Three of a kinds are not too tricky as a pai gow poker hands. You leave the three of a kind together in the high hand unless they are aces or kings. If you are dealt three aces you should split them to put an ace in the 2nd high hand. Always. It goes against the grain to break up such a nice poker hand as three aces, but it gives you the best opportunity to win the bet by besting the dealer on both hands.
You would also split 3 kings unless you can post a queen or higher to the 2nd high hand. Everything else you would always keep together to ensure your best chance of winning at least the high hand.
Let's look at a few examples:
Do we split the kings?
Our guidance above states if we can post a queen or higher to the 2nd high hand we can keep our cowboys together, This is not the case, so we should split them here, setting our hand as folllows:
2nd high:
High hand:
How about this hand?
This is easy - if its not three aces or three kings then there is not any reason to split the three of a kind.
2nd high:
High hand:
One more:
The bug is an ace here, so we can justify keeping our three kings together in the high hand. Set the hand like this:
