What about the second player to be dealt? What are their odds? Well, here’s where it gets a little confusing. It depends on who is calculating. If you are the first player, or the commentator in a live tourney, you know the first 2 cards dealt. The second player does not, and has to calculate their odds the same way as the first player did.
The odds from the omnipotent perspective (i.e., the real one) would be as follows. Say two 10 pt cards have been dealt to the first player. The second player then has (20-2)/ (52-2) =~ 0.36 = 36.00% odds of also getting a 20-hand, in reality. But they don’t know that. They either have to assume 38.46%, as with the first player, or better. For example, if the first player did not get a 20, then the second player has 20/(52-2) = 40.00% odds of getting a 20. So the easiest, as a player, is to assume the worst case scenario, 36%, and then try to guess what the other player holds.
Now that you know the difference between real odds and perspective Cheri Casino odds, you can figure out what the odds are for each successive player in a match to get a 20 hand. Obviously, since there 20 10-pt cards in a deck and no more than 10 players in a game of Texas Hold’em, they could conceivably all have 20-hands.
What are the odds of that happening, though? I leave that as an exercise for you, but it’s very small. (Hint: multiply the real odds for each player.)
What about the player odds you see on TV, during a Texas Hold’em tourney? Those are “real” odds, calculated only because the commentators (and audience) know exactly what every player is holding. We have an advantage that obviously the players do not.
So how do they calculate the real odds of a player winning a Cheri Casino hand? Let’s talk post-flop, as it’s way too complicated to talk pre-flop just yet. Recall the rules of Texas Hold’em. Post-flop occurs after “burn one, turn three.” That is, after the players have been dealt their two cards apiece, and the first betting round ends, the dealer “burns” the top card. That is, puts it aside, face down. Then three community cards are revealed.
At this point, it’s likely every player’s hand odds have changed, both from their perspective and from the omniscient perspective. There is no way you can generalize a formula at this point. You have to calculate your own odds or the omniscient odds on a case by case basis.