One card from a flush, and your opponent fires half the pot — call or not?
You meet this every session. Most people decide on “the hand feels okay” and then feed their stack to the other player on the river.
To get it right, most guides tell you to work out your equity first. But sitting at the table with three people waiting on you and your palms sweating, nobody is computing percentages. So at the table I only ask one question:
How often do I have to win for this call to be worth it?
This post covers that way of asking end to end, using only arithmetic you can finish at the table. If you are not yet solid on the four rounds of dealing and betting, read what Texas Hold’em is first and come back.
Every time you face a bet, it is only ever two numbers being compared, and the two are independent of each other:
- The price: how often this bet needs to win. Set entirely by your opponent’s bet size, and completely unrelated to what you are holding.
- The hand: how often your hand actually gets there. Set by your outs, and completely unrelated to how much he bet.
Both numbers are in the same unit — one time in how many — so they compare directly. What follows takes the spot from the opening line and works both numbers out step by step.
1. The Price First: How Often This Bet Has to Win
Pot 100, opponent bets 50, and it costs you 50 to see the next card.
First question: if I win, how much do I collect? The original pot of 100 plus the 50 he just bet, so 150. Second question: what do I pay? 50.
Pay 50 to win 150, a ratio of 3:1. That is your pot odds.
In plain terms: play this spot four times, lose three and win one, and I break even exactly. The three losses cost 50 each, −150; the one win is +150. So I need to win one time in four, and anything better than that is profit.
Notice what did not appear anywhere: a percentage.
A Three-Second Shortcut: Times = Pot ÷ Bet + 2
You do not have to derive it from scratch each time. The whole method is one rule:
Times = pot ÷ bet + 2
Half pot: 100 ÷ 50 = 2, plus 2 gives one win in 4. Two-thirds pot: 100 ÷ 66.7 = 1.5, plus 2 gives one in 3.5. The +2 is not a fudge either: you pay one unit, and the pot gains two units on top of the original (his bet and your call).
A simplification you often hear is “take the fraction of the pot he bet and add 2 to the denominator”. That only happens to work when the numerator is 1. For 1/2, 1/3 and 1/4 the numerator is 1, so 4, 5 and 6 come out right; but a two-thirds bet is not one in 5, and a three-quarter bet is not one in 6. With fractional sizes, the correct mental step is to invert the whole fraction, then add 2: 2/3 inverted is 3/2 = 1.5, plus 2 is one in 3.5; 3/4 inverted is 4/3 = 1.33, plus 2 is one in 3.33. When the numerator is 1, inverting gives you the denominator itself — the old shortcut looking right for 1/2, 1/3 and 1/4 is a coincidence, not a rule.
The moment the numerator is not 1, reading off the denominator makes the threshold look looser than it is: read 3/4 pot as one in 6 and you will think a flush draw at one in 5.2 clears it, when the real threshold is one in 3.33 and the call should never have been made. The error always points the same way — in your own favour — which is the most expensive kind. And an overbet has no denominator to read at all (is the denominator of a 1.5x pot bet 2?), so just do the division once.
Take the pot as 100; every row below is the same formula:
| Opponent’s bet | Win one time in | Equity required |
|---|---|---|
| 1/4 pot (÷ 25 + 2) | 6 | 16.7% |
| 1/3 pot (÷ 33.3 + 2) | 5 | 20% |
| 1/2 pot (÷ 50 + 2) | 4 | 25% |
| 2/3 pot (÷ 66.7 + 2) | 3.5 | 28.6% |
| 3/4 pot (÷ 75 + 2) | 3.33 | 30% |
| Full pot (÷ 100 + 2) | 3 | 33.3% |
| 1.5x pot (÷ 150 + 2) | 2.67 | 37.5% |
| 2x pot (÷ 200 + 2) | 2.5 | 40% |
Two-thirds and three-quarters are the two sizes you meet most, and they are also the two rows where the numerator is not 1 and the misreading happens (the two overbet rows are more honest about it — there is no denominator to read). Worth memorising outright: one in 3.5 and one in 3.33.
The right-hand column has exactly one use: at the table work in “one in N”, because there is no division involved; when reviewing hands or reading somebody else’s article, use percentages, because almost everything out there is written that way and you need to line up with it. The conversion is one step: required equity = 1 ÷ times. Half pot is 1 ÷ 4 = 25%, the same number the textbook formula — your call ÷ (pot + his bet + your call) — gives as 50 ÷ 200. Sizes not on the table work identically: pot ÷ bet + 2 for the times, then invert once if you want the percentage. The two columns are two spellings of one number, not two methods.
