Quote:
Originally Posted by scheier
You can be the best player in the world, play perfectly but still lose your 70/30 flip at 15th place like 10 times and be losing a lot of money over a significant period of time.
Let's dig deeper on this one, because it is an important issue. If we collect a really big sample, variance should start to shrink. Comparing two players that have been through 10 life-or-death flips is clearly way too small. You might win four; I'd win six, and even though you're a better player, I've got better results.
What if we got our sample size big enough that we could be 99% confident that both of us were within 1% of the true statistical mean for the risks we took? To make the math simple, let's assume that we're talking about 50/50 flips every time. We want an outcome where you always win at least 49% of them; I never win more than 51% of them.
With a sufficiently big sample, the last vestiges of my luck edge will linger on, but they shouldn't cloud the picture much. I might be artificially two percentage points ahead of you, which means 2/51st of my win rate would be bogus, or about 4 percentage points. It shouldn't get any more egregious. Worst case, I've got a 6% ROI; you've got a 4% ROI, but our true strengths are reversed.
Playing around with Raosoft (
http://www.raosoft.com/samplesize.html), I learn that a sample size of about 16,000 flip situations will get us there.
Let's assume that in each MTT, our fate depends on how we do in five high-stakes flip situations. (We'll be playing more than that, but most of them will be for small enough stakes that they won't seal our fate.) If you'd rather assume a different frequency, it's totally okay to rework the math that follows. We'll get to a similar place either way.
So, if we each play 3,200 tournaments with five flip situations, we're there. That's a lot of tournaments.
If you're willing to live with 95% accuracy and a variance of two percentage points in either direction, we need only 480 tournaments, with about five flip situations each. (Note: the Hellmuth WSOP sample size is about that big.)
Bear in mind that our results won't be distributed evenly across specific hand-to-hand clashes. You may be frustrated that you've had AA cracked four times in a row. I may be annoyed that AK v. JJ has gone against me repeatedly, no matter which side I'm on. Most of those examples of luck average out.
On a larger scale, luck might have make-or-break implications 20 times in a tournament. Frequencies of AA/KK vary greatly. Success at set-mining does, too. But if we believe that the cards are random, the more abundant such luck events are in a tournament, the more everyone's overall luck quotient should eventually cluster around the mean. High incidences of events create large sample sizes ... which are our friend.