Shaheen Acheche

I love creating stuff.

3 minute read

the incredible depth of the Chkoba (a traditional tunisian card game)

I’m a huge fan of chkobba. It’s by far my favorite card game, and I love playing it with my grandmother, who herself learned it from my great-grandfather—tracing the game back to the 19th century in our family.

At the start of each round, after the cut, the first player draws a card and decides whether to keep it or discard it. Generally, if the card is weak (Ace, 2, or 4, for example), players tend to discard it. If you keep the card, you draw 2 more cards to complete your hand. The second player then deals themselves 3 cards and places 4 cards face-up on the table.

My question: From which card is it profitable to keep the first drawn card?

As with any good question, we first need to clearly define the problem. I define “profitable” as the card that allows me to capture the most cards (and thus earn the most points). I’m not considering the special cases of 7s and diamonds, which are tied to three other ways of scoring points (dinari, barmila, and sab3a el haya). So, “profitable” here simply means: which card allows me to earn the most points on average.

I wrote a short Python script to investigate this. For those interested, you can find the code on GitHub. With this script, I simulated 2 million first rounds and collected the statistics. This is essentially a Monte Carlo simulation, for those familiar with the method.

Disclaimer: When I play a card, I can either capture a card of the same value or capture a combination of cards. In the case of a combination, I always choose to capture the maximum number of cards possible.

My Findings (Math Ahead!)

  1. The expected number of cards captured, based on the first card drawn (and kept), follows a non-linear law (a second-degree polynomial fit works very well, with R² = 0.999). However, this is just a fit; the underlying distribution is more complex. In other words, the average number of cards you can capture with the first card drawn is not proportional to its value. This makes sense when you consider the number of possible combinations for each card. A 2, for example, can only capture another 2 or two Aces. A King, on the other hand, offers many more combinations. In fact, every turn in chkobba is a variant of the subset sum problem, which is NP-complete and becomes increasingly complex as the card value increases. In chkobba, the highest card, the King (el rey), is only worth 10, so it remains manageable for both computers and human brains. From the Queen onward (inclusive), keeping the card allows you to capture an average of at least one card (1.06 cards for the Queen, 1.36 for the 10).

  2. If we look at the probability distributions of the number of cards captured based on the value of the first card drawn, three broad categories emerge:

    • Weak cards (Ace, 2, 3): These don’t allow you to capture many cards (certainly fewer than the table cards). The probability of capturing at least one card ranges from ~30% to 38%.
    • Mid-range cards (4, 5, 6, 7): These show a gradually increasing efficiency. The 7 captures an average of 0.93 cards, with a ~63% chance of capturing at least one card. Given the central role of the 7 in other chkobba rules, I’d argue it’s worth keeping from the 7 onward—even though, technically, stronger cards exist.
    • Strong cards (Queen, Jack, King): These have the highest capturing power, averaging more than one card captured. The Queen captures at least one card 64% of the time, while the King does so 75% of the time!

Conclusion

If we ignore other scoring methods (dinari, barmila, sab3a el haya), it’s best to keep your card starting from the Queen. However, since these rules do exist and the 7 plays a central role, I personally keep cards starting from the 7. The 6 can also be interesting, but I don’t keep it—you’ve got to take risks in life!

It’s also funny to note that most chkobba players already play optimally. Simulating 2 million first rounds to reach a well-known conclusion isn’t exactly groundbreaking. Still, I’m glad we now have quantitative insights into the advantages of each card.

What about you? What’s your chkobba strategy? Do you keep the 6?