How I try to remember it - as long as you get 3 of each in Triple Dice Poker (3 one's, 3 two's, 3 three's, etc...) then you will get the bonus. (So if you get 4 six's - you know you have 6 additional points to play with... so for example, if I have 4 six's, I know I can get away with only 1 three - as long as I have 3 of each other dice.)

... And then in the 6D version - you need 4 of each dice instead of three.