Middle Position Push/Fold Range at 5 BB with BB Ante (9-Max)

Range legendPush alwaysMixedFold

Top-left = strongest hands (AA), pairs on the diagonal. Upper-right = suited, lower-left = offsuit. Brighter green = always push. Dim = fold.

What percentage of hands should the Middle Position push at 5BB (9-Max) with a BB ante?

The Middle Position pushes 43% of hands at 5BB (9-Max) with a big blind ante. The most marginal hands at this frequency are K3o, Q5s, J7s, Q8o.

How much wider does the Middle Position shove at 5BB with a big blind ante?

20 percentage points: 43% of hands with the ante against 23% without it. The ante brings 36 more hands (296 of 1,326 combos) into the shoving range, including K8s, K7s, K6s, K5s, K4s, K3s, K2s, Q9s.

Is K3o a shove from the Middle Position at 5BB with a BB ante?

It is a mix: with a big blind ante the Nash solution shoves K3o 51% of the time from the Middle Position at 5BB in 9-max. With no ante the same hand is shoved 1% of the time.

What does this chart assume about the ante and stack size?

With a big blind ante the Big Blind posts 1 extra big blind for the whole table, so 2.5bb is in the pot before anyone acts instead of 1.5bb. 5BB means 5 big blinds behind everything already posted: the blinds and, for the Big Blind, the ante. The ranges are chip-EV Nash equilibria with no ICM, solved from 1 to 25bb against the Nash calling ranges of the players left to act.