Tianxia

In the board game Tianxia there is a phase in which the nomads descend from the North. There are four armies, each with its own strength track and distance from China.
When they reach the end of the track separating them from the players’ fortifications, a battle is triggered.

The number of advances and the strength of the nomads are determined by a deck of cards. Each round, a card is drawn indicating how many steps to advance and how much to increase the strength of each nomad army.

During setup, players choose which deck to use: a red one (more aggressive) or a white one (less “difficult”). This choice influences the overall behavior of the invaders throughout the game.

Verifying the difference in “aggressiveness”

In this analysis we want to understand concretely what “aggressiveness” means for the nomads and how the game’s difficulty changes depending on the selected deck.
We conducted a small statistical analysis which does not claim to define personal play experience, but provides numerical data on nomad behavior.

Monte Carlo analysis approach in Tianxia

To evaluate nomad behavior, we used a Monte Carlo method, simulating the drawing of the four cards used during a game and virtually updating the advancement tracks.

The experiment is repeated from 100,000 up to 1,000,000 times, in order to obtain a large sample suitable for reliable statistical analysis.

Code sharing and peer-to-peer review

The quality of the results depends on the soundness of the chosen model. The simulation code has been published on GitHub, where anyone can inspect it, provide feedback, or propose revisions.

🔗 Tianxia Battle Simulation – GitHub repository

Simulation structure

The simulation follows these steps:

• Shuffle the 16-card deck.
• Repeat 4 times:
  • Draw the top card of the deck.
  • Update each army’s track (maximum strength 15). In the fourth round, each army advances two additional steps compared to the value shown on the card.
  • Check whether one or more armies have reached space 6 (battle trigger):
    • If so, record which army fought and at what strength.
    • Reset the army to the starting position specified for the next round.

The process is repeated for the total number of simulations, after which statistical analysis is performed.

Results and analysis

We analyze two main aspects:

• Battle frequency per game.
• Average army strength at the moment of battle.

Battle frequency

Regardless of the deck used, each army enters battle approximately 1.72 times per game.

Strength distribution in battle

Army strength varies significantly depending on the selected deck.

Example interpretation:

• Red deck: 23.55% probability of strength 15, mean 12, standard deviation 2.6
• White deck: 6.62% probability of strength 15, mean 11, standard deviation 2.4

Cumulative probability and further details:

• Red Deck: more variable damage (σ = 2.62), more predictable (H = 3.18 bit), concentrated on extreme scenarios.
• White Deck: more stable damage (σ = 2.45), less predictable (H = 3.32 bit), evenly distributed around medium values (9–14).

Conclusions

The statistical analysis shows that the Red deck, as stated in the rulebook, leads to more challenging battles, where nomad armies reach higher strength.
However, the expected number of battles in a game does not change depending on the chosen deck.

The analysis considers only the effect of the cards, as defined by the Tianxia rules.
The game includes additional effects that may modify army strength. Player interactions with the nomads are not taken into account.

Finally, this statistical analysis is purely recreational and cannot provide any feedback on the actual play experience depending on the chosen deck.