It is well known that there are 9,223,372,036,854,775,808 (or 2**63) possible brackets. If each game is viewed as a toss-up, then each of these brackets are equally likely to occur. However, basketball aficionados know that since 1985, a No. 1 seed has never lost to a No. 16 seed. This means that not all games are toss-ups, and that using some basketball knowledge can reduce the odds of picking a perfect bracket.
What about the odds of a perfect round? The following table estimates these odds values, assuming that each game is a toss-up, or each seed will perform exactly as it has historically.perfomed.
We can use this information to estimate the odds of picking a perfect bracket. If all games are toss-ups, then the odds are 9,223,372,036,854,775,807 (or (2**63)-1) to 1. If all seeds are expected to perform exactly as they have historically, then using the third column in the table, the estimated odds of getting all the seeds correct drops to just over 4.4 billion to 1. If all seeds are expected to perform exactly as they have historically and taking into account the four regions, then using the fourth column in the table, the estimated odds of getting all the seeds correct in their respective regions is just over 106 billion to 1. Note that 4.4 billion to 1.odds is for getting all the seeds correct, though not necessarily in the correct regions. The 106 billion to 1 odds is for getting all the seeds correct in the correct regions, a true perfect bracket.
|Round||Toss-up||Historical Performance, Seeds||Historical Performance, Teams||Round of 64 (32 games correct)||4,294,967,295||839 thousand||20 million|
|Round of 32 (16 games correct)||4,294,967,295||182 thousand||4.4 million|
|Sweet Sixteen (8 games correct)||1,677,215||1,709||41 thousand|
|Elite 8 (4 games correct)||65,535||299||7190|
|Final Four (2 games correct)||1,023||11||143|
|National Champion (1 game correct)||63||1.5||9|
|All Rounds (63 games correct)||9,223,372,036,854,775,807||4.4 billion||106 billion|
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