Probability to get a royal flush on the board - Gambling and Probability

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Probability to get a royal flush on the board

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02-09-2015 , 06:13 PM

Marco Trevix

journeyman

Join Date: Sep 2002 Posts: 214

What's the probability to get a royal flush in the exact order (T,J,Q,K,A) on a hold'em board?

It recently happened at Aria casino and somebody told it's about a 1/78.000.000 shot.

Thanks in advance!

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02-09-2015 , 07:27 PM

statmanhal

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Join Date: Jan 2009 Posts: 4,987

The probability of a ten first card is 4/52, ignoring what players hold. Then the jack of the right suit on the second card is 1/51, next 1/50, then 1/49, then 1/48.

So, prob = 1/52*1/51*…*1/48 =1.28*10^(-8), equivalent to odds against of almost 78 million to 1.

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02-09-2015 , 07:46 PM

whosnext

Carpal \'Tunnel

Join Date: Mar 2009 Posts: 6,733

I think statmanhal meant "4/52" rather than "1/52" as his first term in the product (as he explained in his first line). Of course, the 4, as explained, reflects that there are 4 suits (4 different royal flushes).

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02-09-2015 , 08:07 PM

statmanhal

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Join Date: Jan 2009 Posts: 4,987

Yep, that's why I rarely got 100% on math tests.

My numerical result is correct as I did use 4/52 in doing the multiplication.

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02-11-2015 , 10:06 PM

David Sklansky

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Join Date: Aug 2002 Posts: 17,096

In real life its rarer. Do you see why?

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02-11-2015 , 11:08 PM

RickySteve

banned

Join Date: Sep 2014 Posts: 655

Quote:

Originally Posted by David Sklansky

In real life its rarer. Do you see why?

z0Mg ur da jeenyuzeSt mAf jeenyuz

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02-12-2015 , 12:18 AM

yukoncpa

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Join Date: Oct 2004 Posts: 3,127

Quote:

Originally Posted by David Sklansky

In real life its rarer. Do you see why?

My first thought is that the deck starts out with all these cards ( except maybe the ace ) together. As it gets shuffled many of the cards will still be together. But since there is a burn before each card is turned, the chances of all cards being turned in order on the board is lessened from a truly randomly shuffled set of cards

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02-12-2015 , 12:52 AM

heehaww

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Join Date: Aug 2011 Posts: 5,081

Quote:

Originally Posted by yukoncpa

<snip>

Hint: how might unseen flops & boards compare to seen ones? What might increase the chance of a flop happening?

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02-12-2015 , 01:05 AM

yukoncpa

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Join Date: Oct 2004 Posts: 3,127

Quote:

Originally Posted by heehaww

Hint: how might unseen flops & boards compare to seen ones? What might increase the chance of a flop happening?

Ha ha, yeah, I see what you're saying. I haven't been in a brick and mortar since the days when all they had was limit and you saw a flop nearly every single hand regardless of what people were holding.
My answer is still good, at least for the first few deals after a fresh deck.
edit - obviously your answer is correct and way better. I actually wasn't envisioning a no flop type of game so I'm laughing at myself.

Last edited by yukoncpa; 02-12-2015 at 01:18 AM.

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02-23-2015 , 08:14 AM

#10

DecisionMade

grinder

Join Date: Nov 2012 Posts: 557

Quote:

Originally Posted by David Sklansky

In real life its rarer. Do you see why?

Burn cards?
E: grunched. Maybe not then.

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02-23-2015 , 08:54 AM

#11

heehaww

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Join Date: Aug 2011 Posts: 5,081

Burn cards do not affect probabilities because a random card is a random card whether it's the top card or 2nd card or bottom card in the deck. Each card is as likely in the 1st, 2nd ... last position.

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02-23-2015 , 09:46 AM

#12

Renton555

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Join Date: Jun 2012 Posts: 5,905

It's somewhat lower than that because the heavy ranks are often downweighted by the high-card heavy ranges that people see a flop with.

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02-26-2015 , 04:40 PM

#13

ZuneIt

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Join Date: Mar 2009 Posts: 2,160

Quote:

Originally Posted by David Sklansky

In real life its rarer. Do you see why?

Even I know the answer to this. If someone doesn't know the answer, they shouldn't be playing poker. Do you understand why?

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03-01-2015 , 10:13 PM

#14

Bantam222

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Join Date: Aug 2006 Posts: 2,388

You also need to take into account the number of boards where we do not see the turn/river. IE flop comes 10JQ suited and then the hand ends.

The badly shuffled deck (which started in suited order) argument is pretty weak. I would say this might even improve the chances of this scenario happening rather than hurt them. Sure you have to fight against the burn cards taking out the card you need, however having the 5 cards you need all in the same ~10 card part of the deck gives us pretty good odds (with respect to the real odds) at this scenario. Sure you get beat by the burn in some cases, but it can't be worse than a true shuffled deck.

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03-01-2015 , 11:08 PM

#15

statmanhal

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Join Date: Jan 2009 Posts: 4,987

Quote:

Originally Posted by Bantam222

. Sure you get beat by the burn in some cases, ...

and sure you gain an advantage in other cases because the burn card is not one of the possible royals you need.

See heehaww's posting above.

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03-02-2015 , 12:19 AM

#16

e1cnr

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Join Date: Jul 2011 Posts: 2,008

Quote:

Originally Posted by ZuneIt

Even I know the answer to this. If someone doesn't know the answer, they shouldn't be playing poker. Do you understand why?

Calling stations shouldn't play poker? Whats wrong with wanting to see the river?

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