How to Play Straight Draws in Criss Cross Poker

The Across and Down decisions are made blind. You have two hole cards, no community card has been turned, and there is nothing to draw to yet. The Middle decision is different. The dealer has exposed the top, left, right and bottom community cards, you are looking at your own two hole cards, and that is six cards you can see. One card, the centre, is still face down. Everything about a straight draw in this game comes out of that gap.

Six known cards leave 46 unseen cards in the deck, and exactly one of them is going to land in the centre. Every one of those 46 is equally likely. That is why the Middle bet does not need estimating: you can walk the whole list.

Six cards known, one unknown, 46 candidates

This site’s strategy coach now prices the Middle bet by enumeration rather than by rule of thumb. It takes the six known cards, deals each of the 46 remaining cards into the centre in turn, evaluates both rows for every one of them, and takes the payout on whichever row finishes higher. Averaging those 46 outcomes gives an exact expected value per unit staked. There is no sampling and no approximation anywhere in it, because with one unknown card there is nothing left to approximate.

Here are four positions the engine has priced, so you can see the range the Middle bet actually covers.

Note the second row before you go any further. An open-ended draw is worth +0.369565 per unit in practice, and the straight itself accounts for only +0.043478 of that. Almost all of the value in a straight draw at the Middle comes from somewhere other than the straight. Sections three and four take that apart.

This page is about the Middle decision, not about which hands to open with. If you are looking for the Across and Down calls, start with the strategy guide

A row at the Middle decision holds four cards and waits for the centre. If four of those cards make a straight draw, the number of ranks that finish it is fixed by the shape, and each of those ranks has four cards in the deck. That first number is your nominal out count.

The two end draws are the ones people over-value. J-Q-K-A looks like the biggest straight in the deck and A-2-3-4 looks like four connected cards, but both are blocked at one end by the top or the bottom of the rank ladder, so both need a single rank and both are four-out draws. They are worth exactly what an inside draw is worth, not what an open-ender is worth.

Now subtract what you can already see

Nominal outs assume all four cards of each finishing rank are still in the deck. At the Middle they very often are not, because the opposite row is face up in front of you. If your Across row is drawing to a nine and there is a nine sitting in the left or right position, that nine is gone. It cannot be the centre card, because it already is a card.

The same applies to your own hole cards and to any completing card anywhere else you can see. Count six known cards, take out every one of them that would have finished your straight, and the rest of the page uses what survives.

Three visible outs is not a freak case. Two of the four cards in the opposite row plus one of your hole cards is enough to do it, and it happens most often precisely when the board is full of the middle ranks that build straights in the first place. The board that gives you the draw is the same board that eats the outs.

Take the pair rescues away for a moment and imagine a row that either makes its straight or wins nothing at all. The Middle bet pays 5 to 1 on a straight, so you collect five units when the centre card completes and lose one unit when it does not. Call the chance of hitting p and set the two sides equal.

The exact value of every out count

You do not have to stop at the break-even test, because with 46 candidates the expected value itself is short arithmetic. Each out wins five units. Every card that is not an out loses one unit, and there are 46 minus your outs of those. Add the two and divide by 46.

The middle column below shows that calculation written out, so you can check any row of the table with nothing but the numbers on the page.

Read the six-out row slowly, because it is the one that gets miscopied. Six outs win five units each, which is 30. The other 40 cards lose a unit each, which is 40. Thirty against forty is a net of −10, not −8, and −10 divided by 46 is −0.217391. If you have seen a smaller number attached to six outs, work the subtraction again: 46 − 6 = 40 losers, and all forty of them are paid for out of the same 46.

The shape of the table is worth holding on to. The eight-out draw is barely above water at +0.043478, which is a little under a twentieth of a unit. Lose a single out to the opposite row and you are at −0.086957. An inside draw at four outs is −0.478261, and a reduced inside draw at three outs is −0.608696, which is the same number this site’s engine returns for a complete miss with 7-2 offsuit. On straight hits alone, a three-out draw is worth nothing more than holding the worst hand in the game.

The previous section priced a draw as though a missed straight were a total loss. It is not. The Middle bet is settled against the same pay table as the Across and Down bets, and that pay table pays a bare pair. When the centre card pairs one of the four cards in your row, the row still has a result, and depending on the rank it can be a winner, a push or a loser.

