What are the odds of flopping quads?

[snoopy1239]

It took me a while to click on that REAL monsteas - Royals, Quads - are rarely worth much, there is no action to be had unless you have a serial thief, a Camel, Penly, Thewy, Bradley type on the table.

The ones, perversely, that get paid best are the siily ones, 7-4 kinda jobbie catching hidden straights.

Sometimes betting it isn't a bad idea.

[tikay]

Yeah, but if trips flopped and any one of Thewy, Penly, Camel or At It Bradley bet, you'd beat 'em into the pot!

[ariston]

There are 3 different ways of flopping quad queens, QQx, QxQ,xQQ. These must being taken into the calculations. The odds on each of these is obviously the same but the problem can be worked out easily as 2/50*1/49 divded by 3(as there are 3 different permiatations of flopping it). This comes to 408.3333 to 1 meaning reds calculations are roughly correct- how dare you question the mans maths Tikay, there was a time we both used to answer maths questions on another forum eh red

[redsimon]

Quads (using one of your pocket cards) from two non-pair cards - 9799/1

Nicked from:        
 
http://www.homepokergames.com/odds.php

[AdamM]

what about flopping royal flush?

[redsimon]

There are 3 different ways of flopping quad queens, QQx, QxQ,xQQ. These must being taken into the calculations. The odds on each of these is obviously the same but the problem can be worked out easily as 2/50*1/49 divded by 3(as there are 3 different permiatations of flopping it). This comes to 408.3333 to 1 meaning reds calculations are roughly correct- how dare you question the mans maths Tikay, there was a time we both used to answer maths questions on another forum eh red

There was a time we used to play the same online stakes, now you are having a go at being a pro and I'm grinding it out at 2/4...cest la vie

[ariston]

Vegas goes wrong I may be back at those same 2/4 games red 

[redsimon]

what about flopping royal flush?

Let's say you hold the AJ of diamonds.  In order to flop a royal flush you need to hit the KQ10 of diamonds in no particular order on the first three cards.   You have three cards that you can hit on the first card rolled over, out of 50 remaining cards in the deck, so the odds of the first card rolled over being either the KQ or 10 of diamonds is 3/50. 

After you hit that card, you have two cards left to hit out of 49 remaining cards.  The odds the next card on the flop will be one of those is 2/49.

After you hit that card you must hit the remaining card, whatever it may be, out of 48 remaining cards in the deck, or 1/48.

The trick is, that you have to hit precisely all three of those cards.  we have figured out the odds of hitting each one individually.  To figure the odds of hitting all three of them precisely, you must multiply them all together.

50 x 49 x 48 = 117600

3 x 2 x 1 = 6

117600 / 6 = 19600 which means you will flop a royal if you hold two of the cards 1 time in every 19600, or 19599 to 1 against it.

Shamelessly nicked from a forum. I only know both times I got a Royal at Gala I got NO ACTION

[tikay]

Ah, point taken Ariston, but if you had read the thread (ooh-er) you would note I eventually clicked that the stat I was confusing it with was holding one Q in hand, and flopping 3. Which, spookily, Red has just completed his research on, & come up with 9799/1. As ever, Red anticipated my thoughts exactly. Hope he's not on my table tonight.

By the way, Crypto have just been on the phone to me. They have had a lot of requests from players asking to be on my table tonight. Thery have resolved it by making it a 48 man table. I'm delighted, the blinds will only come round every fortnight.

[ariston]

To flop a royal flush you have to hit 3 specific cards to go with your 2 suited pictures, eg 3/50*2/49*1/48= 19600-1

[redsimon]

Ah, point taken Ariston, but if you had read the thread (ooh-er) you would note I eventually clicked that the stat I was confusing it with was holding one Q in hand, and flopping 3. Which, spookily, Red has just completed his research on, & come up with 9799/1. As ever, Red anticipated my thoughts exactly. Hope he's not on my table tonight.

By the way, Crypto have just been on the phone to me. They have had a lot of requests from players asking to be on my table tonight. Thery have resolved it by making it a 48 man table. I'm delighted, the blinds will only come round every fortnight.

48 man table, that would be cool, no chance of being anted out!

[TightEnd]

Rainman alert, rainman alert

redsimon and ariston incoming......

[TightEnd]

Ah, point taken Ariston, but if you had read the thread (ooh-er) you would note I eventually clicked that the stat I was confusing it with was holding one Q in hand, and flopping 3. Which, spookily, Red has just completed his research on, & come up with 9799/1. As ever, Red anticipated my thoughts exactly. Hope he's not on my table tonight.

By the way, Crypto have just been on the phone to me. They have had a lot of requests from players asking to be on my table tonight. Thery have resolved it by making it a 48 man table. I'm delighted, the blinds will only come round every fortnight.

48 man table, that would be cool, no chance of being anted out!

would give a new meaning to thoughts of early positioin and waiting til the button to steal

[ariston]

397 toothpicks 

[Nightfly]

Considering that 2 hole cards and the three flop cards form a unique 5 card poker hand then the odds of flopping quads must be the same as being dealt quads in 5 card stud.

there are 2,598,960 different 5 card combinations
624 of these are 4 of a kind (each of the 13 Ranks * any one of the 48 other cards)

odds of flopping quads is therefore

4,164 - 1