Champion Pool Math (Set 17)

Every TFT champion is shared across all eight players from a fixed pool. Once those copies are bought, they're gone until someone is eliminated. Knowing the exact numbers turns "should I roll?" from a vibes question into an arithmetic one. This is the math high-elo players use to decide between rolling 30 more gold and pivoting to a different carry.

Quick reference (Set 17)

Cost	Copies per champ	Distinct champs	Total tier pool
1-cost	30	15	450
2-cost	25	13	325
3-cost	18	13	234
4-cost	10	13	130
5-cost	9	10	90

The rest of this guide is the why behind those numbers — and what they mean when you're staring at 40 gold on stage 4-2 wondering whether to hit "roll" or "level."

Why pool sizes matter

When the shop rolls a slot at a given cost tier, it picks a random copy from every remaining copy of that tier in the shared pool. The probability of seeing one specific champion in a single slot is:

P(your target) = your_target_copies_remaining / total_cost_tier_copies_remaining

Smaller pool → smaller numerator. Heavy contestation → smaller numerator. Both compound.

Worked example: rolling for a 4-cost two-star

Set 17 patch 17.1b, level 8, looking for Karma (a 4-cost). You already own 3 copies. No other player has any.

• Karma copies left in the pool: 10 − 3 = 7
• Total 4-cost copies left: (13 × 10) − 3 = 127
• Chance one shop slot is Karma: 7 / 127 = 5.5%
• At level 8, each slot has a 30% chance of being a 4-cost (Set 17 odds — bumped from 22% in earlier sets)
• Chance a single slot is Karma: 0.30 × 0.055 = 1.65%
• Chance of at least one Karma in a 5-slot shop: 1 − (1 − 0.0165)⁵ = 8.0%

What that means for your gold:

The classic "50 gold rolldown is 80%" advice is from older sets. Under Set 17's higher level-8 4-cost odds, 30 gold gives you the same odds the old math said you needed 50 gold for — as long as you're uncontested. The catch: contestation crushes that fast.

How contestation destroys your odds

The pool is small. A single contested 4-cost can drop your effective rolldown odds by half. A 4-cost that's hard contested becomes mathematically unrollable.

4-cost contestation example

You have 2 Karmas, need 1 more for a 2-star. There are 8 Karmas left in the pool by default. Each contestor pulls copies out:

When 7 Karmas are spread across other boards, only one is left. Your rolldown odds drop to one-eighth of the uncontested rate. That's the difference between "roll 30g, probably hit" and "roll 50g, probably bleed out."

The golden rule

Fewer copies remaining = exponentially harder to find. And not linearly — as your target's copies drop, they shrink as a fraction of the total tier pool too, so odds degrade faster than the count itself suggests.

When the math says to pivot

Hard signals to abandon the current carry plan:

• 5 or fewer copies of a 4-cost remain in the pool (e.g. you have 2-3, others have 5+) — your per-shop odds have dropped enough that you'd need 50+ gold of rolling for a coin-flip chance. Pivot to an uncontested 4-cost, even if it's not your A-team carry.
• 3 or fewer copies of a 5-cost remain — with only 9 total to start, heavy contestation makes a 2-star nearly impossible. Cap at the 1-star and play around it.
• You've spent 40+ gold rolling and haven't found a single copy — pool's more depleted than you thought. Scout other boards (count the unit on each enemy) before spending more gold.

If you're not sure who's contested, the comps page shows what other people are running on the current patch — match it against the enemy boards in your lobby.

Eliminated players return their champions

When a player is knocked out, every champion on their bench and board returns to the shared pool immediately. This is mathematically large:

• A contested player eliminated holding 4 copies of your target → those 4 copies are now back in the pool. Your per-shop odds can double or triple.
• Late game (4-5 players left), a meaningful fraction of the entire pool has been recycled through eliminations — which is why level 8/9 rolling at 4-7 or 5-1 often feels generous compared to mid-stage 4. The effective remaining pool is bigger than the start-of-game numbers suggest.
• Track what eliminated players were holding. If the player who just 8th'd had 3 of your carry, you know those copies are now available — that's your signal to commit, not pivot.

Three-starring: the numbers

A 3-star needs 9 copies. Set 17 numbers:

A 1-cost 3-star is genuinely available even in contested rerolls. A 4-cost 3-star is a once-a-month occurrence that needs the lobby to ignore your carry entirely. A 5-cost 3-star is a meme target — chase it only if the lobby has handed it to you on a silver platter.

Key takeaways

• The pool is shared and small. Every copy bought elsewhere is one fewer in your shop.
• Calculate before committing. At level 8, uncontested, 30g of rolling for a 4-cost two-star is ~71%. That's the new baseline expectation in Set 17.
• Contestation compounds. Two contestors is rough; three is catastrophic.
• Eliminations return copies — track them and time your rolls accordingly.
• 3-starring 4-costs and 5-costs requires near-zero contestation. Don't chase them as a plan; accept them as gifts.

Related

• 4-cost econ and gameplan — when in the game to actually do the rolldown described above
• Rolling strategy — the broader decision tree of when to roll vs level vs save
• When to level — the level-up cadence that determines what shop odds you're rolling on
• Stats Explorer — pull live numbers for any patch / unit / item combo
• Comps — see what's actually being played in the current meta so you can scout effectively