How to determine odds of this happening(Poker)

[stevew]

I just saw a 5 cards dealt in order from 6 thru 10 to the table, from flop thru river. Cards were not suited. How would you determine the odds of this happening? My math skills are not that great, but i think this would have to be a very low odds thing to happen, but i could also see it not being that rare.

[Z²+]

i think this would have to be a very low odds thing to happen, but i could also see it not being that rare.

Are you running for political office or something? If so, I have some ideas on how to save PAT Transit ;)

[mckerney]

I just saw a 5 cards dealt in order from 6 thru 10 to the table, from flop thru river. Cards were not suited. How would you determine the odds of this happening? My math skills are not that great, but i think this would have to be a very low odds thing to happen, but i could also see it not being that rare.

I would think it's 4/52*4/51*4/50*4/49*4/48= 1024/311875200

[Ragone]

i've seen that happen at least 3 times that i can recall

[Axxon]

I just saw a 5 cards dealt in order from 6 thru 10 to the table, from flop thru river. Cards were not suited. How would you determine the odds of this happening? My math skills are not that great, but i think this would have to be a very low odds thing to happen, but i could also see it not being that rare.

Whatever the odds, it's the exact same odds of any particular five cards being dealt in a row. The only difference is that this event is memorable to the viewer not the odds of it happening.

Who remembers or cares about the odds of a 4D,7C,10S, 3S and 2H being dealt in order? ;)

[finkenst]

I just saw a 5 cards dealt in order from 6 thru 10 to the table, from flop thru river. Cards were not suited. How would you determine the odds of this happening? My math skills are not that great, but i think this would have to be a very low odds thing to happen, but i could also see it not being that rare. you have a deck of cards with 5 suits?

however, if we are talking in particular the 6 through 10 with no flush possibility then the odds are something like:

4/52*4/51*3/50*2/49*1/48 = 96 ways to get 6 through 10 without a flush possible / 311875200 possible hands dealt out.

Note that this doesn't take into account burned cards or cards in players' hands and it eliminates any 3 cards to a flush.

mckerney, your math is correct for any 6-10 straight.

[Draft Dodger]

but if it was just ANY straight, in order, it would be...2,560 possible combinations our of 311,875,200 (10/52*4/51*4/50*4/49*4/48). plus, if you assume, say, a 10 person table, you're now looking at 10/32*4/31*4/30*4/29*4/28, or 2,560 out of 24,165,120...about 1 in 10,000?

(um, am I right?)

[RPI-Fan]

What has been calculated here is the odds of those cards coming up on <i>a specific hand</i> - the calculation made by mckerney is pretty much correct.

However, what we should really do is think about how we want to analyze this problem. The question that should really be looked at is "What are the odds of this happening in the game I played, with 200 hands dealt, last night?"... or, if I play once a week for 4 hours for 5 years, what are the odds of seeing this happen?

I don't really care to go into the math involved; it's certainly a bit draconian, but all in all not too terribly difficult.

Just wanted to chime in, though, as it's always a small pet peeve of mine to see people calculate these kind of probabilities so haphazardly without thinking about what kind of information is really being sought out.

[QuikSand]

Another, more subtle, question is: "Over the course of playing some poker for a few nights, how likely is it that something will happen that makes me think - 'wow, what are the odds of that?'"

This weekend, I saw a flop come 8-8-8, A, 8. People acted like Jesus dealt it himself. I just kept raising, with my wired nines. (I'll leave the eventual hand outcome as an exercise for the reader)

[finkenst]

but if it was just ANY straight, in order, it would be...2,560 possible combinations our of 311,875,200 (10/52*4/51*4/50*4/49*4/48). plus, if you assume, say, a 10 person table, you're now looking at 10/32*4/31*4/30*4/29*4/28, or 2,560 out of 24,165,120...about 1 in 10,000?

