Unbelievable Hands

[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[img]/images/graemlins/diamond.gif[/img]2[img]/images/graemlins/heart.gif[/img] with a board of J[img]/images/graemlins/spade.gif[/img]8[img]/images/graemlins/club.gif[/img]3[img]/images/graemlins/heart.gif[/img]A[img]/images/graemlins/spade.gif[/img]7[img]/images/graemlins/spade.gif[/img]

Hand 2 I'm dealt 3[img]/images/graemlins/club.gif[/img]4[img]/images/graemlins/spade.gif[/img] with a board of K[img]/images/graemlins/heart.gif[/img]Q[img]/images/graemlins/club.gif[/img]5[img]/images/graemlins/diamond.gif[/img]2[img]/images/graemlins/spade.gif[/img]Q[img]/images/graemlins/heart.gif[/img]

Hand 3 I'm dealt A[img]/images/graemlins/diamond.gif[/img]J[img]/images/graemlins/diamond.gif[/img] with a board of 9[img]/images/graemlins/heart.gif[/img]6[img]/images/graemlins/spade.gif[/img]Q[img]/images/graemlins/diamond.gif[/img]K[img]/images/graemlins/diamond.gif[/img]7[img]/images/graemlins/club.gif[/img]

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[img]/images/graemlins/club.gif[/img], 6[img]/images/graemlins/club.gif[/img].
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[img]/images/graemlins/heart.gif[/img], 5[img]/images/graemlins/heart.gif[/img], 5[img]/images/graemlins/club.gif[/img] <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[img]/images/graemlins/club.gif[/img] <font color="blue">(4 players)</font>
<font color="CC3333">UTG+1 bets</font>, MP1 calls, MP3 calls, Hero calls.

River: (9.50 BB) 3[img]/images/graemlins/club.gif[/img] <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[img]/images/graemlins/club.gif[/img], 6[img]/images/graemlins/club.gif[/img].
<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[img]/images/graemlins/club.gif[/img], 4[img]/images/graemlins/spade.gif[/img], 8[img]/images/graemlins/club.gif[/img] <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[img]/images/graemlins/club.gif[/img] <font color="blue">(3 players)</font>
BB checks, <font color="CC3333">MP3 bets</font>, CO calls, BB folds.

River: (8 BB) 8[img]/images/graemlins/diamond.gif[/img] <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. [img]/images/graemlins/grin.gif[/img]