---

🎯 Core result
- Chance of winning a single game:  
\[
\frac{1}{201} \approx 0.497\%
\]

- Chance of not winning a single game:  
\[
1 - \frac{1}{201} = \frac{200}{201}
\]

- Chance of not winning across 10 games:  
\[
\left(\frac{200}{201}\right)^{10} \approx 95.2\%
\]

- Chance of winning at least one game:  
\[
1 - 0.952 \approx 0.048 = 4.8\%
\]

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📌 What this means in practice
- In a hall with 201 players, the odds are stacked simply because the pool is large.  
- Over 10 games, you’re still fighting the same ratio each time, so the cumulative chance only rises to about 1 in 20.

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🧠 Want to explore variations?
I can calculate your odds if you:  
- Play more cards  
- Play more games  
- Face fewer/more players  
- Want the probability of winning multiple games  

Which scenario do you want to test next?