Ti4 Combat Calculator

Advanced Probability Engine for Twilight Imperium 4th Edition

What is a TI4 Combat Calculator?

A ti4 combat calculator is a specialized statistical tool designed for players of the board game Twilight Imperium 4th Edition. In the high-stakes galaxy of TI4, knowing whether your fleet of Dreadnoughts and Carriers can successfully take a planet or hold a system is the difference between victory and galactic obscurity. This tool calculates the exact probability of landing a specific number of hits based on the varying combat values and dice counts of your units.

Who should use it? Competitive players, strategy enthusiasts, and anyone who wants to move beyond “gut feelings” when committing their precious Plastic. A common misconception is that simply having more units guarantees victory. In reality, a single ti4 combat calculator check might reveal that your fleet has a surprisingly low chance of punching through a well-defended system with Planetary Shield and Meka units.

TI4 Combat Calculator Formula and Mathematical Explanation

The math behind a ti4 combat calculator is more complex than a standard binomial distribution because different units hit on different numbers (e.g., a Fighter hits on 9, while a War Sun hits on 3). We use a method called the Poisson Binomial Distribution, solved via iterative convolution.

Variable	Meaning	Unit	Typical Range
CV (Combat Value)	Number required to hit on a D10	Integer	3 to 9
N (Dice)	Number of dice rolled for that unit type	Integer	1 to 3
P(hit)	Probability of a single die landing a hit	Percentage	10% to 80%
E(H)	Expected number of hits (Mean)	Float	0 to 20+

The step-by-step derivation involves calculating P(hit) for each die: P(hit) = (11 - Combat Value) / 10. Then, we convolve these probabilities to find the distribution of total hits. If you have a Destroyer (9) and a Cruiser (7), the expected hits are 0.2 + 0.4 = 0.6 hits per round.

Practical Examples (Real-World Use Cases)

Example 1: The “Small Skirmish”

An attacker sends 2 Destroyers and 1 Cruiser into a system.
Destroyers hit on 9 (0.2 prob each), and the Cruiser hits on 7 (0.4 prob).
Total Expected Hits: 0.2 + 0.2 + 0.4 = 0.8.
Using the ti4 combat calculator, we find there is only a 55.2% chance of landing at least 1 hit. This might be too risky if the defender has a Dreadnought!

Example 2: The “War Sun Siege”

An attacker has 1 War Sun (rolls 3 dice hitting on 3).
P(hit) for each die is 0.8. Total Expected Hits = 2.4.
The ti4 combat calculator shows an 8% chance of missing entirely, a 99.2% chance of at least 1 hit, and a 51.2% chance of landing all 3 hits.

How to Use This TI4 Combat Calculator

1. Enter Unit Counts: Use the number inputs to specify how many of each unit type are in your fleet.
2. Adjust Combat Values: If you have technologies like Morale Boost or Plasma Scoring, adjust the “Hits On” value (e.g., change a 9 to an 8).
3. Verify Dice: Some units roll multiple dice (like the War Sun or Fragile fighters). Ensure the “Dice” field is correct.
4. Analyze Results: Look at the “Expected Hits” for the average outcome and the “Probability Table” to see your “fail rate” (the chance of 0 hits).
5. Strategy Adjustment: If your chance of landing the required hits is below 60%, consider bringing more units or using a tactical retreat.

Key Factors That Affect TI4 Combat Calculator Results

• Unit Technology: Upgrades like Dreadnought II or Carrier II don’t just add movement; they often improve combat values, drastically changing the ti4 combat calculator output.
• Action Cards: Cards like “Morale Boost” (+1 to rolls) effectively shift all combat values down by one, significantly increasing hit probability.
• Faction Abilities: The Jol-Nar have a permanent -1 to combat rolls, while the L1Z1X have better bombardment. These must be manually adjusted in the calculator.
• Promissory Notes: “Tecren Prophecy” or similar notes can provide situational bonuses that alter the math of a ti4 combat calculator.
• Number of Dice: Adding more dice (like the Argent Flight’s Destroyers) is often more effective than simply improving the hit value of a single die.
• Risk Tolerance: A 70% success rate in a ti4 combat calculator might be “good enough” for a minor skirmish, but for Mecatol Rex, you usually want 90%+.

Frequently Asked Questions (FAQ)

Does this calculator account for Anti-Fighter Barrage?

This ti4 combat calculator focuses on the main combat roll. For AFB, input your Destroyers separately to see their specific hit distribution against fighters.

What is a good “Expected Hits” value for a standard battle?

Generally, you want your Expected Hits to be equal to or greater than the number of units the opponent has. If they have 3 units, aim for 3.0+ on the ti4 combat calculator.

How do I factor in “Sustain Damage”?

Sustain damage doesn’t change hit probability, but it changes how many hits you can absorb. Use the ti4 combat calculator to see the chance of your opponent landing enough hits to bypass your sustain.

Why does the probability of 1+ hit stay high while 2+ drops off?

This is the nature of variance in a ti4 combat calculator. Even a single War Sun has a high chance of 1 hit, but getting 3 hits is a 50/50 coin flip.

Can I use this for Ground Combat?

Yes! Simply use the “Infantry” and “Mech” rows. The math for ground combat in Twilight Imperium is identical to space combat rolls.

Does Plasma Scoring add a hit or a die?

Plasma Scoring adds one additional die to one unit’s roll. In our ti4 combat calculator, you would increment the “Dice” field for your best unit by 1.

Are 10s always hits?

Yes, in TI4 a natural 10 is always a hit, regardless of modifiers. Our calculator assumes standard D10 logic.

Why use a calculator instead of just rolling?

A ti4 combat calculator allows for better planning during the Strategy and Status phases before a shot is ever fired.

Related Tools and Internal Resources

• TI4 Movement Guide – Calculate reach across the galaxy.
• Galactic Council Simulator – Predict voting outcomes.
• Tech Path Optimizer – Best tech for your faction.
• Resource Planner – Manage your influence and trade goods.
• TI4 Production Calculator – Calculate unit costs and capacity.
• Fleet Supply Manager – Monitor your command token usage.