This is not an approximation, it is exact. It holds for any bet size, overbets included. But its exactness rests on four conditions, worth stating so it does not get misused:
- Heads-up, with only one player betting.
- “Pot” here means the pot before his bet — do not count the chips he just pushed in twice.
- Rake is ignored.
- It is the threshold for this bet only, and does not include what you will have to pay on later streets. That last one matters most, and section 3 is entirely about it.
The table also speaks for itself: from a quarter pot to a two-times pot, the threshold tightens from one in 6 to one in 2.5, and the required equity climbs from 16.7% to 40% — a factor of 2.4. Which is why somebody keeps betting big at you: he is not gambling, he is raising your threshold.
2. Now the Hand: How Often It Gets There
With the threshold known, look at your side of it.
Start by counting outs — the cards left in the deck that save you.
Back to the opening hand: two hearts in your hand, and two of the three flop cards are hearts. There are 13 hearts in total and you can see 4 of them (2 in your hand, 2 on the board), so 9 are still out there to complete your flush. Nine outs.
Converted into this post’s unit: roughly one in a bit over 5.
Why One Out Is Worth 2%
That figure is not memorised, it is derived. After the flop you can see 5 cards (your 2 plus the 3 on the board), which leaves 47 unseen out of 52 — call it 50 for mental arithmetic. So one specific card coming off the deck is 1 ÷ 50 = 2%.
One out is 2%, nine outs is about 18%, and inverting gives 1 ÷ 0.18 ≈ one in 5.5.
Calling 47 cards 50 deliberately inflates the denominator, which makes each out cheaper than it really is (the true value is 1 ÷ 47 = 2.13% and we write 2%), so “one out is 2%” applied to the next card is always on the conservative side and never hurts you — the mental 5.5 is slightly larger than the true 5.2, and in this unit larger is more conservative. Use 5.5 in your head at the table and the 5.2 from the table below when reviewing; both work, and the only difference is whether you have a chart in front of you.
Note that this 2% is about the next card, not both remaining cards combined. Section 3 takes up the difference immediately.
Common Draws, and How Often They Hit
Every number in this table is for the next card only, over those 47 — that is, “this call buys you exactly one more card”.
| Draw | Outs | Hits one time in |
|---|---|---|
| Flush draw | 9 | 5.2 (19%) |
| Open-ended straight draw | 8 | 6 (17%) |
| Gutshot | 4 | 12 (8.5%) |
| Flush + open-ender | 15 | 3.1 (31.9%) |
| Two overcards looking to pair | 6 | 8 (12.7%) |
| Pocket pair looking to set | 2 | 24 (4.2%) |
The rounding is deliberately one-directional: when in doubt, make yourself look worse. The four rows shown as whole numbers all round up — the open-ender’s true 5.88 becomes 6, the gutshot’s 11.75 becomes 12, two overcards’ 7.83 becomes 8, the pocket pair’s 23.5 becomes 24. These numbers get compared against a threshold, so rounding down would quietly loosen your own standard.
The remaining two rows (flush 5.22, flush + open-ender 3.13) keep a decimal instead of rounding up; less than 0.04 gets dropped, which does not flip a single one of the eight thresholds — but that is as far as it goes, and rounding further does damage, as the two boundaries below show. The percentage column always rounds down (19%, 17%, 8.5%, 31.9%, 12.7%, 4.2%), the same conservative direction as the times column.
Two rounding boundaries deserve naming:
- The open-ender written as 6 meets a 1/4-pot threshold that is also 6, which looks like a break-even. Its true 5.875 beats the threshold by 0.125 (with a pot of 100 and a call of 25, the EV is +0.53 chips), so it is a small profit — but only a small one, and treating it as break-even will not hurt you. The same fact in the language of outs: a quarter pot needs 8 clean outs, and an open-ender has exactly 8, scraping through on the line.
- Never lazily write the flush draw’s 5.2 as 5. The 1/3-pot threshold is exactly 5, so writing 5 turns a small loss into “break-even, so call”. Likewise, do not write the flush + open-ender’s 3.1 as 3; it clears the full-pot threshold of 3 by only 0.13.
The digit after the decimal point is not decoration, it is the answer in that row. If the decimals will not stick, remember the larger side: flush draw about five and a half, flush + open-ender about three and a half — rounding up is always the conservative direction and cannot hurt you.
