Ok, a few things. No, hold'em is not the only choice. But nobody plays draw. And hold'em is pretty much standard.
You guys are missing an important part of the game. Besides "tells" which in all honesty are only things that really bad players have, and the probability of making hands, there is betting patterns. For those of you who don't play, there is something for example, called slow playing. This is when you have the best hand, but you don't want others to know, so you don't bet large to rope them in. There is also bets to minimize the number of players. There are also bets that depend on stack size (money available.) If you are the chip leader, you want to bet high pre-flop to "tax" everyone else. You don't want anybody to see free cards. On the other hand, if you are short stack, you have to pick a spot and go all in, even if the odds are not that great. There is of course bluffing.
There is also recognizing the patterns of other players, and "table image." For example, let's say I have slow played a number of hands, and have won big pots doing so. Players will recognize my pattern, so in the future, I can bet in a similar manner to previous times I was slow playing, and then execute a bluff more successfully. Of course good players understand table image, so there is the expectation that others do as well, and you might be able to anticipate situations where table image is being taken advantage of. There is also pot odds, which refers to the degree of investment in the pot. For example, if there is 100 in the pot, and I only have a 1 in 5 chance of winning, but the cost to stay in the hand is only a dollar, the pot odds suggest this is a sensible bet.
As an aspect of table image it will sometimes makes sense to bet on an unlikely hand to win, because if you do win, people won't see it coming and you can often win large pots (i,e, what could he have? he wouldn't have played with anything on the table) If you get a reputation for doing this, you can then sometimes make wild bluffs.
Or in some cases it might make sense to bet when you know you are going to lose, chasing something extremely unlikely, so you can set up a later bluff or draw someone in when you have a winner.
Anyway, you guys get the idea, and the point is knowing the odds of making a hand is only a small part of the game.
Also, um, I'm no expert in probability, but it's sort of obvious that probability refers to situations where exact information is unknown. Of course in each situation only one particular combination of cards is dealt; what is relevant to the calculation is what you don't know. This is always the way probability works; what information you have and what information you don't. Saying the fact that players have cards changes the probability is like saying the order of cards in the deck changes the probability. Of course it does, IF you have the information.
What is the probability of getting heads on a fair coin flip? If I know the outcome, either 100 percent or zero. But lacking all necessary information (like all the minute details of the universe that lead up to the moment I flip the coin) the probability is 50 percent.( a little less actually cause there is a slight chance the coin can land on its side)