Five anchors · two algorithms · one sanity check
This is the crux skill behind Hand Analyser's §2 — how often you actually win: estimating your equity against a range before you ever open the tool. The numbers below are ballpark anchors for memorization, not exact — Hand Analyser computes the precise figure for your exact cards, board, and range every time. Use this page to build the habit; use the tool to check your work. Preflop and postflop each get their own short algorithm below. Work through it, land on a number, then run the spot for real.
Before you adjust for anyone's actual range, anchor on your hand's equity against a totally random hand — a fixed number your two hole cards alone determine, no board or range needed. Real preflop ranges are always narrower than "any two cards," so your equity against someone's actual range sits at or below this number, never above it. Two formulas below, one for pairs and one for everything else, both simple enough to run at the table — no memorizing 169 numbers.
Rough by design — trades some accuracy for arithmetic you can actually do at the table. Mean error against the real 169-hand table: ~1.8pt, worst case ~6pt (about 1 hand in 25 misses by more than 5pt). See the exact number for all 169 hands at once, colored by which position opens each one, in the Range Chart.
Tightening a range doesn't cost every hand the same amount, and the pattern is not "pairs and big cards are safe, everything else is fragile." It's driven by whether a hand's vs-random number is real strength or borrowed from beating pure junk — measured against 20+ hand types run through the actual simulator, not assumed.
| Your hand | Tight10–15% | Medium15–30% | Wide30–50% |
|---|---|---|---|
| Elite — AA, KK, or AQ+an ace with a queen-or-better kicker | −5 pts−0 to −11 | −3 pts−0 to −7 | −2 pts−0 to −5 |
| The trap — one card nine-or-higher, no pair, no acee.g. KQ, KJ, KT, QJ, JT, J9, T9 | −20 pts−15 to −26 | −15 pts−10 to −20 | −10 pts−7 to −14 |
| Everything else — other pairs, any weaker ace-x, or two cards eight-or-undere.g. 99, A5o, 76s, 45o | −18 pts−8 to −28 | −11 pts−5 to −18 | −6 pts−3 to −10 |
The bold number is the midpoint — a good single-figure default. The lighter range below it is the full simulated spread, and which end of it a given hand actually lands on is not simply "bigger cards land narrower" — see the finer breakdown below for exactly which hands land where and why. The trap row is the one intuition gets wrong: KTo or JTs look like normal, playable hands, but almost all of their vs-random equity comes from simply out-ranking weak junk — exactly what a real range doesn't contain. They lose more than a mediocre pair or a weak ace does, even against a wide range. A big pair or a good ace, by contrast, is winning on real structural strength (a made hand, a dominant kicker) that persists no matter who's actually in the range.
Each row above is itself an average over several structurally different hands. Checked against the simulator, splitting them one level finer moves the pull a few points off that row's own midpoint (tight / medium / wide, shown on the right of each line below) — useful for seeing why a correction is needed, even if it's more than you'd track by hand:
Barely dominated by anything a real range plays.
Loses meaningfully to the range's own share of AK.
Its high ceiling leans on beating other broadway hands and pairs — exactly what a real range, especially a tight one, is stacked with. Still the stronger hand in the end (true equity stays above the rest of the trap row) — it just gives up more points to get there.
Lower ceiling to start, so less room to fall against a tight range — but the real spread of kickers costs more once the range widens.
Still overpair-capable against a real range — the most exposed tier of any pair, not the biggest ones (QQ itself is fine; 99/88/77 give up the most).
Low ceiling to begin with; wins mostly by hitting a set, not by staying the best pair.
Kicker is close enough to big-ace territory to hold up.
Weaker kicker gives up more — though the very bottom (A2–A5) claws a little back on hidden wheel-straight backup.
Positive = pulls more than the row's own midpoint above; negative = pulls less. Big pocket pairs (AA/KK) and low unpaired hands (72o-type) don't get a row here — AA/KK differ too much individually to average usefully (AA barely needs a correction at all; KK needs a real one), and low unpaired hands already scale smoothly with hand strength, no split needed. Full worked math for any specific hand is in the Equity Trainer's "How the heuristic got its number" breakdown after each preflop reveal.
Each extra opponent is an independent chance to already have you beat, so what compounds is the fraction of your ceiling you keep, not the points you lose. Adding the individual pulls from the table above always overstates your equity once more than one opponent is live.
