Texas Hold'em - Bad Beat

Question

Was playing Zynga poker on facebook and had a bad beat.. Saw a similar situation on youtube as well. I am just curious...

Assuming only two people are playing and no cards have been burned for the flop, turn or river, what is the probability that "Player 1" has the upper hand

i) After the flop
ii) After the turn
ii) After the river

Community -   A♥  9♣  Q♦     10♦     A♦

Player 1 - A♣ A♠

Player 2 -  J♦ K♦

jumsumtak · Answer

You cannot calculate unless you know other player's cards as well. (I'm assuming the spoiler indicates you want to do it without that knowledge). The odds will change accordingly. (e.g. if player 2 has an AA - 50%; if player 2 has a 5,8 - player 1 has a significant advantage before the flop is burned).

Even if you know the cards, it will be tough to compute pre-flop odds without using an algorithm. 
I can imagine doing by making cases when the turn has been flopped over or possibly when the flop has been burned.

MacFauz · Answer

I just added the spoiler just to make the post interesting.. What I would like to know is what are the odds of Player 1 getting Quad Aces and Player 2 getting a Royal Flush (I dont think any other straight flush or quad is possible) after the river or in other word.. How unlucky do I need to be to lose this game with Quad Aces?

jumsumtak · Answer

Hmm.. I think I got what you are trying to say here.

the given - your cards; the community cards
the unknown - player 2's cards
to calculate - probability of you getting screwed after 1.) flop 2.) turn 3.) river

Its almost impossible to calculate by making cases before the river is burned because even you did not have quad aces before that. That will be crazy amount of work. After the river is flopped, only a J and K of diamonds can beat you. So the probability is 1/(number of ways of selecting 2 cards of the remaining deck i.e. selecting 2 out of (52-7) cards)

Most of the algos of the holdem odds calculators work the opposite way. 
given: both the players' cards
unknown: the community cards
to calculate: odds for both player 1 & 2 after 1.) flop 2.) turn 3.) river

IanStewart · Answer

I think you need to formulate the question more precisely for it to be answered. If the question is: what is the chance I win with AA against KdJd, then you're about 80% to win before the flop, on the flop your opponent has only 4 card that help (the four 10s) and you can still make a full house or four-of-a-kind, so you are about 88% at that stage; after the turn, you need to help your hand, and only 9 cards give you a full house, so you have a 9/44 = 20% chance to win. If instead your question is: "I have AA here, and my opponent has two completely random cards, what is the probability I lose when the river looks like this?" then we know 7 cards, so there are 45 left. Your opponent's first card must be Kd or Jd, which is a 2/45 chance, and the remaining card needs to be exactly the other royal flush card, so a 1/44 chance. So there's a (2/45)(1/44) = 1/990 chance you lose to two random cards on the river. That said, people don't normally play just any two random cards in poker, unless they don't care about money very much. Well, on Zynga they might, I guess.

But because someone is more likely to play Kd Jd than they are to play 8c 3h, it's a bit more likely than 1/990 that you lose here. Of course it's still extremely improbable. And if you're asking "what's the probability someone makes a Royal Flush and someone else makes four-of-a-kind on the same hand", that's a pretty complicated calculation, but the short answer is "very very very unlikely". You'd probably have a better chance of winning the lottery than of seeing that if you play just one hand of poker.

Texas Hold'em - Bad Beat

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