What are these odds?

[Kevin J]

I'm terrible with math, but I DO know that if a coin lands heads 90 times in a row that the chance it will land heads on the 91st time is still 50-50. But what are the odds of a coin landing heads two times in a row? Wouldn't it be 25%?

I had the most incredible two events happen to me today and I was wondering if anyone here can help me in figuring the odds.

Event #1. Without going into details, I had 22 on a JTT flop and beat a guy with JT when the board came a perfect 2-2. Wow! I'm pretty sure that's the worst beat I've ever put on somebody in 6000+ hours I've played hold'em!! I was still contemplating my luck when...

Event #2. I flopped a set of tens on an AT7 flop and got beat by pocket fives when the board came a perfect 5-5!!

What are the odds of this occuring once? Is it 1/47 times 1/46? And is there a way to calculate the odds of the same person being involved in this event twice in one day (I realize this NOT like a coin coming up heads twice in a row, or is it?)?

Anyway, I'm stunned that I could be on both sides of this event in the same day. So just out of curiosity I was wondering how unlikely it is. Thanks.

And sorry, I just have to add this... The 22 was a longshot to be sure. But it wasn't near as bad from a "play" standpoing as the 55. For one thing, the pot was MUCH smaller on the flop for 55. For another, my opponent could've hit one of his 5's on the turn and lost to a flush. Lastly, he raised multiple limpers pre-flop from the sb, so I was quick to fear AA. Otherwise, he'd have gotten a lot more bets from me on the turn and river.

[aloiz]

Yea if you want the odds of a series of independent events occuring you multiply them together. So for two heads in a row it would be 25%.

Wow! Two perfect perfects in the same day, that is amazing. 1/47 *1/46 is the correct odds of it occuring. To figure out the odds two occuring in one day is nearly impossible. You need to know the total number of hands played in the day, but also you need the odds that it occurs between you and another person, but that all depends on how you play. If you make the assumption that you play every hand and see the river everytime, you could come up with an answer, but even still coming up with the probability that a perfect-perfect occuring prior to the flop is pretty difficult.

However, my bet is that it'll probably never happen to you again in your lifetime.

aloiz

[Cerril]

The odds are tiny but it's happened. Here's a similar story, albeit with a less happy ending

I go to play in a B&M cardroom, sit down at 3-6 (I still play poorly live for some reason) and start playing... I think the session was 4 hours total.

Two hours in, I get 88; preflop capped, I'm stuck in because it came to me 1,1,2 and I never had a point where it was good to get out. Besides, it was five or six handed. The flop comes AKJ, two to a suit I don't have. Three bets to me, I fold, capped behind me. Turn comes 8 suited with the board. Capped by three players. River is the case 8 (natch!). So I kick myself for what really ended up being a bad play, because of my pot and implied odds. I should have seen the turn. Anyway.

Next hour my friend sits down at the table. I fold, he stays in through a capped preflop. Flop comes AKQ, two to a suit. Capped behind him by four remaining, he folds. Turn comes a 7 suited to the board, capped. River comes a 7, capped. If I recall a flush beat a straight beat trips beat.. I think the fourth guy just mucked. And we all know what my friend dropped on the table (77 for those who failed the foreshadowing portion of the course).

So yeah, it's not likely but it happens and it happens often enough that you've got (at least) two people in one place who can relate roughly the same stories of it happening twice within about a week.

[RunrRunr2Win]

I have a bad habit of misunderstanding this but I had always assumed the odds would be. 2/47 * 1/46.

[aloiz]

Opps no you're correct 2/47 * 1/46.

aloiz

[stinkypete]

[ QUOTE ]

Next hour my friend sits down at the table. I fold, he stays in through a capped preflop. Flop comes AKQ, two to a suit. Capped behind him by four remaining, he folds. Turn comes a 7 suited to the board, capped. River comes a 7, capped. If I recall a flush beat a straight beat trips beat.. I think the fourth guy just mucked. And we all know what my friend dropped on the table (77 for those who failed the foreshadowing portion of the course).


[/ QUOTE ]

must have been a really big flush to beat a full house /images/graemlins/grin.gif

either that or the deck had more than four 7's...

[skp]

The 22 and 55 beats (i.e. when you catch perfect perfect as opposed to just runner runner) are the worst possible beats in hold 'em. Odds of 989:1 which is calculated as 2/45 times 1/44 which is 1 out of 990 or 989:1.

[BrettK]

How about the odds of Player B winning in this scenario?

Nine players are all-in preflop.

Player A holds AdAh.
Player B holds KdKh.
Player C holds KcKs.
Player D holds QcQs.
Player E holds JcJs.
Player F holds TcTs.
Player G holds 9c9s.
Player H holds QhJh.
Player I holds Th9h.

Player B must catch the 9d, the Td, the Jd, and the Qd over five cards to win. Eighteen cards are out of the deck. He has five chances, with 34 cards left in the deck, to catch the 9d(5/34). When he hits, he has four chances, with 33 cards left in the deck, to catch the Td.
To make a long story shorter, his chances of catching those four cards over the five draws are 5/34 x 4/33 x 3/32 x 2/31, which is 120/1113024, or about 1/9275.

Is this the worst possible beat in HE?
Please correct me if I'm wrong.

Brett

[Cerril]

Heh, good point. Okay I don't know what ended up winning, might have been the boat. I was crying about my lost quads, so I couldn't see the cards so well. /images/graemlins/wink.gif