Quote:
Originally Posted by BadBeatEveryDay
In 1000 hands you should be dealt pocket pairs 100 times.
This is false. You will be dealt a pocket pair in 5.88% (78/1326) of your hands. Thus, you should receive, on average, 58.8 pocket pairs per 1,000 hands played.
Quote:
Originally Posted by BadBeatEveryDay
You should flop a set 1/8 times, so I should have had 12 sets.
Also false. Given that you hold any two cards of the same rank, there are "50 choose 3" possible flops. This means that the number of possible flops is 19,600.
The number of flops that contain at least one card of your rank (giving you a set, a full house, or quads) is "2 choose 1" x "48 choose 2". This number is 2,256.
Therefore, the odds of flopping at least a third card of your rank when you hold a pocket pair is 2,256 / 19,600 = 11.51%.
When you combine this with the revised expectation of how many pocket pairs you should get in 1,000 hands (58.8), then you should flop, on average, 6.77 sets per 1,000 hands.
NOTE: This assumes that you see a flop with EVERY SINGLE pocket pair that you are dealt, which is obviously ridiculous. Thus, the true expectation is lower.
Quote:
Originally Posted by BadBeatEveryDay
I had none. That's far beyond any normal tolerance level for randomness
Really?
Again, we will make the EXTREMELY generous assumption that you reach the flop with every pocket pair you are dealt.
With that assumption, your chance of flopping a set on any given hand is 5.88% x 11.51% = 0.677%. Thus, your chance of not flopping a set on any given hand is 100% - 0.677% = 99.323%.
Since each hand is independent, your chances of not making a set on any of a given sample of 1,000 hands is 99.323% ^ 1,000 = 0.112%.
HOWEVER
We have already said that assuming you reach the flop with every pocket pair is completely ridiculous, and I'm sure you agree. Thus, let's dig a little further.
The database I currently have for my play on WSOP New Jersey contains 38,979 hands. In this sample, I have had 2,255 pocket pairs. In the 2,255 hands in which I was dealt pocket pairs, I have seen the flop 1,500 times. This means I saw the flop with a pocket pair 66.5% of the time.
Lets assume that holds up for the sample of 1,000 hands. If so, now my chance to flop a set in any given hand drops to 5.88% * 11.51% * 66.5% = 0.450%. Consequently, the chance of not flopping a set in a 1,000 hand sample rises to (100% - 0.450%)^1,000 = 1.1%!
So, consider the following to events:
(A) You flop a set on the very next hand you play.
(B) You do not flop a single set in the next 1,000 hands you play.
Event (B) is more than twice as likely as event (A). So, next time you DO flop a set, you should post about it here, because that **** was way more rigged than your 1,000 hands without a set.
*
I should actually admit that I made a small mistake in my post. The odds of flopping a set that I gave do not count the times that you flop quads.
Including quads, it would be "2 choose 1" x "49 choose 2" / "50 choose 3" = 12.0%.
Last edited by Mike Haven; 03-07-2014 at 06:19 AM.
Reason: 2 posts merged