A confusing but interesting question...

I know i'm just bringing up an old subject (which was discussed in a very lenghty and kind of annoying thread because it got so many arguments going)
But i want to ask a confusing but interesting question:

First off, you have certain odds to hit hands...AA for example is 220:1 (if i remember correctly)
So say you get AA in a hand...then the next hand, the odds will be the same.
Though the odds of getting AA twice in a row will be (220*220):1 or 48400:1.
BUT - of course getting AA in one hand has zero effect of what will occur the next hand.

So here's my question:

Say you hit a spade flush in one hand, then the next hand you pick up an A5 of spades in late position, and get a chance to limp into a multiway pot.
Will the fact that you made a spade flush the last hand affect whether or not you call this hand PF for it's flush value?
(I'm assuming you don't see A5 as a strong hand - also ignore strategy in this example, that's not what i'm trying to focus on here)

Assuming the deck is shuffled truly randomly, the previous hand has absolutely no effect on the pure statistical probability (i.e. ignoring the fact that the players may be playing differently as a result of the previous hand and so treating the issue independently of the characteristics of the actual players in the hands etc) of any occurence in the next hand. The two hands should be treated as completely independent events - hence someone saying "I played 5s2s because spades are hitting a lot tonight" is being rather donkesque (assuming the dealer isn't crap).

This is really no different from asking "What are the odds of a coin flipping tails after the last 10 times it's been flipped it's come up heads?" - the answer of course being 50% assuming it's a fair coin.

I don't really understand how you can follow how this applies with a starting hand, but not follow that it applies with postflop probabilities as well.

Past hands should have no bearing on current hands but people seem to think so. That is why Vegas shows you how many time in a row the roulette wheel has come up red or black in a row. People think because the wheel has hit black 3 times in a row the odds of it being red are higher the next time. Wrong, it's still 50/50 excluding the greens. Odds are for predicting something before it happens. The odds of 4 blacks in a row before the first black hits aren't very good but once you have the 1st 3 it's not a matter of 4 in a row anymore but 1 time. Same thing in any game of chance including poker. You saw I hit AA 5 out of 34 hands last night. What are the odds of that? Still doesn't change the fact that I still have a 1 in 221 chance of hitting it again on the 35th hand

The thing is, that with starting hands, you don't get a choice in the matter - you get dealt what you get dealt.

With the example i have laid out (that i have been in several times before, and is why i posted this), you have the choice of gambling to possibly hit another flush/flush draw.
I completely understand the fact that one event will have zero effect on the odds of the next event. I actually had a class in h.s. that studied these kinds of odds and probabilities specifically, and in detail.
Yet in this situation, i will usually fold. I really don't know why - i understand that i have the exact same odds of hitting a draw/made flush on the board that i did last hand, but the thought of hitting both in a row being a (big #):1 shot runs through my mind, and i fold.
Silly - i know