One more thing to say up front: these are how often you hit, and hitting is not winning. When you are not drawing to the best flush, hitting it can still lose to a bigger one (how two flushes are compared is in the full hand rankings); when the board pairs, a flush loses to a full house; and “two overcards, 6 outs” is the dirtiest row of the lot — if the opponent already has two pair or a set, those 6 outs are mostly dead and the 8 is an optimistic ceiling. Only when you are drawing to the nuts are the two numbers close to equal; otherwise the real threshold is stricter, never looser. So clearing the threshold is necessary, not sufficient: you still have to ask whether the outs are clean and whether the opponent will pay you.
3. Does This Call Buy One Card or Two?
Section 1 said pot ÷ bet + 2 gives the threshold for the bet in front of you; section 2’s hit frequencies are all for the next card only. Those are the same point, and it deserves its own section, because it is the one place in the whole method that gets used wrongly.
What does that 50 buy? The turn card. Whether you get to see the river is a price he sets again later, and you pay again — so as long as there is more betting to come, the only number you may compare is the one-card number.
There is exactly one exception: the opponent is already all in and no more money can go in, in which case one payment buys both the turn and the river, and only then do the two-card numbers apply.
| Draw | One card | Two cards (opponent all in) |
|---|---|---|
| Flush draw | one in 5.2 | one in 2.9 (34.97%) |
| Open-ended straight draw | one in 6 | one in 3.2 (31.45%) |
| Gutshot | one in 12 | one in 6.1 (16.47%) |
| Flush + open-ender | one in 3.1 | one in 1.9 (54.12%) |
| Two overcards | one in 8 | one in 4.2 (24.14%) |
| Pocket pair | one in 24 | one in 11.9 (8.42%) |
The table incidentally demonstrates something counterintuitive: seeing one more card does not double your hit frequency, and the “one in N” does not simply halve. Half of the flush draw’s 5.2 is 2.6, but the real figure is 2.9; half of the gutshot’s 12 is 6, the real figure is 6.1; half of the flush + open-ender’s 3.1 is 1.6, the real figure is 1.9. (The pocket-pair row looks like a clean halving, which is an illusion created by the left column rounding 23.5 up to 24 — half of 23.5 is 11.75, and the two-card figure is 11.9, likewise a little more.) The reason is that two cards are not two independent chances: if the turn already got there, the river chance never gets used, so multiplying out counts the same event twice. The right-hand column has to be looked up; it cannot be derived from the left.
And something more important still: which column applies is not your choice, the situation decides it.
The most common beginner mistake is not miscalculating. It is using the number that assumes no further payment in a spot where more payment is obviously coming, arriving at a nice-looking answer, and calling all the way down.
Picking the wrong method costs more than getting the arithmetic wrong.
4. The Comparison: Two Numbers, One Unit
Before comparing, one thing to fix in place, because it is the easiest thing to get backwards in either direction: smaller is better. One in 5 is worse than one in 4, because you wait longer for it. That is the opposite of the intuition percentages give you.
Case 1: he bets half pot
The threshold is one in 4, my flush draw is one in 5.2. 5.2 is larger than 4, so I do not get there often enough.
Concretely: this call loses about 11.7 chips on average every time you make it, roughly 23% of the amount called. On the price in front of you alone, this hand cannot support it.
“Not enough” also comes in degrees. The same flush draw against a 1/3-pot bet loses only 1.42 chips, close to break-even; against half pot it is −11.7; against a two-times pot it is −104. So the tipping point does not land on a round bet size: the flush draw’s real dividing line sits between a quarter pot and a third of the pot — the end of section 5 lists the dividing lines for three draws at once.
Case 2: same hand, he bets only a quarter pot
Pot ÷ bet + 2 says I need to win only one time in 6. 5.2 is smaller than 6, so I get there more often than required. Call.
Same hand, not one out has changed, and the answer reverses — what changed is not the cards, it is the price. Which is why “the hand feels good” is never a reason.
Case 3: he makes it three-quarters pot instead
Threshold one in 3.33, flush draw one in 5.2, further off than against half pot, so fold without hesitating. This row has to be remembered, because it is where the old shortcut does the most damage: read as “denominator + 2” it looks like one in 6, and 5.2 is smaller than 6, so it looks callable — while the real threshold of one in 3.33 makes the call off by nearly a factor of two. (Two-thirds pot is the milder version of the same illness: the real threshold is one in 3.5, and reading the denominator gives one in 5, which makes an obvious fold look marginal.)
