Stop Opening Packs on 'Average Odds': How to Calculate Real Token Budgets by Rarity
Why the Textbook '1/p' Formula Is Ruining Your Savings
I hear this constantly in Blooket communities: "The Mega Bot is 0.3%, so that's 1 in 333 packs. At 20 tokens each, I only need 6,660 tokens!"
If you take nothing else away from my simulator, remember this: Saving 6,660 tokens gives you almost the same odds as flipping a coin. At 333 pulls for a 0.3% drop, your cumulative probability of success is exactly 63.2%. You are walking into a pack opening session accepting a 36.8% risk of complete total failure.
In quantitative risk modeling, you never plan against the mean. You plan against confidence intervals. Here is the real mathematical table of how many pulls and tokens you actually need if you want to feel safe.
The Real Confidence Interval Budget Table
| Target Rarity | Base Drop Rate (p) | Median (50%) | The "Average" (63.2%) | Safe Plan (90%) | Guaranteed Plan (99%) |
|---|---|---|---|---|---|
| King (Medieval) | 1.0% (1/100) | 69 pulls | 100 pulls (~1.6k net) | 230 pulls (~3.8k net) | 459 pulls (~7.6k net) |
| Mega Bot / T-Rex | 0.3% (1/333) | 231 pulls | 333 pulls (~5.8k net) | 766 pulls (~13.4k net) | 1,532 pulls (~26.8k net) |
| Megalodon (Aquatic) | 0.2% (1/500) | 346 pulls | 500 pulls (~8.6k net) | 1,150 pulls (~19.8k net) | 2,301 pulls (~39.5k net) |
| Space Astronaut (Chroma) | 0.05% (1/2,000) | 1,386 pulls | 2,000 pulls (~35k net) | 4,603 pulls (~82k net) | 9,206 pulls (~163k net) |
How to Calculate Your Real Required Tokens
To calculate how many tokens you actually need for your hunting session, use this two-step formula:
Step 1: Pick your risk tolerance. Do not use 63.2% unless you are okay losing all your tokens over a third of the time. If you want high confidence, use the 90% Safe Plan.
Step 2: Factor in the resale refund. In a 20-token pack, common duplicates sell for 2 tokens and uncommon duplicates sell for 5 tokens. On average, you recoup ~2.5 tokens per pull. That means your net cost per pull is approximately 17.5 tokens.
Actual Net Tokens Required = (Pulls at 90% Confidence) × 17.5 Net Cost
For a 0.3% Legendary like Mega Bot, 766 pulls × 17.5 net tokens ≈ 13,400 net tokens. If you go into the Bot Pack with 13,400 tokens, 9 out of 10 times you walk away with the Mega Bot. That is how real pros budget.