Unbelievable Hands

[Officer Farva]

After responding in the post entitled, "How often will quads over quads happened", I became interested in finding the statistics behind some of the more unbelievable hands experienced by posters in this forum. Examples:

quads over quads : 5 times in a million
dealt same trips three times in 7card Stud: 8 times in 100 Billion

What are the most unbelieavle hands you've seen. If you post it, I'll do the math. If its too statistically unlikely, I'll call your bluff.

[Cleveland Guy]

I swear this happened to me, and I know it's really unlikely, but I gotta know how unlikely

Hand 1: Quad Ks
Hand 2: Royal Straight Flush

I got this in back to back hands of a SnG Once.

[meep_42]

Quad 2's over Aces Full of 2s over 5s Full of 2s.
22 v AA v 55, A52 flop, 2 turn, unimportant river.

-d

[crash]

pocket 4s three times in a row (in HE): 10.6 million to one?

[JinX11]

I think I have this one....

On Empire $3/$6, I received AA and another guy received KK pre-flop. The following hand, we both received the same two starting hands, though not the same exact cards (different suits).

Needless to say, he was not happy. I told him that there was a glitch in the Matrix.

Someone on another forum calculated the odds of this happening...let's see how close your numbers come to his.

[Officer Farva]

Ok, well,

P(Quad Kings beaten by any Royal Flush (10 sided)) =

((Royal Suited Connectors(no king) * Pocket Kings w/o critical King*KKRoyalRoyalX Boards)+(RSCs*KingX w/o crit King *KKKRR Board)(Ways to deal out other 8 Hands) /
(Ways to deal 10 hands)(# Boards) =
((48*6*(28*120)) + (48*78*120))(43 P 16)/(52 P 20)(32 P 5) =
.000000001
So this happens once every billion hands

It happens twice in a row once every heptillion hands
, or once every billion billion hands.

That is the most unbelievable thing that I have heard of...I don't think it happened.

[Officer Farva]

Well, because of the deatils and lack of arbitrarity, this is simply

#Aces*#5s*#2s*(# A522x boards)*(Number of ways to deal out remaining hands)/(deals)(boards) =

12*12*12*(4*44)*(43 P 8)/ (52 P 10)(32 P 5)=

.000001282

so 1.2 times in a million

[Officer Farva]

[censored], my denominator is wrong in all of these...

[AviD]

No I think he said he had quad Ks and then the next hand had a Royal...not one over the other twice in a row.

[Officer Farva]

oops thanks

[Cleveland Guy]

Correct, back to back hands - I can't even remember what my opponents had in each of these hands.

To ad to it - on both occasions I used both of my whole cards (KK) and (AQs).

I'm sure this is fairly unlikely, as getting quads or a royal flush by itself is a very rare occurence, what are the odds of it happening back to back.

[Officer Farva]

Ok, the first time this is 6*6/((52 C 2)(50 C 2)) = .000022163

Second time (different suits, im guessing that means at least one suit was different) =
5*5/((52 C 2)(50 C 2)) = .000015391

So, the probability of that exact sequence (with the differnet suits) is (.000022163)(.000015391) =

3.4111 * 10 ^ -10, or 3.4 times every 10 billion hands

In general, this will happen (.000022163)^2 of the time,

or
4.9 times every 10 billion hands

[goofball]

i once beat AKKKK and AAAKK with a royal flush.

board was AdKdKsTdx and i had QdJd against AA and KK

[Officer Farva]

Ok...

In general, you'll get quad kings

48 C 3/52 C 7 = 0.0001292 percent of the time

and a royal flush

47 C 2/52 C 7 = .00000808 percent of the time

so in a row = (.0001292)(.00000808) = about .000000001
roughly once in a billion times.
But that includes using the board..

ill do your instance in a minute..

[sthief09]

a couple of weeks ago I was scrwing around playing stud/8 and one person got dealt (KK)K and the another (AA)A

[Gorgonian]

Best I've got on this topic is back to back rolled up trip fours in 7 card stud. Actually won both hands, too. /images/graemlins/smile.gif

[Officer Farva]

4/ 52 C 3 * 4 / 49 C 3 = (dont have my calculator)
= 16/52*51*50*49*48*47*9*4
= roughly 4/(50)^6*9
=1/30 billiion

[Bulldog]

[ QUOTE ]
i once beat AKKKK and AAAKK with a royal flush.

board was AdKdKsTdx and i had QdJd against AA and KK

[/ QUOTE ]

How'd the betting go on this one? What limits?

[Bulldog]

My two best back-to-back hands, quads and a wheel straight flush:

http://tinyurl.com/5rk6u

Odds?

