Durak Card Game
Play Durak, plus the arithmetic: a trump attack is twice as hard to answer, and the card you defend with can extend the attack against you.
Beat a card with a higher one of the same suit, or with any trump — but a trump can only be beaten by a higher trump. Beat everything and the table is thrown away; fail and you pick it all up. While attacking you may add any card whose rank is already on the table. Everything runs in your browser; nothing is uploaded.
A trump attack is about twice as hard to answer
A card is beaten by a higher card of its own suit or by any trump — unless it is a trump, in which case only a higher trump will do. That single exception is worth an enormous amount, and it is exact arithmetic rather than a simulation: the defender holds six of the other thirty-five cards, so this is a hypergeometric count.
| Attack card | Answered — plain suit | Answered — trump |
|---|---|---|
| 6 | 98.86% | 81.76% |
| 7 | 98.33% | 76.79% |
| 8 | 97.61% | 70.73% |
| 9 | 96.66% | 63.42% |
| 10 | 95.40% | 54.64% |
| J | 93.78% | 44.17% |
| Q | 91.71% | 31.76% |
| K | 89.09% | 17.14% |
| A | 85.82% | never |
| mean | 94.14% | 48.94% |
The average plain card is answered nineteen times in twenty; the average trump barely half the time. Across a random card from the whole pack — three quarters plain, one quarter trump — a single attack is answered 82.84% of the time.
The bottom row is the one worth carrying. The ace of trumps is not merely hard to beat — it cannot be beaten, and that zero is exact rather than rounded, because no card in the pack outranks it. No plain card is ever in that position, however high, since every one of the nine trumps answers it.
And beating a card can hand the attacker another one
The attacker may add any card whose rank is already on the table — and the table includes the card you just defended with. So the act of beating a card can extend the attack against you. Over 194,262 opening bouts:
| Of every opening bout | Share |
|---|---|
| some legal answer arms the attacker | 68.3% |
| …and a different legal answer avoids it | 56.6% |
| …and every legal answer arms them | 11.7% |
So it is neither "always avoidable" nor "unavoidable". The trap is live in about two bouts in three, and five times out of six there is another legal card that dodges it — but in 11.7% of bouts every answer you have arms them and there is nothing to be done. That is what makes it worth a glance rather than a rule: it is a choice that usually exists, and most players never notice it is a choice.
The board above marks your defending cards when they would open a new rank for the opponent, so you can see the choice as it happens. The frozen figures are re-derived at build time on 19,398 deals the table has never seen: 68.3% armed and 11.5% unavoidable.
How to use
- Beat a card with a higher one of the same suit, or with any trump.
- A trump can only be beaten by a higher trump.
- While attacking, add any card whose rank is already on the table.
- Beat everything and the table is discarded; fail and you pick it all up.
- Watch for the marked cards — they open a new rank for your opponent.
Frequently asked questions
How does beating a card work in Durak?
A card is beaten by a higher card of the same suit, or by any trump at all. The exception is that a trump can only be beaten by a higher trump — no plain card, however high, can touch one.
How much stronger is a trump attack?
About twice as strong, and the figure is exact rather than simulated. A defender holding six of the other thirty-five cards can answer the average plain card 94.14 per cent of the time and the average trump only 48.94 per cent. Across a random card from the whole pack it is 82.84 per cent.
Is the ace of trumps really unbeatable?
Yes, and exactly so rather than merely usually. No card in the pack outranks it and no plain card can touch a trump, so the chance of an answer is zero. No plain card is ever in that position however high, because all nine trumps answer it.
Does it matter which card I defend with?
More than most players notice. The attacker may add any card whose rank is already on the table — and the table includes the card you just defended with. Over 194,262 opening bouts, some legal answer would open a new rank for the attacker in 68.3 per cent of them.
Can I always avoid arming the attacker?
Usually but not always. In 56.6 per cent of bouts a different legal answer dodges it, so five times out of six the trap is real and avoidable. In the remaining 11.7 per cent every card you could legally defend with opens a new rank and there is nothing to be done.
What is the largest attack possible?
Six cards, the size of a starting hand, and the attack can never exceed the number of cards the defender still has to answer with. Reaching six needs the ranks to keep matching, which is why the cards the defender plays matter — they are what supply new ranks.
Does this send anything anywhere?
No. Every hand is dealt and played in your browser, and nothing is uploaded.
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