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Baixada · Study · Field guidePart I · The solve, and how to read it
Chapter iv

Ranges — the hands still possible

A range is not a vague feeling about what somebody might hold. It is the complete set of hands still possible at this decision, with a weight on each one. The line you watched filters that set: a hand that rarely chooses the observed actions becomes a small bar; an impossible hand disappears altogether.

§ 1

Build a range, then read it

Start with [? ? ?] for every legal three-card hand. Fix cards by typing their notation, clicking a slot and selecting a card, or dragging it onto a slot; all three inputs stay synchronized. GRID always draws every matching block. Its brass badge changes only the split — H, M, or L — while LIST gives the same arriving range as rows. Choose any holding to make it exact.

YOUR RANGE

Type a hand, click a slot to choose a card, or drag one onto a slot. ? keeps that card unknown.

403 matching handsshare of the arriving range

Every shaded cell is a dealable holding. <0.1% means a tiny share, not a blocked hand.

H \ M5♥5♠5♦32AKJQ764
5♣<0.1%<0.1%<0.1%0.1%0.1%0.1%0.1%0.1%0.1%0.1%0.1%<0.1%
5♥<0.1%<0.1%0.1%0.1%0.1%0.1%0.1%0.1%0.1%0.1%<0.1%
5♠<0.1%0.1%0.1%0.1%0.1%0.1%0.1%0.1%0.1%<0.1%
5♦0.1%0.1%0.1%0.1%0.1%0.1%0.1%0.1%<0.1%
30.2%0.5%0.5%0.5%0.5%0.5%0.5%0.5%0.1%
20.2%0.5%0.5%0.5%0.5%0.5%0.5%0.1%
A0.2%0.5%0.5%0.5%0.5%0.5%0.1%
K0.2%0.5%0.5%0.5%0.5%0.1%
J0.2%0.5%0.5%0.5%0.1%
Q0.2%0.5%0.5%0.1%
70.2%0.5%0.1%
60.2%0.1%
4<0.1%
H \ M5♥5♠5♦32AKJQ76
5♣<0.1%<0.1%<0.1%0.2%0.2%0.2%0.2%0.2%0.2%0.2%0.1%
5♥<0.1%<0.1%0.2%0.2%0.2%0.2%0.2%0.2%0.2%0.1%
5♠<0.1%0.2%0.2%0.2%0.2%0.2%0.2%0.2%0.1%
5♦0.2%0.2%0.2%0.2%0.2%0.2%0.2%0.1%
30.3%0.7%0.7%0.7%0.7%0.7%0.7%0.3%
20.3%0.7%0.7%0.7%0.7%0.7%0.3%
A0.3%0.7%0.7%0.7%0.7%0.3%
K0.3%0.7%0.7%0.7%0.3%
J0.3%0.7%0.7%0.3%
Q0.3%0.7%0.3%
70.3%0.3%
6<0.1%
H \ M5♥5♠5♦32AKJQ7
5♣<0.1%<0.1%<0.1%0.2%0.2%0.2%0.2%0.2%0.2%0.1%
5♥<0.1%<0.1%0.2%0.2%0.2%0.2%0.2%0.2%0.1%
5♠<0.1%0.2%0.2%0.2%0.2%0.2%0.2%0.1%
5♦0.2%0.2%0.2%0.2%0.2%0.2%0.1%
30.3%0.7%0.7%0.7%0.7%0.7%0.3%
20.3%0.7%0.7%0.7%0.7%0.3%
A0.3%0.7%0.7%0.7%0.3%
K0.3%0.7%0.7%0.3%
J0.3%0.7%0.3%
Q0.3%0.3%
7<0.1%
H \ M5♥5♠5♦32AKJQ
5♣<0.1%<0.1%<0.1%0.2%0.2%0.2%0.2%0.2%0.1%
5♥<0.1%<0.1%0.2%0.2%0.2%0.2%0.2%0.1%
5♠<0.1%0.2%0.2%0.2%0.2%0.2%0.1%
5♦0.2%0.2%0.2%0.2%0.2%0.1%
30.3%0.7%0.7%0.7%0.7%0.3%
20.3%0.7%0.7%0.7%0.3%
A0.3%0.7%0.7%0.3%
K0.3%0.7%0.3%
J0.3%0.3%
Q<0.1%
H \ M5♥5♠5♦32AKJ
5♣<0.1%<0.1%<0.1%0.2%0.2%0.2%0.2%0.1%
5♥<0.1%<0.1%0.2%0.2%0.2%0.2%0.1%
5♠<0.1%0.2%0.2%0.2%0.2%0.1%
5♦0.2%0.2%0.2%0.2%0.1%
30.3%0.7%0.7%0.7%0.3%
20.3%0.7%0.7%0.3%
A0.3%0.7%0.3%
K0.3%0.3%
J<0.1%
H \ M5♥5♠5♦32AK
5♣<0.1%<0.1%<0.1%0.2%0.2%0.2%0.1%
5♥<0.1%<0.1%0.2%0.2%0.2%0.1%
5♠<0.1%0.2%0.2%0.2%0.1%
5♦0.2%0.2%0.2%0.1%
30.3%0.7%0.7%0.3%
20.3%0.7%0.3%
A0.3%0.3%
K<0.1%
H \ M5♥5♠5♦32A
5♣<0.1%<0.1%<0.1%0.2%0.2%0.1%
5♥<0.1%<0.1%0.2%0.2%0.1%
5♠<0.1%0.2%0.2%0.1%
5♦0.2%0.2%0.1%
30.3%0.7%0.3%
20.3%0.3%
A<0.1%
H \ M5♥5♠5♦32
5♣<0.1%<0.1%<0.1%0.2%0.1%
5♥<0.1%<0.1%0.2%0.1%
5♠<0.1%0.2%0.1%
5♦0.2%0.1%
30.3%0.3%
2<0.1%
H \ M5♥5♠5♦3
5♣<0.1%<0.1%<0.1%0.1%
5♥<0.1%<0.1%0.1%
5♠<0.1%0.1%
5♦0.1%
3<0.1%
H \ M5♥5♠
5♣<0.1%<0.1%
5♥<0.1%
H \ M5♥
5♣<0.1%
VI A range is every hand still compatible with what you know; its bars add to 100%.
§ 2

Blockers — why hands disappear

A blocker is just a card that is already visible, so it cannot also be in a hand. The turn-up removes one copy before anybody acts; each open card in the line removes another. That is a physical deck constraint, not a solver preference. The lab greys choices with no copies left, and the range editor refuses them too.

A visible dealChance the dealer holds at least one 3
Leader · your rangeH ≥ M ≥ L
Turn-up
Dealer · hidden hand
8.1%opponent has a 3

Click a card in the leader's hand to pin or clear it. The visible turn-up and every pinned card are removed from the deck before the dealer's hidden hand is counted.

VIIThis percentage is conditioned on the cards visible at this table — not an abstract deck baseline. The turn-up picker deliberately excludes 2.