Why Pâsur Cards Add Up to 11 — The Math Behind a Persian Card Game

Once you know the rules of Pâsur (پاسور), the question that nags at most thoughtful players is: why 11? Scopa's matching variant uses 15. Chinese Ten uses, well, 10. Bastra uses face-value matching. Pâsur asks you to add your hand card to one or more pool cards and hit exactly eleven. Who came up with that, and why eleven specifically?

I'll get the disappointing answer out of the way first. We don't really know. The game's documented history (covered in The History of Pâsur) is short — it's a 19th-century import on a 19th-century deck — and the choice of target sum is not attached to any particular person, place, or surviving piece of writing. Iranians have several after-the-fact rationales, none of them airtight. The intellectually honest version of this article isn't "here's why 11 was chosen." It's: here's what 11 actually does in play, and why the game would feel different at any other number.

The good news is that the math is genuinely interesting. Eleven is not a random target. It does specific things to the structure of the game that 10 and 12 don't.

The deck, briefly

Pâsur is played with a standard 52-card deck. The number cards are Ace through 10, with the Ace counting as 1. Face cards (Jack, Queen, King) don't participate in sum captures — they have their own rules. So the cards eligible for the 11-rule are exactly the values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

That set — the integers 1 through 10 — turns out to matter a lot. The choice of capture target is tied to it.

The five-pair property

Here's the cleanest argument for why 11 is interesting. Every number card from 1 to 10 has exactly one cross-rank partner that sums to 11:

Card	Partner
Ace	10
2	9
3	8
4	7
5	6
6	5
7	4
8	3
9	2
10	Ace

Five clean two-card pairs. No card pairs with itself. No card is left out. Every value from 1 to 10 has exactly one matching rank that completes an instant capture.

This property is unique to the target 11 with ranks 1–10. Try any other number:

Target 10: pairs are (1,9), (2,8), (3,7), (4,6), and 5+5. The 5 has no cross-rank partner — it can only pair with itself. The 10 (your largest card) has no partner at all without using zero, which doesn't exist in the deck.
Target 12: pairs are (2,10), (3,9), (4,8), (5,7), and 6+6. The Ace has no two-card partner. The 6 again pairs only with itself.
Target 13: (3,10), (4,9), (5,8), (6,7). Ace and 2 are stranded with no two-card partner.

Eleven is the only target where the small cards (Ace, 2, 3) and the big cards (8, 9, 10) all have direct cross-rank partners. Every card matters. There is no "useless rank."

If you've ever played a hand of Pâsur and noticed that you can almost always make some capture if the right card hits the pool, that's not luck — it's a structural property of choosing 11 as the target.

What the multi-card sums add

Two-card 11s are the headline, but most captures in real games involve three or more cards. The 11-rule allows your hand card plus any number of pool cards to add to 11. So:

1 + 2 + 8 = 11
1 + 4 + 6 = 11
2 + 3 + 6 = 11
3 + 4 + 4 = 11
1 + 1 + 9 = 11
1 + 2 + 3 + 5 = 11
1 + 1 + 1 + 8 = 11

The number of distinct subsets of the multiset of pool cards that sum to 11 grows quickly with pool size. At a typical mid-round pool (5–8 cards), most cards in your hand will have multiple legal captures, and you have to choose between them. This is where Pâsur's tactical depth lives — not in whether you can capture, but in which capture you should take. (Pâsur Strategy walks through real worked examples.)

The choice of 11 as target does something quiet but important here: 11 is small enough that subsets of 3–4 small cards regularly hit it, but large enough that not every combination works. A target of 7 would mean only 1+2+4 or 1+3+3 or 2+2+3 — a thin combinatoric space. A target of 17 would require so many cards in combination that the pool would have to be huge before captures became likely. Eleven sits in a sweet spot where 2-, 3-, and 4-card captures are all common.

Why not 10?

The most natural alternative target is 10, used by Chinese Ten and similar fishing games in East Asia. Why didn't Pâsur take 10?

A few structural reasons:

The 5 problem. With target 10, the only two-card capture for a 5 is another 5. There are four 5s in the deck. So 5s are awkward — they pair only with themselves, which means a 5 in your hand and a 5 in the pool capture each other, but a 5 in your hand and a 6 in the pool can never form a two-card capture. The flow of the game would be much more lopsided around mid-rank cards.
The 10 problem. With target 10 and ranks 1–10, the 10 itself has no two-card partner (you'd need a zero). It would have to be captured via multi-card sums (10 captures 1+2+3+4 or 5+5 or similar), which makes 10s into awkward end-of-pool cards.
The aesthetic. Persian card-game tradition assigns special weight to the 10 of Diamonds (3 points!) and to the 2 of Clubs (2 points). With target 11, those two cards are direct partners — Ace and 10, 9 and 2 — and the whole numerology of the scoring lines up. With target 10, the bonus cards are stranded relative to the capture target.

