Skeptics might say, “What an intellectual pastime! Durak is still Durak wherever you play it.” In fact, they are wrong. For example, former World Chess Champion Anatoly Karpov believes that a two-player Podkidnoy Durak is no less captivating than chess. In a one-on-one match, a lucky deal means little compared to precise mathematical calculation.
And how warming it is to think that this game has Russian roots! This pastime could only have arisen in Russia — after all, the first insult children learn is “durak.” The hero of Russian folktales is Ivan the Fool (Ivanushka-durachok). There are countless proverbs and sayings using this word in Russian: “You can’t teach all fools in the world,” “Teaching a fool is like treating the dead,” “A foolish head gives the legs no rest,” and many others. The game became widely popular in the 19th century. Today, the number of its variations is no less than that of preference-style games.
Of course, there is no official Russian Durak Players Association, let alone an international organization. Nevertheless, numerous fans meet from time to time at tournaments dedicated to the game. The most famous tournament is held annually on March 31, on the eve of April Fools’ Day.
Can probability theory determine your chances of winning?
Luck is nice, of course, but the outcome of any card match mostly depends on the player’s experience and skill rather than on luck.
As early as the 18th century in France, mathematicians coined the term “probability theory in games.” Its author was the well-known Blaise Pascal, who asked: “Can you win, for example, a dice match using mathematical knowledge?”
If you consider probability in a lottery with 49 balls where you must guess 6 correctly, the chance of success is 1 in 14,000,000 — practically impossible. A dice game gives a much better chance (a player wins roughly 16% of played matches). In roulette, luck favors a player in 1 out of 38 cases.
After careful analysis of card games, mathematicians concluded that winning them purely by chance — i.e., relying on a good deal — is almost impossible. In Durak, for instance, it’s practically impossible to determine at the start of a match who will win using only mathematical operations. As for the endgame, the situation hardly changes: a player with good memory, a small set of trumps, and skill can easily beat a luckier opponent.
Using probability theory against an opponent in Durak
It has long been no secret to professional players that knowing basic probability theory — the study of random variables and events — positively influences achieving your goals.
Let us consider this matter mathematically: the deck contains 36 cards, including 9 trumps. In a two-player game, one-third of the deck (12 cards) is used during the initial deal. From this it follows that players will hold roughly 3 trumps between them, plus one is visible on the table as the turned-up card. Thus, it’s easy to calculate that 5 trumps remain in the deck after the deal. One player typically holds 1–2 trumps, so 2–3 trumps are effectively known. Having this knowledge at the start of the game allows you to form a battle tactic immediately and then adjust it as the match progresses.
Note that each card a player draws without contest reduces their chance of drawing a trump by 43.5 percent. It’s simple: after the deal there are 23 cards left in the deck, of which 5 are trumps. That means there are roughly 4–5 ordinary cards per trump (23/5 = 4.6). Therefore, each trick taken together with your partner brings you closer to drawing a trump by 100/4.6 = 21.74 percent. Conversely, if you refuse to beat an opponent, you move away from that chance by the same amount while your opponent draws a new card. Also remember that while you are discarding an extra card, your opponent will have time to draw another. Thus, the cost of your passivity is 21.74 * 2 = 43.5 percent.
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