March Madness Perfect Bracket Has Crazy Odds

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I remember a math puzzle from a long time ago that went something like this: A father offered his pre-teen child two choices for a prize. He could either have $10 a day for an entire month or he could have one penny the first day and the father would double the amount every day of the month.

Which would you pick? Would you change your mind if I made it $100 per day? What about $10,000? How about $100,000? Which would you take – $3,000,000 or one penny on the first day, two on the second, four on the third, etc.?

In a 30 day month, on day 30, your prize would be over $5 million just for that day. You would have amassed over $10 million. This little puzzle is the epitome of what it means for something to grow exponentially. You are really being paid one penny times the power of 2 raised X times (where X is the day of the month – except we start at 0 and not 1.

The same principle works in gambling, sort of in reverse. How many different pools did you see for the NCAA Tournament, offering up big bucks if you could just put together a perfect bracket – a mere 63 games. I mean, obviously, it isn’t easy, but if millions of people enter the contest, eventually someone is bound to do it, right? Probably not.

Let’s assume (a big assumption) every game is a 50/50 tossup. Under this scenario, to get all 63 games right would be a lot like our previous math puzzle – only it would go on for two months instead of one. The payout on Day 63 would be 92.2 quadrillion (that would be 1,000 times a trillion). That would also be the odds of someone getting all 63 games right. Essentially it would be the same as me flipping a coin 63 times and you calling each flip correctly. Try it. See if you get past 10, which would only be about 1-in-1000.

Okay, but my assumption was a big one. Most of the games are nowhere near 50/50. Of course, they aren’t 90/10 either. Not even in the opening round. There are a handful of games where some powerhouse is playing some team that got a bit lucky to even get in.

Then there are the majority of the games where a team is a clear favorite, like in the case of Yale. Oh wait, they were the underdog and won. Lastly, you have probably 10 or 12 of the 63 games that truly are a tossup. Especially the last few rounds where you have quality teams.

But, let’s take this in the other direction a bit. Let’s say every game has a favorite that is 66.67% likely to win. This would be a huge advantage to one team in the world of sports. I’d be surprised if more than five of the 63 games actually have this large of a money line. So, now instead of calling a coin toss, you have to call a dice roll. Call high for 3-6 or low for 1-4. That would be a 2/3 (66.67%) advantage like the basketball games.

You’ve got a much better chance of getting through 10 rolls of the die. Now it is about 1 in 50. Your odds of getting to 63 increase dramatically too. The problem is it is still about 124 billion to 1. So, even if Yahoo gets 10 million entries per year, it would take 12,400 years (on average) for someone to hit this. And this was with our new generous assumption of a prohibitive favorite in every game.

Is it any wonder Yahoo announced that 99% of the brackets were already busted after about half of the games were played last Thursday? Sure, that still leaves 1% who have a “chance.” But, if we’ve eliminated 99% of the entries and there are still 55 games left to go (there were probably 59 when they made this announcement) that still has odds in the hundreds of trillions to 1.

Of course if we are done with eight games that means the odds have been reduced by a factor of 256 and we’ve retained 1%, so maybe this is a good sign this is the year. Of course many of the games were among the easiest. Was Virginia really going to lose to Hampton? Could Stony Brook beat anybody?

On a positive note, most of these pools are free and there is still a significant prize for beating everyone else. So, there is a positive expectation, technically. But, I would suggest you set your sites on one of those realistic prizes and not the teaser amount for a perfect bracket.

I’m not sure why they bother to make it “only” $1 million. The only thing less likely would be a bad beat in Texas Hold’em where you lose with a Straight Flush in one suit to a Straight Flush in another suite (for the record, this isn’t possible in Texas Hold’em).

Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Email: [email protected].

About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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