Reading a Starting Hand

Four cards, four questions

You cannot rank 4-card hands by memory the way you ranked two-card hands. What you can do is ask the same four questions every time, in the same order. This app's classifier asks exactly these, and every range and every drill in the camp is built on its answers.

• Pairs. None, one pair, two pair — or the self-blocking cases, three and four of a rank, which are strictly bad because they eat your own set outs.
• Suits. Double-suited (two suits, two cards each) beats single-suited beats rainbow. Three or four cards of one suit is a penalty, not a bonus.
• Connectedness. How tightly the four ranks sit together, and where the gaps are. A rundown is four ranks close enough that the hand makes wraps.
• Nuttiness. Not "how strong", but "when this hand makes something, is it the best possible version of it?" An ace-high flush draw and a low flush draw carry the same equity and completely different money.

And one disqualifier that cuts across all four: a dangler — a card that pairs nothing, shares no suit, and sits too far from the others to make a straight with them. A hand with a dangler is a three-card hand wearing a fourth card, and you still have to use exactly 2 cards.

The four dimensions are the fields of js/core/plo-class.js, which reports structure only and makes no judgement about whether a hand is playable — that judgement is this course's, and it is stated separately so you can disagree with it without arguing about the facts.

Suits, nuttiness, and blockers

Hold the ranks still and move only the suits. J♠T♠9♥8♥ is 55.8%, J♠T♠9♥8♦ is 52.8%, J♠T♦9♥8♣ is 49.7%. Same four ranks, 6.1 points between the top and bottom. Do it again with aces: A♠A♥8♠3♥ is 67.4% and A♥A♦8♣3♠ is 61.6% — 5.8 points, bought entirely with suits.

Now the uncomfortable one. A♠K♥T♠8♦ (the ace is in the suited pair, so its flush is the nut flush) is 57.0%; A♥K♠T♠8♦ (same ranks, but the suited pair is king-high) is 56.8%. That is 0.2 points. Equity against a random hand barely sees nuttiness at all — and yet the second-best flush is one of the two or three ways stacks actually change hands in this game. Never grade nuttiness with an equity number; grade it by asking who pays you and who you pay.

Suits do one more thing that equity does see: they block. Exact enumeration of all 1086008 boards, same aces both times:

• A♥A♦K♥K♦ against J♣T♣9♠8♠ — suits do not overlap: 61.5%.
• A♥A♦K♥K♦ against J♥T♥9♦8♦ — the opponent needs the exact suits you are holding: 66.4%.

Same hand, same opponent ranks, 4.9 points, and no simulation noise anywhere near it. That is a blocker, and it is why the suits in your hand matter even in the hands where you never make a flush.

Double-suited beats single-suited beats rainbow.

When the other three dimensions are equal. It is a tiebreaker between hands of the same shape, not a licence.

J♠T♥9♠2♥ is double-suited and worth 52.1%; J♠T♠9♥8♦ is only single-suited and worth 52.8%. The single-suited hand wins by 0.7 points because the double-suited one has a 2♥ hanging off the bottom. One dimension does not buy back another one's collapse.

Percentages against a random hand: 1000000 simulations each, standard error 0.05 points. The two head-to-head numbers are exact enumerations, not simulations.

The dangler, and the trap in spotting one

Price the fourth card. A♠A♥J♠T♣ is 68.0% against a random hand. Swap the ten for a 2♣ — A♠A♥J♠2♣ — and it is 65.2%. Losing one working card costs 2.8 points, and it costs more than that after the flop, because the hands you flop are thinner and easier to get outdrawn on.

Now the trap, and it is worth slowing down for. Take J♠T♥9♠2♥. The 2♥ is miles away in rank from everything else: our classifier counts 1 rank-isolated card in this hand. But it counts 0 danglers — because that card shares a suit with the ten, and a card with a live flush route is not doing nothing.

That distinction is not pedantry. Double-suited hands can never have a dangler in the strict sense (every card is in a suited pair), so "no danglers" tells you nothing about a double-suited hand. Look at the ranks separately from the suits, then decide how much the suit is worth.

A dangler is a real penalty. Downgrade the hand.

When that card genuinely pairs nothing, shares no suit, and is more than four ranks from the nearest other card. Check all three, not just the rank.

Downgrade is not fold. A♠A♥J♠2♣ has a textbook dangler, and our reference ranges still open it from every one of the five opening seats — a pair of aces plus a suited ace outweighs one dead card. Danglers decide close hands; they do not veto premiums.

What to take away

Four questions, in this order, every hand:

• Pairs? Two pair gives you two ways to flop a set. Three of a rank blocks your own outs.
• Suits? Worth up to 6.1 points of raw equity between double-suited and rainbow, plus 4.9 points of blocking in the exact case we measured.
• Connected? Any card that does not connect costs about 2.8 points and more after the flop.
• Nutted? Worth 0.2 points of equity and a large share of your win rate. Judge it with your eyes, never with a percentage.

Every number on this page is equity against a random hand, which is the one honest yardstick we can compute for a starting hand in isolation. It is deliberately not a hand ranking: it cannot see nuttiness, it cannot see position, and it cannot see how easy a hand is to play. C6 and C7 add those back.