You’re off by an order of magnitude there. The odds of making quads are about 1 in 600, which narrows to just worse than 1 in 100 if you start with a pocket pair. In practice it will be lower, because you won’t always make it to the river (and replay is only going to count hands that actually make it showdown), but there still not as rare as people think.
No, it’s not what I did. I would ask that you either provide a verbatim quotation in which I told people what to do, or stop putting words in my mouth.
Is that 1 in 600 for a nine-player game where nobody folds?
This is Google’s AI answer for six players where nobody folds:
"In a 6-player Texas Hold’em game where nobody folds, the probability of seeing quads on the board, by the river, is approximately 0.068%, or about 1 in 1,470 hands. This assumes that all six players see all five community cards.
I Googled this question:
How often can a player expect to get quads in holdem?
“In Texas Hold’em, the probability of being dealt quads (four of a kind) is quite low. You’re looking at roughly 1 in 4,165 hands when dealt any starting hand,”
I’m pretty sure the 1 in 600 is seeing Quads after the River card is dealt. The 7th card dealt, I don’t think it matters how many players are in the hand.
The AI is wrong. It’s ~1 in 600 for a single player as long as you always get to the river (with any starting hand). If were only talking about how often we make quads, rather than anyone at the table, it doesn’t matter how many players there are.
The phrase “being dealt quads” is not usually how you’d express that for Texas Hold’em, so maybe it’s conflating stats from stud or something.
Indeed, the case that is always made by the folks who don’t understand randomness is that weird stuff happens and in randomness we should see consistent unweirdness. This is a 100% false argument made by someone who does not understand randomness. Randomness is random. You will consistently see weird stuff very often. If the deals are consistently normal, that’s a guarantee that they;re not random.
It’s like these folks who argue that the deals are not random expect to be dealt AA exactly once every 221 hands. That’s preposterous. It’s completely normal to go 3 days without getting dealt AA and then get it 3 times in one orbit. It’s happened to me. I probably played 1000-1500 hands one weekend without being dealt AA. Then the next day I got AA back-to-back and then a third time 3 hands later. That’s just randomness. It cannot be predicted.