This is still an approximation, not a precise number — it only tracks "who's still ahead," which understates how much a real multiway pot divides between more live hands even when you stay the likely winner. Treat the result as a floor and check it against a real tool when it matters.
Points to add on top of the keep-fraction pull from step 5 above. Same idea as the single-opponent table, but split one level finer — "elite" and "everything else" each turned out to hide multiple hand shapes that need very different corrections once more than one opponent is live (AA barely notices a second opponent; AQo notices a lot).
| Hand shape | Tight2 / 3 opp | Medium2 / 3 opp | Wide2 / 3 opp |
|---|---|---|---|
| Big pocket pairAA, KK | +7 / +11 | +9 / +13 | +9 / +17 |
| Big aceAQ+, AK | +18 / +26 | +16 / +25 | +15 / +24 |
| The trapone card nine-plus, no pair, no ace | −4 / −6 | +1 / −1 | +6 / +5 |
| PairQQ–22 | +1 / −1 | +7 / +7 | +13 / +17 |
| Weak aceA9o–A2o and similar | +7 / +5 | +11 / +12 | +14 / +18 |
| Low, unpairedtwo cards eight-or-under | −10 / −12 | −3 / −5 | +4 / +4 |
Calibrated by running this site's own simulator across thousands of spots per row, then validated on held-out hands never used to fit the numbers — mean error vs. the keep-fraction step alone: trap 3.9→2.6pt, big pair 11.2→4.7pt, big ace 20.8→1.5pt, pair 8.4→2.7pt, weak ace 11.7→1.2pt, low unpaired 5.8→2.1pt. 4+ opponents: reuse the 3-opponent column as a floor — no calibration data past that yet. Mixed opponent widths: average each opponent's own column, not the widest one — tried "widest decides" first and it overshot badly on tight+wide mixes.
A separate, faster pattern-match for common matchups — not part of the ceiling/pull algorithm above. Match your hand's relationship to a typical range hand against the nearest one of these, then adjust from there.
| Matchup | Favorite's equity |
|---|---|
| Pair vs. two live overcardse.g. JJ vs AKo — the classic "race" | ~55% |
| Pair vs. a smaller paire.g. TT vs 55 — no overcards live for the small pair | ~80% |
| Same top card, better kickere.g. AKo vs AQo — domination | ~74% |
| Two big cards vs. two smallere.g. AKo vs QJs — not dominated, just bigger | ~62% |
| Small suited hand vs. a big paire.g. 87s vs AA — preflop, gets crushed | ~80% |
These shift a few points with exact blockers and suits — treat them as anchors to interpolate from, not fixed truths. Hand Analyser's own "Doing this in your head" box regenerates these five fresh from your actual hand every report; watch them enough times and the numbers above stop being something you memorized and start being something you know.
Bare equity is where you'd stand if no more cards ever came — your made hand right now against a typical range hand. Real equity moves from there based on whether you're ahead or behind, how many real outs you have, and how many cards are left. Checked against the simulator across thousands of flop and turn spots, not assumed: the classic "just add outs × 4" oversells it by roughly half once you're weighing a whole range instead of one hand.
| Your outs | Ahead nowflop | Ahead nowturn | Behind nowflop | Behind nowturn |
|---|---|---|---|---|
| Few 0–4, e.g. a gutshot alone | −13 | −8 | −7 | −3 |
| Some 5–9, e.g. an open-ender or flush draw | −10 | −6 | +12 | +4 |
| Many 10+, e.g. a combo draw | −1 | −3 | +30 | +15 |
Points to add to (or subtract from) bare equity. Ahead is always negative — that's their outs eating into your lead, not yours. Counter-intuitively, having a lot of extra outs while already ahead barely costs anything, because those same outs double as redraws if they do catch up; it's being ahead with almost no redraw that bleeds the most. Behind is the familiar case — more outs, more equity — just not the full rule-of-4-and-2 amount once weighed against a real range.
| Draw | Outs | Flop → river | Turn → river |
|---|---|---|---|
| Flush draw | 9 | ~36% | ~18% |
| Open-ended straight | 8 | ~32% | ~16% |
| Gutshot | 4 | ~16% | ~8% |
| Two overcards | 6 | ~24% | ~12% |
| Combo draw (flush + straight) | 12–15 | ~50%+ | ~25–30% |
The rule of 4-and-2 is deliberately rough — it runs a little high at two-cards-to-come and ignores outs that also improve them. treat as an estimate