I'm looking at a setting in a No limit Texas Hold'em hand. We start the hand with 6 people, only two will go to the flop. Ok, I'll admit this is a very unlikely situation:
Player 1 starts the hand with: T♥ T⋄ Player 2 starts the hand with: A♠ Q♠
Flop comes: T♠ T♣ Q⋄
Player 2 bets on the overpair with backdoor straight draw and backdoor flush draw. Betting goes round, player 2 ends up going all in. Player 1 obviously makes the call. Players agree to run it twice.
To win player 2 needs to hit either the Q⋄ Q♣ or J♠ K♠ for the higher quads or the royal flush.
Calculating the odds of player 2 winning both pots, would I be correct in saying:
2/1081 will give me the odds for the first run 1/990 will give me the odds for the second run
Somehow it does not feel right to multiply these two with one another to get the odds of player 2 winning the entire pot. It seems like I treat the two draws as independent, while in fact the results of the two will influence one another. If the first comes Qd Ks the person is drawing dead on the second. (I realise that on such ridiculously small odds this is marginal, but I am curious how to deal with it)
How should I adjust for this ?