Aren't these two things contradictory?

[Bukem_]

A deck of cards has no memory, so any two cards could be dealt to you at any given point.

Given a very large sample of cards, card distribution should be evenly distributed.

Taken alone, each of these seem reasonable. But if you use the second one, it seems to say that if you've been dealt 10,000 pocket Aces, and only 8,000 pocket 2's, you are more likely to be dealt pocket 2's. But that would be incorrect /images/graemlins/confused.gif

[IsaacW]

What is important about dealing two-card hands out of a shuffled deck is that each event (a deck being shuffled and the top two cards dealt off as the hand) is independent of the prior and future events. No string of pocket aces, no matter how long, changes the probability that your next hand will be pocket aces.

Think of this coin flip example: if you flipped a coin 9,999 times and had seen heads 5,500 times and tails 4,499 times, has the probability that the 10,000th flip comes up tails changed? Of course it hasn't. You are equally likely to end that run of 10,000 flips with 5,501 heads and 4,499 tails as 5,500 heads and 4,500 tails, given that the first 9,999 flips were distributed as above.

Many times, the human brain will try to see patterns in events that are truly unrelated. A lot of times, you will hear at a poker table "my, 7's are hot tonight, that's three flops in two hours where two 7's have come up." Strange things happen with random events, but it's important to keep in mind that this is not because of some driving force making 7's come up, but just because of a random string of short duration where 7's happened to come up more than they were "supposed to."

Now I've rambled a bit, but let me answer your question in a short statement here: no, those two statements are not contradictory, because the second one is incorrectly applied (10k pocket aces and 8k pocket 2's are not a large sample).

[Lost Wages]

Read this. (http://archiveserver.twoplustwo.com/showthreaded.php?Cat=&Number=694947&page=&view=&sb =5&o=&vc=1)

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[Bukem_]

That helps.

I know thinking things like I've run bad, now I should run good is wrong. I'm trying to understand things better so I don't have even a tempation to think like that.

On a somewhat related question, is it possible to show that it is less likely for the same hand to hit a certain number of times in a row.

Even though you could say I've gotten pocket Aces, or heads 10 times in a row, but my chances are the same as the first time to get either of the two.

But is there a way, before any results come in to quantify the difficulty of hitting 10 times in a row? If so, what, if anything does that say about what I said above.

[Lost Wages]

is there a way, before any results come in to quantify the difficulty of hitting 10 times in a row?

Just take the probability and raise it to the tenth power. In the case of coin flipping, the probability of your next ten flips comming up heads is .5^10 = ~0.1%, which of course is the same as the probability of flipping HHTHTTTHHT.

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