Board Texture and Sizing

A board needs two numbers

Everyone describes a flop with one word — dry, wet, scary. One word cannot carry it, because two completely different things are being asked, and they do not move together.

• Nut shift: of the possible turn cards, the fraction after which the flop's nuts is no longer the nuts. Pure board arithmetic — nobody's hand is involved, so we enumerate it exactly.
• Draw density: the fraction of random four-card hands that flop a big draw here. Sampled, 20,000 hands per board.

Five flops, both numbers:

• K♠7♦2♣ — nut shift 20.4%, draw density 12.4%.
• A♠K♦Q♥ — 18.4% and 11.2%.
• Q♠T♣J♥ — 18.4% and 28.0%.
• T♥9♦8♣ — 34.7% and 28.2%.
• 9♥8♦2♣ — 77.6% and 30.7%. T♦9♦5♣ — 75.5% and 41.5%.

Describe a flop with both numbers. How easy is it to have a draw here, and how safe is the current nuts — those are separate questions and the answer to one does not predict the other.

Unpaired flops with at least two suits. Paired and monotone boards are pulled out first and handled on their own; that is the next page.

"Wet means dynamic" fails on T♥9♦8♣: its draw density 28.2% is more than double K♠7♦2♣'s 12.4%, yet its nut shift is only 34.7%. Plenty of people have a draw; the flopped nuts survives the turn most of the time. And Q♠T♣J♥ is the sharper case — it looks terrifying, but its nut shift is 18.4%, identical to A♠K♦Q♥, the flop nobody is scared of. The nuts there is already a made straight, and almost nothing takes it away.

Two board types get pulled out first

Paired boards and monotone boards do not go through the two axes at all. They are classified before the axes are computed, and the reason is that on those two textures the nut-shift number is technically correct and pedagogically a lie.

J♥9♥8♥: nut shift 4.1%. That is lower — far more "static" — than K♠7♦2♣ at 20.4%, the flop everybody agrees is the driest in the game.

Rule of the game, and the whole explanation: a showdown hand is exactly 2 cards from your hand plus 3 of the 5 board cards. On three hearts the absolute best possible hand is a straight flush, and a straight flush is nearly impossible to overtake. The number is measuring the right thing; it is just not measuring the hand anybody is actually fighting over, which is the ace-high flush.

Both figures come from the same function that produced the previous page (the postflop rule spec), enumerating every two-card combination against the board and every turn card. We did not patch the metric to make this board behave — we excluded the board from the metric, and wrote down why.

On a paired or monotone flop, stop asking "is the nuts safe" and start asking "which nuts". Name the specific hand people are contesting before you size anything.

Any flop where the three cards share a suit, or two of them share a rank.

A rule written on the nut-shift number alone would call J♥9♥8♥ the most static board on this page — more static than K♠7♦2♣ — and let you bet a made flush as though nothing could go wrong. Q♦Q♠4♥ does the same thing from the other side: nut shift 4.1% and draw density 12.1%, two numbers that together say "nothing is happening here", on a board where one specific card in somebody's hand beats your entire range.

So: which one?

"Ask which nuts" is only useful if the question has an answer, and it does — the same enumeration as the previous page, read one level deeper. Sort every two-card combination by strength, and for each rung count how often a random four-card hand reaches it. That list is a nut ladder.

• Q♦Q♠4♥ — top rung: four of a kind, made by exactly 1 two-card combination, reached by 0.5% of hands. One rung down: a full house, 6 combinations. A full house or better: 4.7%. Three of a kind or better: 17.2%.
• J♥9♥8♥ — top rung: a straight flush, also exactly 1 combination, also 0.5%. But a flush or better: 18%.

There is the answer. On the paired flop the hand being contested is a full house; on the monotone flop it is a flush. On both boards the absolute best hand is a single two-card combination that hardly anybody holds, which is exactly why planning around it is the wrong plan.

On a paired or monotone flop, stop counting rungs from the absolute nuts. Read the ladder, name the rung people are contesting, and then take the only number that decides anything: what fraction of hands beats yours.

