How often do Quads come up at showdown?

[picabo]

Been playing no limit holdem at a site for about 200 hours now and have seen alot of quads.I noticed them several times the first day so I started keeping up with them. So now I have seen them 66 times and thats from approx. 8000 deals to avg 7 players. Seems quite excessive. I originally posted this on the internet forum and they suggested I post here since nobody wanted to take the time to figure up how much more this would be over the going rate. Anybody know?

[kalooki]

The answer depends on the players, the limits, the betting, etc etc etc.

I'll come back with a rough estimate later.

[kalooki]

As I said, it depends on the number of players at the river in each hand.

I have calculated below the odds of quads winning 66 or more hands out of 8000 based on different numbers' of players seeing the river each hand;

One player at river; 637,276,657,159,077,000,000,000 to one.
Two players at river; 4,835,751,110 to one.
Three players at river; 5,951 to one.
Four players at river; 13.5 to one.
Five players at river; 2 to one ON.
Six players at river; 29 to one ON.
Seven players at river; 1561 to one ON.

[Cyrus]

Something looks amiss. Your figures suggest that with 4 players to the river you have more chances of seeing quads than with 6 players but less chances than with 5 players?

What was the method?

"I have calculated below the odds of quads winning 66 or more hands out of 8000 based on different numbers' of players seeing the river each hand;

One player at river; 637,276,657,159,077,000,000,000 to one.
Two players at river; 4,835,751,110 to one.
Three players at river; 5,951 to one.
Four players at river; 13.5 to one.
Five players at river; 2 to one ON.
Six players at river; 29 to one ON.
Seven players at river; 1561 to one ON."

[kalooki]

1. THE DATA

Note; the last three 'odds' are ON (i.e. the numbers should be reversed to get the true odds).

i.e. "2 to 1 ON" means 1 to 2" (about 33% chance)
and "29 to 1 ON" means 1 to 29"

Is this method of quoting odds-on a European thing?

2. THE METHOD

I used a poker simulator to deduce the odds of a hand being won by quads with the requisite number of players seing the river.

For each case; I used a standard method of calculating the exact probabilities of each number of occurrences from 0/8000 to 8000/8000. I then summed the values for occurrences equal or greater than 66.

[Cyrus]

"Note: the last three 'odds' are ON (i.e. the numbers should be reversed to get the true odds). i.e. "2 to 1 ON" means 1 to 2" (about 33% chance)"

If A is the odds-on favorite by 2:1 to win, then the probability of A winning is supposed to be 66.6%, not 33.3%.

"Is this method of quoting odds-on a European thing?"

I have no idea.

"I used a poker simulator to deduce the odds of a hand being won by quads with the requisite number of players seing the river.

For each case: I used a standard method of calculating the exact probabilities of each number of occurrences from 0/8000 to 8000/8000. I then summed the values for occurrences equal or greater than 66."

Sorry for persisting but I still don't understand. The poker sim should provide the answer straight up, shouldn't it? I mean, plug in 2,3,...,10 players, use random hands for every player, run a 10-15 mln hands sim each time and then look up the results. (In PokerWiz, you'd look up the Details menu to get the answer without any "calculations".)

And I know I'm missing something but what's the use for "8000/8000" and "66" ?