Champion Pool Math

Understanding the exact numbers behind TFT's shared champion pool turns vague intuition into precise decision-making. Every purchase, sale, and player elimination changes the probabilities in your shop. This guide covers the math that Diamond+ players use to evaluate whether chasing a unit is realistic or reckless.

Pool Sizes by Cost Tier

Each individual champion has a fixed number of copies shared across all eight players:

These are per-champion numbers. If a set has 13 different one-cost champions, the total one-cost pool is 13 x 22 = 286 units. The total pool size for a tier matters because your shop draws from the entire tier, not from a specific champion.

Calculating Your Odds

When a shop slot rolls a particular cost tier, it selects a random copy from all remaining copies of that tier in the pool. The probability of seeing a specific champion in a single slot is:

P(specific champion) = copies_remaining / total_copies_remaining_in_tier

Worked Example

Suppose you are level 8, looking for a specific 4-cost champion. The set has 12 different 4-cost champions, and you already own 3 copies of your target. No other player has bought any copies of it.

• Copies of your target remaining in pool: 10 - 3 = 7
• Total 4-cost copies in pool: (12 x 10) - 3 = 117
• Chance per 4-cost slot: 7 / 117 = 5.98%
• At level 8, each shop slot has a 22% chance of being a 4-cost
• Chance a single slot is your specific champion: 0.22 x 0.0598 = 1.32%
• Chance of seeing it in at least one of 5 slots: 1 - (1 - 0.0132)^5 = 6.4%
• Expected shops to see one copy: roughly 15-16 shops (30-32 gold)

This means spending 30 gold on rolls gives you roughly a coin-flip chance of finding one copy. Spending 50 gold (25 shops) raises it to about 80%.

How Contestation Destroys Your Odds

The impact of contestation is severe, especially for higher-cost units where the pool is small.

4-Cost Contestation Example

Consider a 4-cost champion with 10 total copies. You have 2 copies and need 1 more for a two-star:

When 7 copies are spread across other boards, only 1 remains in the pool. Your odds have dropped to one-eighth of the uncontested rate. Rolling 50 gold might not find it.

The Golden Rule

Fewer copies remaining in the pool = exponentially harder to find. This is not a linear relationship in practice because as specific champion copies decrease, they become a smaller fraction of the total tier pool. The odds degrade faster than you might expect.

When the Math Says to Pivot

There are clear mathematical signals that you should abandon your current target:

• 5 or fewer copies of a 4-cost remain in the pool (you have 2-3, others have 5+): Your per-shop odds have dropped to the point where you would need 50+ gold of rolling for a reasonable chance. Pivot to an uncontested carry.
• 3 or fewer copies of a 5-cost remain: With only 9 total copies, heavy contestation makes two-starring nearly impossible.
• You have spent 40+ gold rolling and have not found a single copy: This is often a signal that the pool is more depleted than you realized. Scout other boards to count copies before spending more.

Eliminated Players Returning Champions

When a player is eliminated, all their champions return to the shared pool immediately. This creates quantifiable opportunities:

• If a contested player is eliminated holding 4 copies of a 4-cost you need, the pool suddenly has 4 more copies available. Your odds may double or triple.
• In the late game (4-5 players remaining), significant portions of the pool have been returned by eliminated players. This is why late-game rolling at level 8 or 9 can feel surprisingly generous -- the effective pool is larger than at the start.
• Track what eliminated players were holding. If you saw them with 3 copies of your target champion, you know those copies are now available.

Three-Starring: The Numbers

Three-starring a champion requires 9 total copies. The feasibility varies dramatically by cost tier:

Three-starring a 4-cost requires finding 9 of 10 copies, leaving only 1 in the pool. Any contestation makes it nearly impossible. Three-starring a 5-cost requires literally every copy in the game -- no other player can hold even one.

Key Takeaways

• The shared pool is finite and small for high-cost units. Every copy matters.
• Calculate your approximate odds before committing gold to rolling. If fewer than 5 copies of a 4-cost remain, the math is against you.
• Contestation has a compounding effect -- two players contesting is bad, three is catastrophic.
• Eliminated players returning champions to the pool is a real strategic factor. Track it.
• Three-starring 4-cost or 5-cost champions requires near-zero contestation. Do not chase these unless the lobby conditions are exceptional.