Pre Flop Winning Percentage

I'm wondering about pre-flop win percentages and what they mean exactly. If I'm at a full 9-person table and I'm dealt K Q suited hole cards, I know my pre-flop win percentage is about 18.95%. Now, if 4 people fold pre-flop (thus leaving 5 people in the hand pre-flop), is it fair to say my hole cards now go UP in value to about 31.12%, as I'd be facing less people in the hand now?

My guess is yes, since I'd only be dealing with 5 players pre-flop, rather than 9. Or, do I just stick with the original 18.95% pre-flop win percentage figure, regardless of how many people fold pre-flop?

Phaedrus75 responds to this question in the forum:

Technically, the fewer random hands you are facing, the higher your win odds. That is the basic reasoning why starting hand requirements go down as your position at the table improves. On the button for example in an unopened pot you are facing 2 random hands.

That said, I remember posting a thread a long time ago called "how random is the BB anyway?".

My question never really got answered from memory. I was speculating that at a full table when it is folded to the button, the BB is likely to have a better hand than they would under the same conditions at say a 3 handed table.

I was still curious about this, and reposted it below, however in the course of doing so, I think I might have answered my own question.....

Lets start with hands that will probably never fold to a single raise - call it all group 1 and group 2 hands (JJ+, AQo+) 10 hands, comprising 4 PPs and 6 non pairs. Thats 120 in 1326 combinations (9%).

Lets call it 10% at a 10 max table.

So we have 10 trials of a 10% chance event. Probability of the event not happening is 90% for each trial . Probability of it not happening in 10 tries is 0.9^10 = 0.3486784401. Probability of it happening is therefore 1-0.3486784401 = 65%.

Do the whole thing again for 3 players....

0.9^3 = 0.729
1- 0.729 = 27%

The above calcs are sort of a bit general because they do not take into account card displacement, but they are close enough for generalisations.

So at a 10 max table, a big hand will be present at the table 65% of the time. The location of that big hand will of course be random.

The question is, does the fact that 6 or 7 players have folded make it more likely that such a hand will be in the hands of one of the few players left to act (i.e the blinds when you are on the button)?

I think the answer is no. You are really dealing with two separate and independent probability equations. Regardless of what assumptions you make based on the 65% estimate, the blinds are still dealt 2 random cards each and what those cards are is not affected by how many people are at the table.

So the very long winded answer to your first question is that yes, your win rate does go up with KQs based on there being fewer people left to act.