[Cleveland Guy]

I'm gonna go out on a limb here - and say your odds were the same as my back to back quads/royal.


I might be wrong but hitting a wheel straight flush is just as hard as hitting a royal straight flush.

And quads are quads - be it 6666 or kkkk.

[Officer Farva]

You're right, cleve.

The odds I laid out, thought, are for specific quads followed by a specific straight flush.

The odds for getting any set of quads followed by any straight flush are slightly greater.

I'm too burnt out to do any more math for now...unless its a really good problem. (like the probability of having quad kings beat ny a royal flush, that was interesting)

Gearing up for Math 212...

[kem]

[ QUOTE ]
What are the most unbelieavle hands you've seen. If you post it, I'll do the math. If its too statistically unlikely, I'll call your bluff.

[/ QUOTE ]

How about this:
Hand 1 I'm dealt 9/images/graemlins/diamond.gif2/images/graemlins/heart.gif with a board of J/images/graemlins/spade.gif8/images/graemlins/club.gif3/images/graemlins/heart.gifA/images/graemlins/spade.gif7/images/graemlins/spade.gif

Hand 2 I'm dealt 3/images/graemlins/club.gif4/images/graemlins/spade.gif with a board of K/images/graemlins/heart.gifQ/images/graemlins/club.gif5/images/graemlins/diamond.gif2/images/graemlins/spade.gifQ/images/graemlins/heart.gif

Hand 3 I'm dealt A/images/graemlins/diamond.gifJ/images/graemlins/diamond.gif with a board of 9/images/graemlins/heart.gif6/images/graemlins/spade.gifQ/images/graemlins/diamond.gifK/images/graemlins/diamond.gif7/images/graemlins/club.gif

Note that these cards appeared *EXACTLY IN THIS ORDER*

What are the odds???? No seriously, calculate them. It's ASTOUNDING! In fact, I have 10,000 hands here which if you calculate the exact odds of each one occurring in the order in which they did, you will find it mind blowing. But I can attest to the fact that they really did happen.

In case people need help, the odds of these 3 hands occuring as they did is something like:
(1/52*1/51*1/50*1/49*1/48*1/47*1/46)^3
ans = 3.2620e-36

Now, change that "^3" to "^10000" and you will see that it's astronomically IMPOSSIBLE for me to be dealt the hands that I have. Yet I really was dealt them!

If you can figure out this conundrum then you will realize why this whole thread is a huge waste of time.

[Officer Farva]

Its funny cuz those hands arent even important, but they're just as unlikely. Ha!

Waste of time? How long did it take you to write that post...?

And you're math is wrong

[AviD]

[ QUOTE ]
To ad to it - on both occasions I used both of my whole cards (KK) and (AQs).


[/ QUOTE ]

If your cards weren't whole there would be a big problem. Sometimes they do crack tho, you should let floor know immediately...but likely only when you have the cracked cards.

[razor]

What are the odds of me getting straight flush over quads twice within one week with the same hole cards?

Sadly the second one doesn't count as I folded pre-flop...


Party Poker 1/2 Hold'em (10 handed)

Preflop: Hero is Button with 4/images/graemlins/club.gif, 6/images/graemlins/club.gif.
UTG calls, UTG+1 calls, <font color="666666">1 fold</font>, MP1 calls, <font color="666666">1 fold</font>, MP3 calls, <font color="666666">1 fold</font>, Hero calls, SB completes, BB checks,

Flop: (7 SB) 7/images/graemlins/heart.gif, 5/images/graemlins/heart.gif, 5/images/graemlins/club.gif <font color="blue">(7 players)</font>
SB checks, BB checks, UTG checks, <font color="CC3333">UTG+1 bets</font>, MP1 calls, MP3 calls, Hero calls, SB folds, BB folds, UTG folds.

Turn: (5.50 BB) 2/images/graemlins/club.gif <font color="blue">(4 players)</font>
<font color="CC3333">UTG+1 bets</font>, MP1 calls, MP3 calls, Hero calls.

River: (9.50 BB) 3/images/graemlins/club.gif <font color="blue">(4 players)</font>
UTG+1 checks, MP1 checks, MP3 checks, <font color="CC3333">Hero bets</font>, UTG+1 folds, <font color="CC3333">MP1 raises</font>, MP3 folds, <font color="CC3333">Hero 3-bets</font>, <font color="CC3333">MP1 caps</font>, Hero calls.

Final Pot: 17.50 BB
<font color="green">Main Pot: 17.50 BB, between Hero and MP1.</font>

Results below:
MP1 shows 5d 5s (four of a kind, fives).
Hero shows 4c 6c (straight flush, six high).
Outcome: Hero wins 17.50 BB.