Look at where that split falls and then look back at the draws in section two. The ranks that build straights are the middle ranks, and the middle ranks are exactly the ones that push rather than lose. A connected row is carrying a large block of cards that cannot cost you anything, which is not something the out count ever told you.

A worked row: 7-8-9-J

Here is a row of four cards waiting on the centre. It is an inside draw: only a ten completes 7-8-9-10-J.

Counting only the straight, this is a four-out draw at −0.478261 per unit, which is an obvious pass. Now classify the rest of the 46 candidates instead of throwing them away. Assuming none of these ranks shows up anywhere else among the six cards you can see:

• Four tens complete the straight and pay 5 to 1.
• Three jacks are left in the deck, and each one makes a pair of jacks, which pays 1 to 1.
• Nine cards, the three remaining sevens, eights and nines, make a low pair and push.
• The other thirty cards leave this row with nothing, and the Down row is still live for all of them, because the Middle bet is graded on the better of the two.

Sixteen of the 46 candidates do something for a row that a bare out count writes off as a four-out draw. Nine of those sixteen are cards that make the bet cost you nothing at all. That is the part of a straight draw that never appears in the outs.

The comparison that decides how you play draws

Put the two numbers side by side. This site’s engine priced an open-ended 5-6-7-8 row across all 46 centre cards, and the answer is not the answer the straight alone gives.

This cuts the other way too, and section five is where that bill arrives. Because the same centre card can complete a straight, make a pair and improve the opposite row all at once, it is very easy to count that card two or three times over and talk yourself into a bet that is not there. Every card gets counted once, classified by the strongest result it produces.

A single centre card can do two or three jobs at once. It can complete your straight, pair one of your hole cards and improve the opposite row, all on the same turn. It still arrives once. The most common way to talk yourself into a bad Middle bet is to tally straight hits, then tally pair rescues, then tally opposite-row rescues, and add the three numbers together. That counts the same card more than once and inflates the value of the bet every time.

The fix is a single pass. Take each of the 46 unseen cards, work out the strongest result it produces on whichever row finishes higher, give it that one label, and move on. A card that completes a straight and pairs your jack is a straight card. It is not also a high pair.

The order in that table is the pay table’s own order, which is why it settles every tie. Work down it and stop at the first line that applies. Because the Middle is graded on the better of your two completed rows, you judge each card on the row it helps most, not on the row you happened to be watching.

The check that catches the error

Once every card carries a label, add the labels up. There is only one number they can make:

straight cards + made hands + high pairs + low pairs + losing cards = 46

If your total comes to more than 46 you have given a card two labels, which is the double count. If it comes to less, you have skipped a rank or forgotten that a card visible on the opposite row is not available. Either way the arithmetic is telling you the answer is wrong before you stake anything on it. Nothing else about the Middle decision is worth doing until that line balances.

The Across bet rides on the Ante Across. The Down bet rides on the Ante Down. Both antes are posted before you have seen a card, and giving up either line forfeits the ante beneath it. The Middle bet rides on nothing. There is no Middle ante and there never was one, so declining the Middle takes exactly zero out of your stack. That one structural difference settles the sizing question, and it settles it more sharply than most tables play it.

The whole decision in one line

Write the value of the Middle bet at a stake of N units, where N is 0, 1, 2 or 3:

value of the Middle at stake N = N × (edge per unit)

Nothing else belongs in that expression. There is no ante term, because there is no ante. The edge per unit is fixed by the six cards you can already see and does not change when you push out more chips. So the value of the bet is a straight line through zero, and a straight line through zero takes its best value at one end or the other, never in the middle.

• Edge positive, so bet 3x. Every extra unit adds the same positive amount, so you want as many units as the game allows. Stopping at 1x collects a third of an edge you were entitled to in full.
• Edge negative, so pass. Every extra unit subtracts the same amount, so you want none of them. A 1x bet here takes a third of a loss you could have avoided completely, and it buys nothing back because there is no ante at risk.
• Edge exactly zero, so it does not matter. Every stake is worth the same nothing. This is the only case where a 1x is not strictly worse, and it is a boundary rather than a strategy.

That is the entire argument. It does not depend on which cards are showing, on how the draw looks, or on how the earlier decisions went. One unit collects one share of the edge, two units collect twice that share, three units collect three times it, and passing collects none of it at no cost. Whenever the edge has a sign, the best stake is at one extreme.

