Billion Dollar NCAA Challenge

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Anyone sign up for this? I have been thinking of the math behind the bracket. Specifically is there a way to hedge from the beginning to guarantee a positive return (if only a penny). The only way to do this as a thought exercise is to imagine each game as a pick'em which obviously isn't the case.

 

The equation to determine the number of combinations remaining is: 2 ^ [number of games left]

 

This is the same formula to determine the mathematical odds of hitting a given parlay. Early on, taking a parlay on every possible combination won't work because the house gets its edge so you would always lose money. Parlays only become slightly possible if you make it to the Final Four with your bracket intact because the odds won't be there in Elite Eight and earlier.

 

Final Four Parlay

 

2 ^ 2 = 4 possible results

 

Example: Bet $100M on each of the three results that aren't in your bracket for a total of $300M. So you would need to find someone willing to pay you more than 3:1 on a 2 game parlay to turn a profit (pretty tough but maybe possible). In the Elite Eight round, you would need to find someone willing to pay you 15 to 1 against a mathematical probability of 16 one, good luck with that.

 

The more interesting question is when can you make it worth your while to bet individual games to hedge?

 

Individual Game Bets

 

The problem with individual bets is which teams do you bet on? If you bet each game the exact opposite of your bracket, you could hit the nightmare scenario of losing your bracket and more individual game bets than you win. This is a real issue with many games left to play with several games being played at once. Making it simple, let's say you have gotten everything right to the Final 4 and you are left with:

 

Florida v. UNC (bracket picks Florida)

Arizona v. Witchita State (bracket picks Arizona)

FINAL: Florida v. Arizona (bracket picks Florida)

 

You can't just bet $100M on UNC and $100M on Witchita State and enjoy the games. If Florida and Witchita State advance, you lose your bracket and $10M on the vig for your one winning bet. You could do the Final Four parlay above but even then you won't get a huge return because you need 3:1 odds to break even, which is very generous on a 4 game parlay. So are you screwed? As long as the UNC game finishes before the Arizona game you are fine. Put $100M on UNC. If UNC loses, put $200M on Witchita State. If Witchita State loses, you bet $375M on Arizona in the Final and you are locked in for that amount either way. For the Elite Eight you could do something very similar. It gets more complicated in earlier rounds because games are played at the same time. If all games were played one at a time, you could start hedging in Round 2. Put a buck on the first game opposite your bracket and escalate slowly from there the longer your bracket survives. But for practical purposes it probably only becomes possible in the Sweet 16 (betting multiple games that play at the same time, increasing your risk and reducing your potential payout) and really economically advantageous in the Elite 8.

 

However, there is one wildcard. There is a person who also becomes more willing to hedge the farther you get and isn't concerned with game times and point spreads: Warren Buffett himself. I imagine if anyone makes it to the Sweet 16 with a perfect bracket, you may see a "Deal or no Deal" situation start to play out.

 

# of Possible Results In Each Round

Round 1: 2 ^ 32 = 4.3 billion results

Round 2: 2 ^ 16 = 65,536

Sweet 16: 2 ^ 8 = 256

Elite 8: 2 ^ 4 = 16

Final 4: 2 ^ 2 = 4

Final: 2 = 2

 

Including the Sweet 16, there are 256 * 16 * 4 * 2 = 32,768 possible combinations remaining in the tournament. The net present value of a perfect bracket through the first two rounds is $30,517 ($1B divided by 32,768 combinations). So I could see old Warren offering $10,000 to someone at that point. It is highly doubtful that person would accept such an offer (I wouldn't even take the mathematically correct $30k). If they make it to the next round it gets very interesting. At that point, there are 16 * 4 * 2 = 128 combinations left, giving the bracket a net present value of just under $8M. Would Warren offer someone $4M at that point to cash it in? It would be mathametically sound for him to do so. Would you turn down $4M? I sure wouldn't. Here is the net present value chart:

 

Net Present Value of Correct Bracket Before the listed Round is Played

Round 1: <10 cents

Round 2: ~50 cents

Sweet 16: $30,517

Elite 8: $7.8M

Final 4: $125M

Final: $500M

 

Warren Buffet is probably your only option until at least the Elite Eight because you couldn't afford to hedge in the amounts needed to maximize your winnings and would need the media attention of making it that far to get a casino to step up and let you use the bracket as collateral. Due to the amounts involved, the fact that a lot of games are played at the same time early on, and the house edge on betting, I don't see a real way to start hedging at all until the Sweet 16, and for big money in the Elite 8 with media help. I think Warren would give you a very low percentage of net present value so you would need to keep him honest by setting up your other hedge options quickly. Hopefully you can use that option to get Warren to give you 60% or so on NPV.

 

When I make it to the Sweet 16 I will crunch the numbers to see if I can lock in a couple grand.