Party Poker 1/2 Hold'em (9 handed)

Preflop: Hero is UTG with 4/images/graemlins/club.gif, 6/images/graemlins/club.gif.
<font color="666666">3 folds</font>, MP2 calls, MP3 calls, <font color="CC3333">CO raises</font>, <font color="666666">1 fold</font>, SB calls, BB calls, MP2 folds, MP3 calls.

Flop: (9 SB) 7/images/graemlins/club.gif, 4/images/graemlins/spade.gif, 8/images/graemlins/club.gif <font color="blue">(4 players)</font>
SB checks, BB checks, <font color="CC3333">MP3 bets</font>, CO calls, SB folds, BB calls.

Turn: (6 BB) 5/images/graemlins/club.gif <font color="blue">(3 players)</font>
BB checks, <font color="CC3333">MP3 bets</font>, CO calls, BB folds.

River: (8 BB) 8/images/graemlins/diamond.gif <font color="blue">(2 players)</font>
<font color="CC3333">MP3 bets</font>, <font color="CC3333">CO raises</font>, MP3 calls.

Final Pot: 12 BB
<font color="green">Main Pot: 12 BB, between MP3 and CO.</font>

Results below:
MP3 shows Ts Th (two pair, tens and eights).
CO shows 8s 8h (four of a kind, eights).
Outcome: CO wins 12 BB.

[Peter Harris]

miaow you're talking, chickenfu**er!

[Officer Farva]

This is a very interesting event, and a very difficult problem.

Probability depends on how you define certain things...

I will answer the problem defined as: The probability of getting two identical suited connectors and using both of them to make straight flushes over quads and that we are given that at least one person has a PP of rank not involved in our straight flush and he/she will make the quads. Otherwise, this problem will take too long.

For each suit, we have 46 suited connectors that can make straight flushes (A2,A3,A4,A5,23,24,25,26...QA,KA), for a total of 178 possible starting hands...

=P(Suited Connector for Hero)P(Made Straight Flush and Villain Made Quads)

Now here is the tricky part, we must use weighted probability to find the P(Straight Flush), since the Hero could have any of straight flush 46 rank pairings.

For the 10 3 gappers (A5,26,37...10A), there is only one board (three inner cards)

For 9 two gappers (excl. A4, JA), there are two possible straight fluh boards (2 innner, one outer on either side)

For A4 and JA, there is only one board

For A3,QA, there is only one board

For 24,JK, there are two boards

For 35-10Q (8) there are 3 boards

For A2, AK there is one board

For 23, QK, there are two boards

For 34, QJ, there are three boards

For 45-10J (7), there are four boards

so there are an average of (16(1) + 13(2) + 10(3) + 7(4))/46
= 100/46 (2.17) Boards per starting hand that will make a straight flush

For each of the 2.17 Boards, the quads will be made by filling in the board with two specific quad cards, which can only happen one way (the two cards of the villain's pair's rank), so there are 2.17*1 ways to make our board.

Thus, we have P =

=(168/1326)((100/46)/(48 C 5))= .0000000161 (Once in a 100 million)

The second time, Hero must recieve the same hand, so

P=
(1/1326)((100/46)/ 48 C 5)) = .0000000009036641481

Combined, the P(What you claim happened) =
(1.61*9.0366)*10^-18 = roughly 1.45 * 10^-17

That will hapen about 1.5 times for every 100 quadrillion hands you play...the true probability is actually a little greater depending on how you define the problem.

Did that really happen?

[mostsmooth]

i got an 872 rainbow 3 times in 4 hands playing 7stud, hows that grab ya?

[Officer Farva]

Look at kem's post, that should make you happy.

[Bulldog]

[ QUOTE ]
And you're math is wrong

[/ QUOTE ]

I hope you have English 101 to go with Math 212. /images/graemlins/grin.gif

[Officer Farva]

[ QUOTE ]
I hope you have English 101 to go with Math 212.

[/ QUOTE ]

We dont have that class at are school, but their is a class called Writing 1A.

[razor]

[ QUOTE ]
Did that really happen?

[/ QUOTE ]

Well it woulda happened if I had decided to gambOOOl it up UTG with 6/images/graemlins/club.gif4/images/graemlins/club.gif on my last hand of the night last night (is there a lesson there??).

As the last bets went in on the hand, I typed in chat that I'd kinda like my cards back. Quads guy says 'I doubt it' as he's turning over pocket 8s. I respond that 'In fact, yes I do'

The first hand occured last week Wednesday and the second last night.

[Officer Farva]

Snap.

I thought they were back to back.

Nonetheless, amazing. Id never fold 46c again, if I were you...

[BarronVangorToth]

While I know a few examples above are more unlikely than my example, and I also realize that the example I'm about to give isn't my oddest of statistics, but a few months back I got pocket 7's (different ranks) in Hold 'em FOUR hands in a row.

