What is rarer in Hold'Em, Quads over Quads or Royal? (nt)

[Rotterdaum]

Anyone else seen quads over quads?

[Tom1975]

Empirically, I'd say quads over quads. I've only witnessed this once, while I've see a few royals in my day.

[rbenuck4]

another empirical is that the bad beat jackpot at party is much biger than the high hand jackpot, and gets hit with much less frequency, leading me to believe that its definitely the quads over quads that is rarer.

[Nottom]

I've seen quads over quads twice I think (where both players had a pocket pair). I personally have had at least 5 royals using both cards.

Quads over quads are much rarer ... as others have mentioned this would explain why the Party bad beat jackpot is > $100,000 while a high hand jackpot is a couple grand.

[Jouster777]

The relative probabilities will depend upon how many players there are. A better question might be "how many players do you need to make quads over quads equally as likely as a royal" or "is there a certain number of players that makes quads over quads equally as likely as a royal"

I'll try the calculation later if I get time

[Jouster777]

Probability of quads
= P(4 identical cards in a row) x number of ways they can be ordered in within 7 cards
= 3/51*2/50*1/49*C(4,7)
=.00168

Probability of royal flush
=P(5 specific cards)*4 suits* ways they can be ordered in within 7 cards
=5/52*4/51*3/50*2/49*1/48*4*C(5,7)
=.00000323

Probability of quads over quads (estimate) with 2 players = P(quads) squared = .00000282
Probability of quads over quads (estimate) with X players = P(quads) squared * (X-1) = .00000282X-.00000282

Setting this latter sum equal to P(RF)…
.00000282X-.00000282 = =.00000323
X=2.14

Thus, a royal flush is more likely heads up while quads over quads are more likely with 3 or more players.

There is minor error introduced by the fact that getting quads vs. quads or quads vs. RF are not completely independent events. I am very rusty so I'd appreciate it if anyone sees other errors in the calculations.