# 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)

##### 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
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
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.

#### 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.

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.

##### 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

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

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

##### Dormant account
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?

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