Poker hand ranking difference

This is a question that has stumped me for a while:

Playing Pai Gow poker, if you bet the fortune bonus, it pays out 3 to 1 on trips, and 2 to 1 on a straight. This would imply that it is more difficult to obtain a 3 of a kind than a straight with 7 cards. Scrolling down to "Fortune Pai Gow Poker Detailed Return Table for Paytable 2" on this page:says that there are 7672500 ways to get 3 of a kind, and 11034204 ways to get a straight. Clearly, with seven cards, a straight is more likely than a three of a kind.

So, why when playing Hold em, which also uses seven cards, is a straight higher than 3 of a kind?

The only explanation I can think of, is that you use your best 5-card hand, and there are 10,200 ways to get a straight if dealt five cards, while 54,912 ways to get three of a kind. I believe (not 100% certain however) that poker originated as a five-card game, so perhaps this was a holdover of some sort. Any help on this would be appreciated. Thanks.

That pesky joker. It helps make a lot of busted straights, but will only improve Aces to 3 of a kind. I believe once you introduce the 'bug', straights become more common. Note, from the same wiki page, the 7 card probabilities for a 52-card deck:

Straight 6,180,020
Three of a kind 6,461,620

Straight is still harder to make in 7 cards with no joker. So, in holdem, it actually is harder to get a straight, and the rules should stand. It would have been really confusing to the poor players if they changed the poker rules just for paigow.

In hold-em the winning hand is the best five-card hand you can make using your 2 cards and the 5 community cards. In Pai Gow Poker you need to win a five-card hand and a two-card hand. But the sucker bet pays for seven cards, not five.

Suppose you're dealt Ac, Ah, Kh, Qh, Jh, 10h, 9h. You split your cards to a king-high straight flush and a pair of aces. Regardless of whther you win the hand, you'd still get the royal flush payout in the bonus bet.

In other words the side bet is determined by seven-card hand odds, but the main bet is determined by five-hand odds. So for the player vs dealer action a straight beats three of a kind.

Oh duh. I hadn't been thinking about the joker. Makes sense, thanks.