This is a question I've always wanted to know..

I don't see why it would make a difference.

I would say slightly more, yes. There will be slightly more pairs in hands on flops seen during the full ring game than in the heads up game.

level?

Or perhaps you misunderstand the question? OP is asking about pairs on the flop not in the players' hands.

There is no difference in the number of paired flops.

What even makes you ask the question?

I don't see how there could be more paired flops one way or the other.

It's like asking the question if Ace of spades is more likely to appear in the first card of the deck or 28th card of the deck.

my intuition tells me it should be slightly more likely to have a paired flop in a ring game if we assume that flops in general are slightly more to be seen with paired hands.

If I have AK then there are 6 paired combos of AA and KK combined. If I have AA there is only 1 combo of AA but a full 6 combo's of KK, making 7 in all.

This might be utter garbage though.

This. Card removal effect.

I feel that the difference would be minimal, but I certainly wouldn't mind seeing someone calculate the probability. You would need to input preflop calling, raising, 3bet, 4bet ranges (and call ranges for raise, 3bet, 4bet etc) for all 9 players and calculate the chanes of a many of different situations, or you could just run many simulations from the ranges. Or maybe you could just look at a huge database and see how often the flop is paired in 9 player hands vs 2 player hands. Anyone got a hands database with over 1,000,000,000 hands?

I think the most reasonable way to do it would be to do the simulation. Once preflop action is finished it would be best to simply calculate the probability of the flop being paired and use that number instead of dealing a flop and adding to the total number of pairred flops if it is paired.

No its not. The range of hands people see the flop with in heads up is different to the range people see the flop with 9 players. If you're in the BB
and you're debating calling a person whose range is KK+, you know that it's less likely there will be a K or A on the flop. Pre flop ranges affect what's on the flop.

The order of all 52 cards are predetermined. The only thing changes between full ring and HU is the order of the cards that are dealted as flop.

For example a pair of 10s would have the same probability of being the first 2 cards as the last 2 cards.

Your argument includes whether we even see the flop. I was discussing the probability regardless actions of players, an entire sample size, not selective base on plays.

As said previously, the number of players can matter--what percent of the time do we see a flop full ring? What about HU? Those probabilities are likely not the same. One's hole cards are correlated with those probabilities (maybe in a difficult-to-figure-out way, but they are) which affects the probabilities of seeing those three flop cards.

That is, if you're asking 'if we dealt a flop 100% of the time, even if it's raise-and-take-it or a walk, what is the probability of a paired board' your answer would be correct. But that doesn't necessarily appear to be what the OP is asking.

To me it seems that is exactly what OP is asking. It would be strange to read the question as: "are there more flops in full ring than HU?"

Well, I could see the impetus for the question to be someone who was watching a lot of HU and a lot of full ring games, and thought he noticed there were more pairs on the flop for one of the games. And then was asking why that might be.

Of course, from a strategy viewpoint one might ask 'if I know I'm going to take a flop, what is the probability that it will be paired', which is a different question.

The effect is so minimal that no one would notice this.

Op should clarify his question then. From strictly math point of view where the flop is predetermined, there is no difference between HU and full ring.

Isn't the deck in a continuous shuffle on Full tilt/pokerstars and if so wouldn't card removal effects be noticeable (even if slight)?

i think full tilt does a continuous shuffle, but stars doesn't. either way it is unrelated to card removal effects.

Christ I wish sites, whichever ones do, wouldn't do this continuous shuffle ********. It makes absolutely no difference to the outcome but it causes people to come up with all kinds of bizarre theories.

From a database of millions of hands, it has been shown that a seen flop will have slightly more low cards than theory would indicate for both seen and unseen flops. This is true because if a flop is seen it is more likely that the players have high cards thereby increasing the chances for low flop cards.

I would think the same phenomenon happens with pairs. You can show that if a player has a pair, then that increases the probability that another player has a pair. Here, with a little transference of logic, we can say that if a player has a pair, then a) it is likely a flop is seen than if no player had a pair and b) it is more likely the flop also has a pair.

Check out the riggie thread in the Zoo. They notice things that aren't even there.

Why would that be the case?

Let's run a simple example:

QQK are 3 cards that are stuck together. How is someone dealt pocket kings going to change the odds of these 3 cards showing up as flop? The order of all 52 cards is predetermined before the cards are dealt, and where the pairs are lied within the cards aren't going to change just because more players are dealt with pairs.

The reason why the odds of at least 1 player with pocket pair is higher in full ring than HU is quite simple: there are more hands dealt, hence more chance to meet desired result.

Do you think it's more likely for 3 random cards chosen from 50 to contain a pair if the 50 cards consist of 4 of every card and 2 aces? Or four of every card, 3 kings, and 3 aces?