Middle disappears. If you fold the Across bet and the Down bet, the Middle is not offered at all, and only the Five Card Bonus can still be paid. It is not a decision you get to make in that spot, which is another reason the fold on a line is a heavier action than passing on the Middle.
• What A-7 costs to open. At a $10 table, opening A-7 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. Only the third is the decision this page is about, which is why calling it $40 up front misreads the order of play.

None of this makes the game beatable. The 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 to arrive. Maximum exposure in a single hand is 11 units, which is $275 at a $25 ante or $110 at a $10 ante. Playing A-7 correctly does not turn a losing game into a winning one. It removes the avoidable part of the cost.