So 11 isn't arbitrary. It's the smallest target that gives every card 1–10 a cross-rank partner.

Why not 12 or 13?

You could ask the same question on the high side. Why not 12? Or 13, the number of ranks?

Twelve has the same problem in mirror image. The Ace has no two-card partner under target 12 in a 1–10 deck. (Ace+11 = 12, but there's no 11 in the deck.) So Aces become awkward — they capture only via multi-card sums. That's tactically interesting in its own right, but it strips Aces of their snappy two-card power.

Thirteen is worse: both Ace and 2 are partnerless. You'd have a deck where the smallest number cards can never form a two-card capture. That's a very different game. (It's also the game Chinese Ten's target if you flipped it: kind of a coincidence.)

There's a particular elegance to the way 11 falls out as the smallest workable target. Take ranks 1 to N. The smallest target T such that every rank has a cross-rank partner in 1..N is exactly T = N + 1. With ranks 1–10, that's 11. With ranks 1–7 (a Scopa deck minus face cards), it'd be 8. With ranks 1–9, it'd be 10. Pâsur uses the standard 52-card deck where the highest number rank is 10, so the natural target is 11.

This may genuinely be why 11 was chosen — by whoever made the choice, in 19th-century Iran, on the cards they'd just imported. It's the smallest workable target where the math holds together.

The Persian rationales

Iranians have always assigned meaning to the number 11 after the fact. The most common one is Haft-o Chahâr Yâzdah — seven and four, eleven. This phrase combines the Haft Khâj (the 7-club bonus) and the Chahâr Barg (the 4-card hand size) into a mnemonic ending at Yâzdah (eleven). It's neat, but it's almost certainly post-hoc — the rule didn't get its target because 7+4=11; the rule has 11 as a target and people noticed 7+4=11 and built a rhyme.

A few other Persian numerologies attach to 11. Eleven is sometimes treated as a number of completion or transition — between the 10 fingers and the 12 hours, between the visible and the abstract. None of these has solid documentary backing as a reason for the rule. They're cultural folk-wisdom layered onto the game after the fact.

I'd treat the Persian rationales as charming side-notes rather than as historical explanations. The deeper reason Pâsur uses 11 is mathematical: it's the simplest target that makes the whole 1-through-10 deck combinatorially complete.

What 11 produces in play

Here's the practical upshot for someone sitting at a Pâsur table.

Every hand has captures available. Because every value 1–10 has a partner that sums to 11, almost any reasonable pool will offer a capture for almost any hand. Trailing — playing a card you can't capture with — is the exception, not the rule. That keeps the game flowing forward.

Mid-rank cards (4–7) are the most flexible. They have the most multi-card combinations available. A 5, for example, captures: a 6, or 1+4, or 2+4, or 3+3, or 1+1+4, or 1+2+3, or 1+1+1+3, or 1+1+2+2, or 6 stripped down by even more options, and so on. By contrast, a 10 captures only an Ace, or 1+1+1+1+1+1+1+1+1+1 (which never happens). Mid-cards do the heavy lifting.

Aces and 10s are tactically opposite. An Ace pairs with a 10 — and the 10 of Diamonds is a 3-point bonus card — which gives Aces inherent tactical value. The Ace's only two-card capture is also the most rewarding. By contrast, a 10 in your hand is hunting for an Ace, and Aces are eaten quickly. Late-round 10s often end up trailing.

The 2♣ shows up everywhere. The 2 has nine different multi-card combinations that sum to 11 (1+8, 1+1+7+... and so on). Combined with the 2♣ being a 2-point bonus and a club, it's worth chasing in nearly every situation.

These tactical patterns aren't accidents. They emerge from the fact that 11 is the minimal target that lets the deck's full range of values participate.

So is 11 special?

Yes, but in the way that "the speed of light in vacuum" is special — not because someone chose it for mystical reasons, but because the rest of the system constrains it. Given a standard 52-card deck with number values 1–10, the smallest target sum that lets every rank capture cleanly is 11. Whoever first played this game in 19th-century Iran landed on the smallest workable answer to the question "what target sum makes a fishing game with this deck?"

Or maybe they didn't. Maybe someone with a Russian deck just picked 11 because their grandmother liked the number, and the math worked out. We don't know. The honest historical record is silent.

What we do know is: the math is good, the rule produces an elegant tactical game, and the choice has stuck for over a century in Iranian living rooms. If 11 was chosen by accident, it was a fortunate accident.

For more on the actual game-history side of this question, see The History of Pâsur. For how the 11-rule plays out in practice — including the tactical dance around the 2♣ and the Haft Khâj — see Pâsur Strategy and How to Win the Haft Khâj. And if you'd like to test the math against a live opponent, the rules are implemented exactly at playpasur.com.