Rank Utilities

Rank utilities reason about which ranks (2 through A) appear in a hand or on the board. They return either a TRankSet, a single TRank, or a count.

Set-returning

boardRanks(street)

TStreet → TRankSet

The set of distinct ranks present on the board at the given street.

handRanks(player, street)

TPlayer × TStreet → TRankSet

The set of distinct ranks in the player’s hole cards. (For Hold’em the answer doesn’t depend on the street; for stud variants — when added — it would.)

duplicatedBoardRanks(street)

TStreet → TRankSet

The set of ranks that appear more than once on the board (e.g. on a paired board).

duplicatedHandRanks(player, street)

TPlayer × TStreet → TRankSet

Ranks that appear more than once in the player’s hand. For Omaha this lets you spot pocket pairs and trips inside the four hole cards.

intersectingHandRanks(player, street)

TPlayer × TStreet → TRankSet

Hand ranks that also appear on the board.

nonIntersectingHandRanks(player, street)

TPlayer × TStreet → TRankSet

Hand ranks that do not appear on the board.

Scalar

maxRank(ranks)

TRankSet → TRank

Highest rank in the set. Errors on an empty set.

minRank(ranks)

TRankSet → TRank

Lowest rank in the set. Errors on an empty set.

nthRank(n, ranks)

TInteger × TRankSet → TRank

The n-th highest rank in the set, 1-indexed. For instance, on boardRanks(flop) = {A, K, J}:

nthRank(1, boardRanks(flop)) = A
nthRank(2, boardRanks(flop)) = K
nthRank(3, boardRanks(flop)) = J

rankCount(ranks)

TRankSet → TCardCount

Cardinality of the set (number of distinct ranks).

handBoardIntersections(player, street)

TPlayer × TStreet → TCardCount

How many of the player’s hole cards share a rank with at least one board card.

Predicates

hasTopBoardRank(player, street)

TPlayer × TStreet → TBoolean

true if the player has at least one card matching the highest rank on the board at the given street.

hasSecondBoardRank(player, street)

TPlayer × TStreet → TBoolean

true if the player has at least one card matching the second-highest board rank. Returns false on a board with only one distinct rank.

Example

Frequency hero flops top pair:

select count(hasTopBoardRank(hero, flop)) as pct_toppair
from   game='holdem', hero='AxKy', villain='*', board=''

Average highest rank on the river:

select avg(maxRank(boardRanks(river)))
from   game='holdem', hero='*', villain='*'