Help with the math, or do I get an aluminum hat

[dogmeat]

I posted yesterday as a response to questions about not making flush draws because I had a bit of a bad streak. Not a bad-beat post, just the fact that streaks happen.

Well, maybe I don't understand the math, but I've played 4100 hands in two days and these are the results:

170 times I had an ace and a face card, only 30 times did I flop a pair to my cards - that's 17.6% Now help me here - isn't this a 1.5-1 shot and shouldn't I be a little closer to 40%? What are the odds that this streak hits? I know my stats are tainted because I can't count anything when I win preflop, and I didn't count anything when I folded because I 4-table and didn't go back to check to see if I would have flopped anything. However, with just this info - how far from the norm and is this happening something in the neighborhood of 1000-1?

Should I get my aluminum foil hat and join the conspiracy buffs?

FWIW, my other stats suck too, I'm in the middle of a 200BB loser at $5/$10

Dogmeat /images/graemlins/spade.gif

[Grendel]

Well, the probability of pairing at least one of two random cards on the flop is
1-(44/50)*(43/49)*(42/48) = 32.4%

Your results certainly are tainted because of the reasons you mentioned, especially because if you hold two high cards (and likely raise), you're more likely to see the flop if someone else also has high cards. That is, your chances of pairing AQ is less than 32% when someone else has KQ. Also, does your 30/170 stat include the times you flopped two pair or trips? Just to make the math easier, I'll assume that it does, but you might want to check that.

Given that the probability of flopping a pair is 32.4%, the probability of pairing exactly N times out of 170 tries is:

nCr(170,N) * (.324)^N * (1-.324)^(170-N)

Now if we sum up the results from N=0 to N=30, we get... 0.0012%. Wow, that's 1-in-83,000 aluminum foil hat time. Help me, did I do something wrong here?

Yikes. Now if we assume that one of your opponents always has one of your two cards, the odds of your flopping a pair drop to
1-(44/49)*(43/48)*(42/47) = 28.1%

And summing N=0..30 of
nCr(170,N) * (.281)^N * (1-.281)^(170-N)
Is 0.1077%. There's your 1-in-1000 streak.

Before I run out and buy a roll of aluminum foil myself, how often did you flop two pair, trips, or quads with your hands?

-Grendel

[dogmeat]

I considered any of my two cards on the flop to be "hitting the flop", therefore it was a hit for a pair, two pair, trips or a boat.


Believe me, I was trying to make a point about streaks happening by mentioning it in an earlier thread, then I continued to see very few flops hit today........I have been preaching that internet games are perfectly safe, and I've been playing for the last 13 months for a living. However, this little sample of 4000+ hands is a bit much for me.

This is all from the Party Bad Beat $3/$6 and $5/$10 tables. I'm playing now, looking at the jackpot of $405K

I'm 0-4 since starting playing again after lunch.........

Dogmeat /images/graemlins/spade.gif

[dogmeat]

Well, JP at $406K, I think it will hit at $412 - so, I hope to still have some money left when it does. I've dropped down to $2/$4

Dogmeat /images/graemlins/spade.gif

[BruceZ]

[ QUOTE ]
Given that the probability of flopping a pair is 32.4%, the probability of pairing exactly N times out of 170 tries is:

nCr(170,N) * (.324)^N * (1-.324)^(170-N)

Now if we sum up the results from N=0 to N=30, we get... 0.0012%. Wow, that's 1-in-83,000 aluminum foil hat time. Help me, did I do something wrong here?


[/ QUOTE ]

No, you're right, except some roundoff error. It's actually 1-in-89,686.

[dogmeat]

I'm quitting now - no real improvement. The odds of this happening are?

5000 hands over two days

209 times I play A-k,q or j preflop and hit at least a pair only 39 times............... 18.6% When do I say WTF! I'm not playing anymore at the BBJ Party games?

Dogmeat /images/graemlins/spade.gif