Standard Deviation

[Bozeman]

You should only expect to make a pair (or two pair, trips, or quads) with an unpaired hand on the flop 32.43% of the time, so you are actually getting luckier than average here.
In addition, if you always raise with these hands preflop, you will see somewhat less than this because when people play against you it is somehat more likely that they will have some of your aces, kings, and queens.

33K hands is a rational sample size, but it still will have reasonable expected deviation.

Craig

[MyNameIsMud]

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You should only expect to make a pair (or two pair, trips, or quads) with an unpaired hand on the flop 32.43% of the time

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Can you show me how you come up with 32.43?

-MyNameIsMud

[uuDevil]

This is 1-P(the 6 cards that match yours do not show up on the flop):

1-(44/50)*(43/49)*(42/48)=0.32428

or about 32.43%

Bozeman would not steer you wrong on this kind of problem.

[DPCondit]

[ QUOTE ]
In addition, if you always raise with these hands preflop, you will see somewhat less than this because when people play against you it is somehat more likely that they will have some of your aces, kings, and queens.


[/ QUOTE ]

Yes, that is exactly what I was going to say. Good point. These are not showdown simulations. Some times you won't even see a flop when you have premium cards. On the actual flops seen, you should expect a lower number of premium cards. Unless there is a flop 100% of the time, then you cannot logically expect there to be as many aces, kings, and queens.

Don

[Thythe]

On the non math side of this question (it's long since left the front page of the zoo), Party has no incentive to give you LESS sets. If it wanted to cheat it should give you MORE sets and have them be beaten by flushes/straights by the river. The goal would be to increase the rake of course, but if you aren't making sets, then you are folding and not contributing much more money to the pot.

[delirium]

Actually, if Party wanted to cheat (and not be obvious, obviously), then the best way might actually be to even up the game among the players. Standard statistically random shuffle, but distribute the hands in such a way as to help the weaker players and handicap the stronger players. That way everyone plays longer (swapping the same money more or less around the ring) and Party increases its rake.