This year Buffet says he will make it easier to win, but has not released details….yet. When these rules are defined, the strategy will be adjusted further. But let’s get a starting point to discuss a possible stategery to tackle this billion dollar challenge. Even to an FBGer, a billion is not exactly chump change.
Odds assuming 63 games are even matchups: 1 in 2^63, or 9.2x10^18 possible combinations. We need to reduce that.
So it is CRAZY you say, and you are right. A perfect bracket has never been done. But what if we really wanted that billion dollars, how could we attempt to do it? This means we are going to have to make the best assumptions we can to reduce the number of combinations. Let’s start making some assumptions and see where how close we can get.
1. All #1, #2, #3, and #4 seeds will win the first round. (100%, 95%, 86%, 79%, respective winning percentage)
Lowers the number of combinations down to 2^47….1.4x10^14. The problem has been reduced by four orders of magnitude! A start. All 16 top 4 seeds have won in 4 out of 28 tournaments (14% chance of success). Could be we need to assume a 3rd and/or 4th seed fails, may revisit that assumption later to improve odds.
2. All #1 seeds will win round 2. (57% chance)
Lowers combinations to 2^43……8.8x10^12 combinations.
3. Kentucky wins it all….(about 50% chance by Vegas odds)
Further lowers number of combinations to 2^39…..5.5x10^11 combinations
At this point our odds of winning are about down to about 4% going with those assumptions. Sounds bad, except we have lowered the number of combinations by a factor of over 16 million! Only about half-way to the promise land, but it will get tougher from here.
4. At least 3 #2 seeds and at least 3 #3 seeds advance and at least 3 #4 seeds get past round 2.
This reduces the number of combinations for those games from 4096 down to just 125. Now 1.68x10^10 combinations.
5. At least 2 of the 5th and 2 of the 6th seeds will advance past 1st round…..
I am just starting thinking about this and throwing out ideas. Definitely a work in progress, and my calculation in 4 is not quite right, but it is late and my mind is shot for the day. The only real chance we have is if there are fewer upsets than normal. In round 1, the range of upsets varies from 3 to 13 with the average of 8 upsets out of 32 games. We can probably only allow about 5 upsets or the combinations will get out of hand.
Another stat to keep in mind is 76% of final four teams are #3 seeds or better, so will need to narrow it down to those.
Most of these assumptions are empirical data, but we may have to look at special circumstances and try to further lower the combinations. For instance, the Kentucky pick makes sense since they are a more dominant than typical team. Maybe Wisconsin or Duke is strong enough to assume in the final four.
Dates to keep in mind:
Tournament Selection Date: Sunday, March 15, 2015, 6:00 PM EST
Real First Round (Playins don’t count): Thursday, March 19, 2015, Noon?
So we have Sunday Night, Monday, Tuesday, and Wednesday to participate. The one entry per person rule of the past really kills the opportunity to improve the odds down to something winnable. If one of the changes that Buffet wants to make is to increase the number of entries per person, that would be huge. Keep in mind besides the $1 billion to prize, which is probably still a lottery pick, there are 20 $100,000 prizes.
Odds assuming 63 games are even matchups: 1 in 2^63, or 9.2x10^18 possible combinations. We need to reduce that.
So it is CRAZY you say, and you are right. A perfect bracket has never been done. But what if we really wanted that billion dollars, how could we attempt to do it? This means we are going to have to make the best assumptions we can to reduce the number of combinations. Let’s start making some assumptions and see where how close we can get.
1. All #1, #2, #3, and #4 seeds will win the first round. (100%, 95%, 86%, 79%, respective winning percentage)
Lowers the number of combinations down to 2^47….1.4x10^14. The problem has been reduced by four orders of magnitude! A start. All 16 top 4 seeds have won in 4 out of 28 tournaments (14% chance of success). Could be we need to assume a 3rd and/or 4th seed fails, may revisit that assumption later to improve odds.
2. All #1 seeds will win round 2. (57% chance)
Lowers combinations to 2^43……8.8x10^12 combinations.
3. Kentucky wins it all….(about 50% chance by Vegas odds)
Further lowers number of combinations to 2^39…..5.5x10^11 combinations
At this point our odds of winning are about down to about 4% going with those assumptions. Sounds bad, except we have lowered the number of combinations by a factor of over 16 million! Only about half-way to the promise land, but it will get tougher from here.
4. At least 3 #2 seeds and at least 3 #3 seeds advance and at least 3 #4 seeds get past round 2.
This reduces the number of combinations for those games from 4096 down to just 125. Now 1.68x10^10 combinations.
5. At least 2 of the 5th and 2 of the 6th seeds will advance past 1st round…..
I am just starting thinking about this and throwing out ideas. Definitely a work in progress, and my calculation in 4 is not quite right, but it is late and my mind is shot for the day. The only real chance we have is if there are fewer upsets than normal. In round 1, the range of upsets varies from 3 to 13 with the average of 8 upsets out of 32 games. We can probably only allow about 5 upsets or the combinations will get out of hand.
Another stat to keep in mind is 76% of final four teams are #3 seeds or better, so will need to narrow it down to those.
Most of these assumptions are empirical data, but we may have to look at special circumstances and try to further lower the combinations. For instance, the Kentucky pick makes sense since they are a more dominant than typical team. Maybe Wisconsin or Duke is strong enough to assume in the final four.
Dates to keep in mind:
Tournament Selection Date: Sunday, March 15, 2015, 6:00 PM EST
Real First Round (Playins don’t count): Thursday, March 19, 2015, Noon?
So we have Sunday Night, Monday, Tuesday, and Wednesday to participate. The one entry per person rule of the past really kills the opportunity to improve the odds down to something winnable. If one of the changes that Buffet wants to make is to increase the number of entries per person, that would be huge. Keep in mind besides the $1 billion to prize, which is probably still a lottery pick, there are 20 $100,000 prizes.
