A question on probabilities. I was playing Pai Gow at the Golden Nuggest yesterday, and was dealt three aces, a king, a jack, and two low cards.
I put the king and the jack in the up and held the three aces in the down. My thought was ‘well, I have three aces, so it’s unlikely that the dealer will have an ace available for her up hand. In fact, it’s probably more likely that she’ll leave two pair in the down hand, which would beat two aces.’ Plus there was the fact that if I split them, I’d push on any two pair, while the dealer would play a low two pair in the down hand and leave the up hand vulnerable, making it likely I’d win.
Anyhow, long story short, I would have won the hand with either hold (dealer had a pair), but she chided me for not spliting the aces. Her arguement was that it was the house way, because ace-queen is the average up hand, ace king would be strong and a pair of aces in the down would still be strong.
I ended up telling her that I understood why the dealer would do that, as the dealer wants to beat all the bad hands and lose only to good hands, but I felt that the average dealer up hand when one player has three aces would be much lower than ace queen, and quite likely lower than king jack.
Since this was my first time playing the game, I’m still thinking this over. Did I play it correctly?
-lv