Any flop that is paired or monotone — precisely the two textures the axes hand back. One caveat that belongs to the measurement rather than to the small print: the ladder deals opponents random four-card hands. Somebody who is putting money in is not random, so every percentage here is a floor, not an estimate. It is a fraction of all possible hands, never "the opponent's range" — this project has no postflop range data at all.

"The absolute nuts is rare here, so this board is quiet" gets both of these boards wrong, in opposite directions. The two top rungs are identical: one combination each, 0.5% each. Now put a hand on each. On the frightening monotone flop, A♥6♥K♠2♣ is not the nuts — it sits on rung 7 — and only 1.2% of the 148,995 hands an opponent could hold beat it. On the quiet paired flop, Q♥J♠T♣9♦ is three queens on rung 6, and 6.9% beat it: nearly six times as many, from one rung higher up. The rung numbers say the two hands are about equally placed. They are not.

What a bet size actually does

A bet size has exactly one measurable job: to make some of the hands behind you unable to call profitably. So measure that. Hero holds top set and bets; we deal 3,000 random four-card hands per board and count how many of them can call and show a profit — at one-third pot they need 20.0%, at a full pot 33.3%.

• K♠7♦2♣ with K♥K♦9♠4♥: 0.1% · 0% · 0% · 0%.
• A♠K♦Q♥ with A♥A♦9♠4♥: 9.2% · 8.3% · 8.3% · 8.3%.
• 9♥8♦2♣ with 9♣9♠A♦K♥: 34.5% · 26.6% · 15.5% · 8.1%.
• 7♥6♦2♠ with 7♣7♠A♦K♥: 30.6% · … · 7.6%.
• T♦9♦5♣ with T♥T♣A♠K♥: 46.9% · 41.5% · 26.0% · 19.1%.

Size for what the size can change. On a dynamic board, betting big genuinely shuts hands out; on a static board it shuts nothing out, so choose the size for what you want called instead.

Flop, heads up, holding a strong made hand. The numbers above are against random four-card hands, which is a deliberately crude stand-in — it is a board property we are measuring, not a read.

On K♠7♦2♣ the whole range of sizes does the same thing: 0.1% at the smallest and 0% at the largest. Nothing could call anyway. On A♠K♦Q♥ the sizes are equally useless but for the opposite reason — 9.2% down to 8.3%, barely moving, because the hands that can call there are big enough to call anything. Two static boards, two identical conclusions about sizing, two completely different causes.

What to take away

One more thing before the summary, because it is the piece people import wrongly from elsewhere. Deep stacks do not imply small bets. Bet the pot and get called and the ratio behind you goes from 13 to 4 to 1 — three streets, and the last one is exactly all in. From 20 the same sequence runs 6.33 then 1.78, and the stacks never go in at all. If you want the option of playing for everything by the river, the pot has to be built on the flop.

• Two numbers per board. How dense the draws are, and how safe the nuts is. T♥9♦8♣ is 28.2% dense and still not dynamic.
• Paired and monotone are separate species. Name the contested hand instead of trusting the axis.
• Size for what it changes. On T♦9♦5♣ going from small to full pot takes callers from 46.9% to 19.1%; on K♠7♦2♣ the biggest size still leaves 0%, so nothing was gained.
• There is no default size in this course. The same size does different work on 9♥8♦2♣ (nut shift 77.6%) than on a static board, so a single default would be wrong on one of them.

What we cannot give you here: range advantage and nut advantage. Our own rule layer takes those two as inputs from the question rather than computing them, because computing them needs postflop range data and this project has none — not thin data, none. There is no date on it — the full-street engine shipped without postflop range data, and this is exactly the piece that data was needed for. Until then, treat every sizing statement on this page as a fact about the board, never as a fact about who has the better range.

Everything above is a rule of this course, not an equilibrium solution. The board numbers are enumerations and samples from our own engine; the sizing conclusions are what those numbers support and nothing more.