(um, am I right?)
okay.. c(52,5) ( i think it's combinations) = 52!/(52-5)! = 311875200 number of 5 card poker hands.

we have 10 possible straights (startings from low to high): 5, 6, 7, 8, 9, 10, J, Q, K, A (without regards to straight flush) so 10*4*4*4*4 = 2560 as DD said.


specifically for stevew, there are 4*4*4*4*4 possible 10 high straights = 1024.

where this gets less straight forward is non-suited cards. So, eliminating straight flushes you get 4*4*4*4*3 = 768. (i feel like i'm talking about bandwidth channels on a T1 ;) )

To eliminate the possibility of a flush you have 4*4*3*3*2 = 288, only 2 cards suited (2 X, 2 Y, something else)
+
4*4*3*2*1 (2 X, 1 of everything of else) = 96.

so maybe it's more like 384 (6 channels of a t1) / 311million
or 1 in 812175 to get a 10 high straight without a flush possibility.

[finkenst]

Another, more subtle, question is: "Over the course of playing some poker for a few nights, how likely is it that something will happen that makes me think - 'wow, what are the odds of that?'"

This weekend, I saw a flop come 8-8-8, A, 8. People acted like Jesus dealt it himself. I just kept raising, with my wired nines. (I'll leave the eventual hand outcome as an exercise for the reader)
I bet the guy holding AA or AK was pretty ticked off. :)

so, Who won?


http://dynamic.gamespy.com/%7Efof/forums/images/smilies/wink.gifhttp://dynamic.gamespy.com/%7Efof/forums/images/smilies/tongue.gif

[Raven]

Actually, I think Mckerney's probability is a bit high because it leaves the possibility of getting a straight flush (which didn't happen here).

Using his math, I'd say its more like his "4/52*4/51*4/50*4/49*4/48= 1024/311875200"
but minus the flush possibilities -4/311875200, so should be 1020/311875200.

Correct me if I am wrong.

[FishFan]

The odds of any combination of five cards being dealt are 1 in 2,598,960.

[finkenst]

Actually, I think Mckerney's probability is a bit high because it leaves the possibility of getting a straight flush (which didn't happen here).

Using his math, I'd say its more like his "4/52*4/51*4/50*4/49*4/48= 1024/311875200"
but minus the flush possibilities -4/311875200, so should be 1020/311875200.

Correct me if I am wrong.
cards are not suited... I wonder what that meant... i think yo have to eliminate all the flush possiblities (3,4,5 cads to the flush)... if not, then you are likely correct, Raven.

[finkenst]

The odds of any combination of five cards being dealt are 1 in 2,598,960.
i hated statistics.http://dynamic.gamespy.com/%7Efof/forums/images/smilies/mad.gif

i refine my answer to 384/2598960 ~ 1 in 6768

can i change my IWS#98 answer to stats.

[mckerney]

cards are not suited... I wonder what that meant... i think yo have to eliminate all the flush possiblities (3,4,5 cads to the flush)... if not, then you are likely correct, Raven.

I took it to mean that the cards don't necessarily have to be suited, though left the possability that they could be.

[stevew]

cards are not suited... I wonder what that meant... i think yo have to eliminate all the flush possiblities (3,4,5 cads to the flush)... if not, then you are likely correct, Raven.


Just meant that it wasnt a Straight Flush.

[finkenst]

Just meant that it wasnt a Straight Flush.
there are 4^5 ways to make a 10 high straight (6-10)... 1024

there are four 6-10 straight flushes.
so 1020?

man, my head hurts.
http://dynamic.gamespy.com/%7Efof/forums/images/smilies/mad.gif

[mckerney]

there are 4^5 ways to make a 10 high straight (6-10)... 1024

there are four 6-10 straight flushes.
so 1020?

man, my head hurts.
http://dynamic.gamespy.com/%7Efof/forums/images/smilies/mad.gif

yes, chances for a straight flush are 4/52 * 1/51 * 1/50 * 1/49 * 1/48 = 4/311875200

subtract this from my previously calculated solution and you get 1020/311875200

[mckerney]

Whatever the odds, it's the exact same odds of any particular five cards being dealt in a row. The only difference is that this event is memorable to the viewer not the odds of it happening.

Not exactly in this situation, because with any five cards there is one possible card, while with a particuar number there are four possible cards. To be exact, theres the same possability as there being 5 unsuited and unpaired cards occuring.