The NCAA’s official schedule shows that the first three rounds are the First Round, Second Round, and Sweet 16. Quote: “First round: Thursday, March 19 and Friday, March 20 … Second round: Saturday, March 21 and Sunday, March 22 … Sweet 16: Thursday, March 26 and Friday, March 27.”

With 266 entries, the number of possible 4-person groups is$$\binom{266}{4}=203{,}927{,}570$$

For a specific group of 4 brackets to all match on one game under this chalk model, the probability is$$q^4+(1-q)^4$$

because either all 4 take the favorite, or all 4 take the other side. Across 56 games total, the probability that a specific group of 4 matches exactly through the first three rounds is$$\left(q^4+(1-q)^4\right)^{56}.$$

So for any 4 out of 266 entries, the rare-event approximation is$$\boxed{ \binom{266}{4}\left(q^4+(1-q)^4\right)^{56} }$$

That is the revised “chalk bias” formula.

Here are a few illustrative versions.

If entrants pick the favorite 70% of the time, then:$$\binom{266}{4}\left(0.7^4+0.3^4\right)^{56}\approx 2.62\times 10^{-26}$$

which is about 1 in 38,161,420,710,655,820,000,000,000.

If entrants pick the favorite 75% of the time, then:$$\binom{266}{4}\left(0.75^4+0.25^4\right)^{56}\approx 4.18\times 10^{-20}$$

which is about 1 in 23,899,365,976,853,120,000.

If entrants pick the favorite 80% of the time, then:$$\binom{266}{4}\left(0.8^4+0.2^4\right)^{56}\approx 4.97\times 10^{-14}$$

which is about 1 in 20,116,393,414,950.

A more realistic version is to let chalkiness vary by round. For example:

• First round favorite rate $q_1=0.75$q1​=0.75 across 32 games
• Second round favorite rate $q_2=0.70$q2​=0.70 across 16 games
• Sweet 16 favorite rate $q_3=0.65$q3​=0.65 across 8 games

Then the formula becomes$$\boxed{ \binom{266}{4} \left(q_1^4+(1-q_1)^4\right)^{32} \left(q_2^4+(1-q_2)^4\right)^{16} \left(q_3^4+(1-q_3)^4\right)^{8} }$$(4266​)(q14​+(1−q1​)4)32(q24​+(1−q2​)4)16(q34​+(1−q3​)4)8​

Plugging those values in gives about$$1.25\times 10^{-23}$$1.25×10−23

or roughly 1 in 79,736,844,641,242,890,000,000.

So the bottom line is: once you add chalk bias, the odds become vastly higher than the pure-random model, but they are still extremely small unless the pool is very chalk-heavy, brackets are copied, or many entrants are using near-identical heuristics.

Quote used for the round structure: “First round … Second round … Sweet 16.”

I can also turn this into a one-line explainer you could quote in a story, with a conservative, moderate, and aggressive chalk scenario.