Odds of Royal Flush?

nafanny29

Dormant account
I was wondering what are the odds of completing a Royal Flush by the river (Holdem) when playing 2 Royal cards ie. AKs, QTs etc

My mate has had 3 online and ive had 0 and weve both played over 100000 hands. Mine mostly on Crypto, his at many sites (apex and party mostly)
 

pokeraddict

Webmaster
The odds of making a royal is about 1 in 34,000 before cards are dealt. If you have 2 thats a long math problem i cant do quickly. Perhaps a math wiz can tell us, ,if not I will do my best.
 

nafanny29

Dormant account
pokeraddict said:
The odds of making a royal is about 1 in 34,000 before cards are dealt. If you have 2 thats a long math problem i cant do quickly. Perhaps a math wiz can tell us, ,if not I will do my best.
Wow if the odds are 34000 to 1 before cards are dealt then im seriously overdue a royal. Thanks for the reply pokeraddict. :notworthy
 

paul1

Dormant account
pokeraddict said:
The odds of making a royal is about 1 in 34,000 before cards are dealt. If you have 2 thats a long math problem i cant do quickly. Perhaps a math wiz can tell us, ,if not I will do my best.

I just ran AK-suited a million times on Poker Probe. There was a little over 600 royals. I guess that is about 1600 to 1.

So nafanny29, you better get back to the table. :D
 

nafanny29

Dormant account
paul1 said:
I just ran AK-suited a million times on Poker Probe. There was a little over 600 royals. I guess that is about 1600 to 1.

So nafanny29, you better get back to the table. :D
I will mate, thank you and pokeraddict for your info, much appreciated.

I am seriously overdue my 1st royal though!!!
 

Aindreas_Daoc

Dormant account
FWIW, I have around 60k hands in PT, and maybe another 10-20k that I didn't record in PT, and haven't gotten a RF either.

However, 1 in 34000 does sound about right if you go to the river, but remember often you will not go to the river.
 

pokeraddict

Webmaster
In 417,000 Pokertracker hands I have 4. You have to take into consideration the times you raised a start hand that could make a royal and everyone folded preflop or the number of times you flop 4 to a royal and everyone folds. Also its not just big suited cards that make it. One of my royals is from pocket queens.
 

nafanny29

Dormant account
Never thought of it like that. I guess im just about due my virgin royal then :D :D

On a side note I would have have had 19 straight flushes with my hole cards according to pokertracker... alas only saw the flop 3 times :( :(
 

winbig

Keep winning this amount.
nafanny29 said:
Never thought of it like that. I guess im just about due my virgin royal then :D :D

On a side note I would have have had 19 straight flushes with my hole cards according to pokertracker... alas only saw the flop 3 times :( :(

But again, that would mean going to the river in most cases....19 is a rather high number considering...
 

GrandMaster

Ueber Meister
CAG
nafanny29 said:
I was wondering what are the odds of completing a Royal Flush by the river (Holdem) when playing 2 Royal cards ie. AKs, QTs etc
If I understand it correctly, you assume that you have two of the cards for the RF and you want to know the probability that the remaining 3 cards will show up among the 5 community cards.

Using excel notation, combin(50,5)=2118760 ways of choosing the 5 community cards out of the 50 unseen cards, disregarding order. Three of these cards are fixed, and there are combin(47,2)=1081 ways of choosing the other 2 out the remaining 47. This makes the probability of having a RF 1081/2118760=1/1960=0.00051.

It does not matter that there are other people at the table or how many there are, unless you know something about their cards.
 

paul1

Dormant account
GrandMaster said:
1/1960=0.00051.
Again, I ran some hands on Poker Probe. I matched AK-spades against AK-hearts, ran them 2,500,000 times. Between the two of them, they came up with about 3100 royal flushes out of 5 million hands.

That's 1/1600.

So, what am I doing wrong? :confused:
 
Top