Same decision, framed once as “just barely off” and once as “not worth thinking about”.
5. So Do You Call the Half Pot or Not?
Three layers:
- He is already all in and no more money can go in: use the two-card number, one in 2.9 against a threshold of one in 4. Call, and clearly so.
- There is more betting to come: only the one-card number is allowed. Honestly, on the price in front of you this call loses money, about −11.7 chips a time. Making it work relies on implied odds — you are betting on extracting more from him after you hit. In this spot you need roughly 61 more chips, about 1.2 times the 50 you are calling, just to break even. Deep stacks, drawing to the nut flush, and an opponent who pays when you get there: call.
- Short stacks, not drawing to the best flush, an opponent who shuts down when the card comes, or another big bet expected on the turn: you cannot make it back. Fold.
That 61 in layer 2 carries three unspoken conditions that have to be remembered with it: you pay only this 50 with this hand and give up on the turn if you miss (paying for another street pushes the amount you need to recover higher); he really does pay you that 61 when you hit; and hitting means winning (see the end of section 2 again).
If you do miss the turn and face another half-pot bet, do not use “I have come this far” as a reason. Run section 1 again: pot 200, he bets 100, the threshold is still one in 4; and now 9 of the 46 unseen cards help you, one in 5.1, which is still not enough. That call loses about 21.7 chips, 1.86 times what the flop call lost — the threshold has not moved and your equity only nudges from 19.1% to 19.6%, while the price doubles. Calling the flop is fine, calling all the way to the river is not.
Layer 3 has one more variable that gets overlooked: OOP it is harder to realise your implied odds, because you do not get to decide whether to pay again. For that, go back to the full guide to position.
And do not treat implied odds as a universal exemption. Move one size up: against a full-pot bet the threshold is one in 3, and the two-card 2.9 only just squeezes past with less than 0.15 to spare, and only if he is already all in. Further up, past about 1.16 times the pot, even the two-card number fails — a 1.2x pot bet has a threshold of one in 2.83, and the flush draw’s true two-card figure is one in 2.86 (rounded up to 2.9 in the section 3 table), which no longer clears it. One card not enough, two cards not enough, and more money still to pay: implied odds do not rescue that. Fold.
One last set of numbers explains the whole thing at once. Solve the rule backwards and you get how many clean outs each size requires: a quarter pot needs 8 (7.83 exactly), half pot needs close to 12 (11.75 exactly), a full pot needs 16. It says the same thing the “one in N” figures say; one asks how often, the other how many, so use whichever comes more naturally.
Check the common draws against it: 9 outs for a flush and 8 for an open-ender only clear the quarter-pot column (the open-ender exactly on the 8-out line), and fail at every other size; a 4-out gutshot does not even reach the 8 outs a quarter pot demands, so not one of the eight sizes is callable — even at the smallest, a quarter pot, that call loses 12.2 chips on average, which is worse than the 11.7 a flush draw loses calling half pot.
Turned around once more it is clearer still. The largest bet each draw can afford to call — the three numbers most worth taking away from this post:
- Flush draw, 9 outs: 0.31 of the pot, between a quarter and a third.
- Open-ender, 8 outs: 0.26 of the pot, a shade over a quarter.
- Gutshot, 4 outs: 0.10 of the pot, about a tenth, which in practice means never enough.
Which is to say ordinary draws are already dead at a third of the pot — not because I picked awkward sizes, but because “one bet buys one card” is expensive in itself. That feeling at the table that a flush draw is strong enough to call comes from the two-card number, and the two-card number only counts when somebody is all in.
What you can compute at the table is the threshold (pot ÷ bet + 2) and the hit frequency from the chart, and that takes three seconds. What you cannot compute there is the other two things: whether you were honest about counting only one card, and whether the opponent actually pays on the river. That part belongs to reviewing hands afterwards.
So if only one thing sticks, make it this: the hard part was never the arithmetic, it is admitting you just used the number that looked nicer. Ask how often the bet has to win, then how often the hand gets there, and only when both are done does feel get a turn.
The quickest way to find your own leaks is to go back over the calls that “felt fine at the time” and check them one by one against the answer. That is exactly what I started writing RushCraft for: record the hands and look afterwards at how many of those calls were really worth it. The result is not flattering, which is precisely where improvement starts.