Kind of kooky....


Barron Vangor Toth
www.BarronVangorToth.com (http://www.BarronVangorToth.com)

[IlliniRyRy]

Barron, your website is AWESOME. I got nothin else to say except check it out people. Extremely well done.

[Bulldog]

[ QUOTE ]
[ QUOTE ]
I hope you have English 101 to go with Math 212.

[/ QUOTE ]

We dont have that class at are school, but their is a class called Writing 1A.

[/ QUOTE ]

I love your posts. I'm not sure if this one was intentional or not. I think Sports Guy would give it a 93 on the Unintentional Comedy Scale.

[Officer Farva]

[ QUOTE ]


[ QUOTE ]
We dont have that class at are school, but their is a class called Writing 1A.


[/ QUOTE ] I love your posts. I'm not sure if this one was intentional or not. I think Sports Guy would give it a 93 on the Unintentional Comedy Scale.

[/ QUOTE ]

What was intentional??? Am I missing something here???

[mikeyvegas]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
I hope you have English 101 to go with Math 212.

[/ QUOTE ]

We dont have that class at are school, but their is a class called Writing 1A.

[/ QUOTE ]

I love your posts. I'm not sure if this one was intentional or not. I think Sports Guy would give it a 93 on the Unintentional Comedy Scale.

[/ QUOTE ]

You really think it rates up there with:

-A.C. Cowlings driving the White Bronco and doing his "This is A.C.!" routine.

I thought it was closer to:

- Latrell Sprewell, yacht owner.

[goofball]

3 bets PF, 1 bet on the flop, capped on the turn and river. i was all in after the turn

[Sundevils21]

[ QUOTE ]
[ QUOTE ]


[ QUOTE ]
We dont have that class at are school, but their is a class called Writing 1A.


[/ QUOTE ] I love your posts. I'm not sure if this one was intentional or not. I think Sports Guy would give it a 93 on the Unintentional Comedy Scale.

[/ QUOTE ]

What was intentional??? Am I missing something here???

[/ QUOTE ]

[PokerSlut]

[ QUOTE ]
Watt was intentional??? Am I missing something hear???

[/ QUOTE ]

[Blarg]

[ QUOTE ]
dealt same trips three times in 7card Stud: 8 times in 100 Billion

[/ QUOTE ]

This one was mine. /images/graemlins/smile.gif Thanks for figuring it out -- I had always wondered. Seems so staggeringly impossible. Couldn't possibly blame someone for leaving the table after seeing that happen, or claiming even the Pope himself had just cheated. It would really be more likely by far than any alternative.

By the way, I remember Mike Caro used to regularly "debunk" poker tall tales in Card Player magazine some years back in his column. His column was often pretty poor and read like it was grudgingly slapped together out of scrounged up odds and ends at the last minute in a haze, but I thought he really got out of line when he started saying that if someone told you "X" he was full of it because the odds were just too long. Out of all the things to happen in all the poker casinos, what are the chances that none of these unlikely stories would EVER happen? Caro really got his brain messed up there. I knew that if I could get trip 9's three times in a row in 7-stud, then the stuff he was saying was impossible was actually definitely possible.

[Officer Farva]

I agree. There are so many poker hands played day to day around the world that very unlikely occurences are more than likely to happen. It would be interesting to get an estimate of just how many hands of what games are played during a given day, month, and year.
Still, of all the hands played, only are very small percentage are played by the 2+2 posters of the world. And getting the same trips dealt to you 3 times consecutively is amazing.

Mike

[Bulldog]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
I hope you have English 101 to go with Math 212.

[/ QUOTE ]

We dont have that class at are school, but their is a class called Writing 1A.

[/ QUOTE ]

I love your posts. I'm not sure if this one was intentional or not. I think Sports Guy would give it a 93 on the Unintentional Comedy Scale.

[/ QUOTE ]

You really think it rates up there with:

-A.C. Cowlings driving the White Bronco and doing his "This is A.C.!" routine.

I thought it was closer to:

- Latrell Sprewell, yacht owner.

[/ QUOTE ]

Nice. /images/graemlins/smirk.gif

[Bulldog]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]


[ QUOTE ]
We dont have that class at are school, but their is a class called Writing 1A.


[/ QUOTE ] I love your posts. I'm not sure if this one was intentional or not. I think Sports Guy would give it a 93 on the Unintentional Comedy Scale.

[/ QUOTE ]

What was intentional??? Am I missing something here???

[/ QUOTE ]

[/ QUOTE ]

Okay, now that has to be in the mid- to high-80s! /images/graemlins/laugh.gif