Dealt vs Opened vs 3-Bet: How Played Ranges Bend the Numbers
Dealt odds are the floor. Real ranges fold low cards and keep suited aces — here is exactly how much that bends every frequency.
PLO4 Hand-class frequencies by range
How often a hand holds each class when it is a random deal, a button open (48.6% of hands), or a big-blind 3-bet vs that open (9.4% of hands). Multipliers are vs the dealt baseline. PLO4, exact counts — no simulation.
| A hand that holds… | Dealt | BTN open | BB 3-bet |
|---|---|---|---|
| Flush drawtwo or more spades on Ks 9s 6h | 21.4% | 23.4% ×1.1 | 26.8% ×1.3 |
| Made flushtwo or more spades on Ks 9s 6s | 18.0% | 20.0% ×1.1 | 24.0% ×1.3 |
| Straight (Q + J)at least one queen and one jack on Ks Th 3d | 7.2% | 9.3% ×1.3 | 9.3% ×1.3 |
| Broadway straight (A + K)at least one ace and one king on Qs Jh Td | 7.2% | 15.1% ×2.1 | 25.5% ×3.6 |
| Wheel (2 + 4)at least one deuce and one four on As 5h 3d | 7.2% | 1.6% ×0.23 | 0.59% ×0.08 |
| Pocket acestwo or more aces, preflop (no board) | 2.6% | 5.3% ×2.1 | 26.2% ×10.2 |
| Pocket kingstwo or more kings, preflop (no board) | 2.6% | 5.3% ×2.0 | 12.6% ×4.9 |
| Pocket queenstwo or more queens, preflop (no board) | 2.6% | 5.1% ×2.0 | 7.0% ×2.7 |
| Flush draw, ace-high boardtwo or more hearts on Ah Qh 6s | 21.4% | 21.1% ×0.99 | 21.5% ×1.0 |
| Flush draw, low boardtwo or more hearts on 7h 5h Ks | 21.4% | 25.1% ×1.2 | 31.7% ×1.5 |
Pocket-pair rows are preflop figures over all C(52,4) deals — slightly different from flop-conditioned numbers, where three known board cards shift the denominator. Board rows remove the named flop cards before counting.
Same draw odds, different range
Both flops leave a random hand exactly 21.4% to hold a flush draw. The played ranges disagree.
Players keep high suited hands and fold low ones, so the suit equity of a played range lives in its big cards. On the low two-tone board the 3-bettor holds a flush draw 31.7% of the time — ×1.5 the rote 21.4%. On the ace-high board the same range runs slightly under baseline at 21.5%: the ace of the draw suit sits on the board, blocking the suited-ace combos that carry most of its flush draws.
Practical read: on low two-tone boards, credit a 3-bettor with flush draws (and flushes) well above the ~20% deck number. On ace-high two-tone boards, the deck number is already a slight overestimate.
The low-card caveat
A random hand holds the 2 + 4 wheel combo on As 5h 3d 7.2% of the time. The button open holds it 1.6%, the 3-bettor just 0.59% — ×0.08 baseline. Low cards get folded preflop; never credit a played range with wheel combos at deck odds.
Pocket-pair concentration
AA is 2.6% of all deals but 26.2% of the BB 3-bet range — ×10.2. KK concentrates to 12.6% (×4.9), QQ to 7.0% (×2.7). Over a quarter of a tight 3-bet range is aces.
Methodology
Source: the 6-max 100bb PLO4 preflop solve (6max_100bb) — 16,432 canonical hand classes covering all 270,725 four-card combos.
- Open range: line RFI, actor BTN (folded to the button; node path [0, 0, 0]). Width 48.6% of hands.
- 3-bet range: line 3BET, actor BB vs a BTN open (node path [0, 0, 0, 40100, 0]). Width 9.4% of hands.
- Decode: Two uint8[16432] arrays per entry: raise freqs then call freqs. frequency = byte / 200.0 The raise block supplies each class's action frequency.
- Counting: every figure is an exact weighted count over all 270,725 combos — each combo weighted by its class's action frequency (dealt = uniform weight 1). No Monte Carlo anywhere.
- Boards: combos containing a board card are removed before counting; percentages are shares of the remaining weight.