What are the odds? Texas Hold'em poker.

Factual Questions
1

I’ve only played a few low-stake tournaments (all on holiday in Vegas :cool: ), but there were a couple of hands that stick in my memory. I’d like to know the odds in these two pre-flop situations.

  1. A player goes all-in from seat one on the first hand of the tournament. :eek:
    I have A♣ K♣ , so decide to call.
    He shows up with A♠ 2♦. :smack:

What are my chances?

  1. There are just two players left. I have more money than him. He goes all-in and I call.
    He has 8♣ 3♦.
    I have K♠ Q♦.

What are my chances?

2

Are you asking for your odds of winning given just the hands that you held, or given the behavior of the other players at the table? If the latter, we’d have to know how the other players are behaving. Ordinarily, we’d assume that they were behaving rationally, except that, given your after-the-fact knowledge of their actual hands, we know that they weren’t. Maybe base our assumptions on how they’re playing on the range of how real players play? But that would take empirical data, which might be hard to come by, and which certainly can’t be calculated from scratch.

3

Sorry - I should have said that in both cases all other players either had folded (case 1) or been eliminated (case 2.)

So given there are just two players, what are the odds of me winning each hand?

4

First scenario approx. 73% to win and 5% to tie
Second scenario approx 68% to win and 1% to tie.
Check for yourself

5

Thanks!

6

Have I mentioned that game solving via computer is my avocation? :slight_smile:

(1)
You win 73.04%
You lose 22.25%
You draw 4.71%
The high chance of a tie is due to Ace-high straight.

(2)
You win 67.63%
You lose 31.67%
You draw 0.70%

Ninja’ed by Saint Cad and the website so, to “add value” I’ll show the chances for various hands you might finish with in (2):
No pair 18.225%
One pair 44.169%
Two pair 23.032%
Triplets 4.553%
Straight 5.545%
Suit flush 1.934%
Full house 2.388%
4-of-a-kind 0.139%
Str flush 0.014%