The four priced examples

Six cards are known at the Middle decision and exactly one is unknown, so the bet does not have to be estimated. Our coach enumerates all 46 candidate centre cards, evaluates both rows for each one, and averages the payout on whichever row finishes higher. These are its figures, per unit staked:

Four boards, four verdicts, and not a 1x or a 2x among them. There is no board that produces one, because producing one would need an edge that is positive enough to bet and negative enough to want less of, and no number is both.

The open-ended row is worth a second look while you are here. It prices at +0.369565 against +0.043478 from the straight alone. The pair rescues are worth several times the draw they sit beside, which is why a draw you would have passed on its own turns into a full 3x. Where the rest of that number comes from

Why 1x is right on Across and Down and wrong here

The same reasoning does not carry back to the earlier two decisions, and the reason is the ante. At the Across decision your choices are not 0, 1, 2 and 3. Folding does not return you to zero. It forfeits the Ante Across, which costs exactly −1.000000 unit. The smallest stake that keeps the ante alive is 1x, and that is a real option with a real price rather than a dominated one.

So a hand with a losing line bet can still be a correct 1x, because the 1x is bought against a fold that already costs a whole unit. A-2 suited is the clean case. Betting 1x on it comes to −0.754336. Folding comes to −1.000000. The bet loses money and it is still the right action, by a quarter of a unit, because the alternative loses more.

Read down the third column and the whole difference is there. On the first two lines a minimum bet is the cheapest way to stay in a hand you have already paid for. On the third there is nothing to stay in for, so the minimum bet protects nothing and simply buys a fraction of whatever the edge happens to be. When that fraction is positive you wanted all of it. When it is negative you wanted none.

One rule of the game to keep in mind while you count: if you fold both the Across and the Down bets, the Middle bet is not offered at all, and only the Five Card Bonus can still be paid. How the Middle bet is settled

By the time the Middle decision reaches you, both antes are posted and both line decisions are made. Those chips are committed. No Middle stake retrieves them and no Middle pass makes them any cheaper. They are the same number whichever button you press next, which is the definition of a sunk cost and the reason they carry no information about what to do now.

Strip them out and the decision is the one from the previous section, unchanged:

pass = 0   against   3x = 3 × (edge per unit)

The only inputs are the six cards you can see and the 46 you cannot. How much you have already risked is not one of them. Nor is how the session has gone, how close the row looked two cards ago, or how much you would like the hand to work out. The centre card does not know any of that.

The rule this contradicts

There is a common table rule that says never fold the Middle after you have already bet 3x on a line. As a rule it is wrong, and the correction matters more than it sounds: if the Middle edge is negative you pass, whatever you staked earlier. An earlier 3x is money already in the pot. It cannot be won back by a second bet with a negative expectation, and adding a losing wager to a losing hand does not average out to anything better than the losing wager.

The reason the rule survives is that it is usually right by accident. A hand strong enough to justify 3x on an earlier line, a pocket pair say, tends to be a hand that still has a positive Middle edge once the sixth card is placed, so the two answers agree and nobody notices which one did the work. Pocket aces already made price at +1.347826 per unit and are a 3x on the Middle, which the rule also gets right, but the rule is not what made the decision. The edge is.

Where they disagree, the edge wins every time. If the board leaves you with two overcards and nothing more, the Middle prices at −0.543478 per unit and it is a pass. Betting 3x on a line earlier in the hand does not move that figure by anything at all, because those chips were spent on a different wager that is settled on its own row.

The same logic runs the other way, and that half is worth stating because it is the half people skip. A hand you only put a minimum bet on earlier does not owe you caution now. If the centre card prices out positive, it is a 3x, even if both earlier decisions were made at 1x and even if the hand has felt thin all the way through. The Middle is a fresh wager on 46 unknown cards. It carries no history.

Everything on this page collapses into one routine you can run at the table in the time it takes the dealer to reach you. It never asks you to estimate anything, because with six cards known and one unknown there is nothing left to estimate.

The seventh step is the one worth being strict about. Every mistake this page describes shows up as a total that is not 46, so the check catches the double count, the dead out and the forgotten rank without you having to remember which of the three you were prone to. Run it before the stake, not after.