Odds on Ultimate Texas Holdem and Number of Players

Hello All,

I am having a hard time to understand this so I would kindly ask for your help. As I have seen on the Wizzard of Odds website, the Ultimate Texas Holdem Game uses 2 players : The dealer against the player

My understanding is that the odds of winning are the same and the number of players is irrelevant. This is the part that I do not understand and I would like to explain through two scenarios using Aces (since any existent ace means a 4x bet and increased probabilities of winning) :

If we have a game with 4 players (so 3 players and the dealer) , the probabilities for all 4 aces to be given to some players of the game (or all of them) are much higher than when the game is played by two players. In a 2-player scenario, It is very unlikely that the dealer *and* the player will get two aces (so eliminating any chances of any other ace existing in the 5 community cards). The chances of any existing ace in the community cards is much higher when there are two players as opposed to 4 players, correct ?

What I just described can of course hold for other cards of value such as Ks, Qs, Js etc.

So from my -limited- understanding , as the number of players increases, the harder it gets for having a good hand and this is irrelevant as to whether we can see the cards of all other players.

Of course I know I am missing something here but I am unable to get a grasp on what that is.

Many Thanks for your help!

You only get 7 cards to choose from, no matter what. You're not discarding cards expecting to be dealt some replacements.

Quote: ChumpChange

You only get 7 cards to choose from, no matter what. You're not discarding cards expecting to be dealt some replacements.
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Thank you for your reply.

Yes, I was reffering to the odds of getting high value cards among these 7 cards and how these change according to the 2 scenarios I described. In the 4-player scenario you have 4 additional cards being given to players (total of 8 cards given to the 4 players) from the deck while In the 2-player scenario we have 4 cards (total of 4 cards being given to the players)

This means (?) that we have a higher chance of more aces being present among the cards handed to players on the 4-player scenario as opposed to the ones given on the 2-player scenario.

Yes, but you have a higher chance of more twos being present among the cards handed to players on the 4-player scenario as opposed to the ones given on the 2-player scenario.

Or more 5s. Or more Jacks. etc.

As long as you are unaware of what the other players' cards are, it makes no difference that they have been dealt cards.

Think of the sequence of deals as being this:

First you and the dealer are dealt two cards.
Secondly, the five common cards are dealt.
Lastly, the other players are dealt two cards each.

In this sequence, it makes no difference to you that the other players have been dealt cards, because the cards that determine whether you won or lost were dealt first.

And, if you think about it, as long as the cards are being randomly dealt, it makes no difference what sequence the cards are dealt in.