I was wondering if anyone has the odds of a heads up hold em hand. I've done some searching and haven't exactly found the answer. I did try adding up the odds of winning for all 169 possible combinations then dividing by 169. I got 49.0071% to win, 52.96337% to win or tie. My local casino has a texas hold em table where you play against the dealer. You ante, then put up 2x ante if you want to see the flop. You also have the option to bet the ante amount on the turn or river if you so choose. My thinking is if you look at the 52.9%, you bet the same amount every hand including the flop and NEVER fold, you should come out ahead. Of course, I suppose you could bet the turn and/or river if you get dealt very favorable cards to win more but nothing is a sure thing. If anyone can tell me if I'm correct, I would really appreciate it. Thanks!
As you can imagine, your equity in a heads up hand with no rake, where you bet preflop and deal out all community cards without betting, will be 50%. Other variations of this, such as the dealer winning ties or the introduction of a rake, will lower your equity (and since this is a casino game, I'm willing to bet that they have something in their favor). Having the ability to bet/fold gives you an opportunity to make better / worse decisions based on your hand, which will also affect your equity.
As far as your odds of winning with two random heads up hands, you will tie just over 4% of the time, and you will evenly split the wins the rest of the time, over the long run. This means that you will win very close to 48% of the time, assuming that you always go to the river.
In order to provide strategic advice for a casino game, you would need to provide all of the rules of the game, because they can make a huge difference.