Rundowns and Gaps

Why height matters in a rundown

A rundown is four ranks sitting close enough together that the hand flops wraps instead of one-way straight draws. Height is the first thing to grade. All three double-suited, against a random hand:

• K♠Q♠J♥T♥: 58.9%.
• J♠T♠9♥8♥: 55.8%.
• 8♠7♠6♥5♥: 48.8%.

10.1 points from top to bottom, and the equity understates it: the straights a high rundown makes are far more often the best straight available, while a low rundown regularly makes the second-best one and pays off the hand above it. That is nuttiness again, and equity cannot see it.

One wrinkle worth knowing before you go looking for the highest possible rundown: A♠K♠Q♥J♥ is 61.1%, which is higher still — but not because the ace helps the straights. Our classifier counts, for each card, the most five-card straight windows it shares with any one other card in the hand. In that hand the ace shares at most 1 window with any other card, while the king next to it shares 2. The ace connects worse than the king does; its score comes from the nut flush and from raw high-card strength. Do not read the number as "aces improve rundowns".

Higher rundowns beat lower ones: K♠Q♠J♥T♥ over J♠T♠9♥8♥ over 8♠7♠6♥5♥.

Comparing rundowns of the same suit shape. The ladder is about ranks; it says nothing across different suit patterns.

Rainbow K♠Q♦J♥T♣ is 52.8%, which is 3.0 points below double-suited J♠T♠9♥8♥. The reference ranges agree and go further: they fold the rainbow king-high rundown from the first three opening seats while opening the double-suited jack-high one from all of them. Suits outrank height whenever the two disagree.

Each percentage is 1000000 simulations against a random four-card hand, standard error 0.05 points.

Where the gap sits

888poker's glossary names the shapes, and we use its names: T♠8♠7♥6♥ is a top gap, T♠9♠8♥6♥ is a bottom gap, T♠8♠6♥5♥ is a double gap. Its claim is that "rundowns are more valuable when the gap is either at the bottom of the rundown structure or when the rundown has no gap at all", because "gaps towards the top of a rundown make it more likely a player will flop non-nut straight draws".

We do not take claims on trust, so we measured all four, double-suited, against a random hand:

• T♠9♠8♥7♥ (no gap): 53.1%.
• T♠9♠8♥6♥ (bottom gap): 52.5%.
• T♠8♠7♥6♥ (top gap): 51.7%.
• T♠8♠6♥5♥ (double gap): 50.5%.

The claim holds: bottom gap beats top gap by 0.8 points, many times the simulation error. Our classifier counts 1 gap in the bottom-gap hand and 1 in the top-gap hand — the number of gaps is identical, only the position differs.

A gap hurts least at the bottom of the hand.

When there is exactly one gap and the other three dimensions match. Comparing a one-gap hand to a two-gap hand is a different question.

Keep the size of the effect in mind: 0.8 points is small. The suit-shape effect on the previous page was 3.0 points and the height effect was 10.1 points — an order of magnitude larger. Never give up a suit or a rank to move a gap downwards; the gap is the last tiebreaker, not the first filter.

888poker, "Rundown": https://www.888poker.com/magazine/poker-terms/rundown — also recorded in docs/M2-SOURCES.md. Worth knowing when you read elsewhere: this source calls double-gap hands rundowns too, while other sources reserve the word for four connected ranks. Our classifier draws its own line and says so; where a source and our engine disagree, this course reports both.

Three of a suit is a penalty

Newcomers see three or four cards of one suit and feel good about it. Hold the ranks still one more time:

• J♠T♠9♥8♥, two suits of two: 55.8%.
• J♠T♠9♥8♦, one suited pair: 52.8%.
• J♠T♠9♠8♥, three spades: 52.0%.
• J♠T♠9♠8♠, four spades: 51.2%.

Three of a suit is worth 3.8 points less than double-suited and is even slightly behind single-suited. The reason is straightforward once you have said it out loud: you must use exactly two cards, so the third spade adds no new flush — it only removes a spade from the deck that would have completed the flush you are chasing. You are blocking yourself.

Three or four cards of one suit is a penalty. Grade the hand as if the extra suited card were offsuit, then take a little more off.

Whenever you are comparing against the double-suited or single-suited version of the same ranks.

A penalty is not a fold. J♠T♠9♠8♠ — four cards of one suit, the worst suit shape there is — is still an opening hand on the button in our reference ranges, and a mixed decision in the small blind; it is only folded from the first three seats. The ranks are doing enough work to survive the suit problem in position. Structure penalties change where you play a hand far more often than whether you play it.

What to take away

Grade a rundown in this order, because that is the order of the effect sizes we measured:

• Height first — 10.1 points between K♠Q♠J♥T♥ and 8♠7♠6♥5♥, plus a nuttiness advantage the equity does not show.
• Suit shape second — 3.0 points, enough to reverse the height ladder outright, and 3.8 points lost to three of a suit.
• Gap position last — 0.8 points. Real, confirmed, and the smallest thing on the page.

The habit to build: when two hands disagree across dimensions, the bigger dimension wins, and you now know which dimensions are bigger. The habit to avoid: treating any of these as a fold rule. Every hand on this page is opened from somewhere, and C7 is about where.