Odds of the mother of all bad beats please

[rfsch]

Party 2-4. A,2 spades under. 3,4,5 spades flop. Straight flush, cool! BUT my opponent had 6,7 spades under so I sucked hind teat while capping the whole way. Had fun with the hand but am wondering if any of you can either indicate the formula for calculating the odds against me losing this flopped straight flush to another flopped straight flush-in sequence yet, or do it for me and give the answer. Must be very high. Happened last night. Ten players, I was in position seven,no raises to me. Hand number 2345130301

Thanks for your help. (Alas, I wasn't at a bad beat table.) Thanks for your help. Just curious.

[AaronBrown]

I don't consider this a bad beat. It was very unlucky, of course, but your opponent didn't play badly then win on the river. If the 6 and 7 of spades come on the turn and river, and your opponent has the 8 of spades, then you have a bad beat.

If you have a non-royal straight flush with the four top cards on the board, the card that beats you is somewhere. After the river card has been dealt, there are 45 cards you haven't seen. At a table of 10, 18 of them are your opponents' holes cards. So there's 18/45 = 40% chance that someone held the card that beats you. However, depending on what the card is and how the hand evolved, the chance that he's still in the hand at showdown could be much smaller.

You got a double whammy, he needed two specific cards; and they were cards most people would have folded. The odds of a single player having the two cards needed to beat you is (2/45)*(1/44) = 1/990. With 9 opponents it's 1/110 that someone could beat you.

[rfsch]

Thank you Aaron

[Orpheus]

Actually, as I have written elsewhere, it is not all THAT unlikely, given that you are in that situation in the first place. The "situation" provides more of the percieved "unlikeliness" than the rarity of the opposing hand.

GIVEN the hand and flop you describe, the chances of that beat are:
In a heads-up game: (2/47)*(1/46) = 0.0925% or 1:1080
At a full 10-table: 9 * ((2*1) * (43!/27!))/ (47!/29!)) = 0.3414% or 1:292

A really long shot, true, but would you regard the equally unlikely AK vs AA on a AKK flop (which has happened to me twice) as equally 'unbelievable'? The SF beat just *seems* more unlikely because SF are so valuable and uncommon.

IMHO, it helps to know that the improbability more like winning the door prize at a school play than God personally striking you with lightning.

Interestingly, the odds of this beat are *higher* after the river than after the flop. There is an 8.3% chance that one of the two danger cards will show up on the turn or river, so if the beat is still possible, it's more likely.

However, these odds may be enough to slightly modify your strategy and pay more attention to your reads, rather than going "monster blind", as I've sometimes done.

Disclaimer: I am a confirmed moron.
[edited to add: "and apparently a slow/careless keyboardist". Aaron posted while I was still trying to get the equations typed right. My numbers are postflop. His are post-river.]

[VivaLaViking]

Arron,

I'm glad you noted that "most people would have folded" but with online playing I'm never surprised at the hands people will go in with, exen in early position and into raised pots. Se La Vie.

[rfsch]

Thank you Orpheus. I much apprecite it.

Alas the liklihood of me not going "monster blind" after flopping any straight flush are zero to none. Too rare as you indicate, and in a 2-4 game I don't mind losing that one cuz the perversity of laughing at the irony of the result is deeply ingrained. We all get to have our foibles, yes?

Thanks again.

[Orpheus]

True, true. Fortunately, it's a rare, rare occasion that you don't get the pot odds to raise with your SF. I'm not sure there's is a player or tell in the world that *should* put you off a 99% winner. If there is, it'd be such a tiny subset of the already rare SFs, that missing the read is a fraction of a penny off your overall BB/100 -- assuming you encouter it at all in a lifetime of poker.

I should set up a "penny fund for tiny leaks" to support the mental health of our community. Just reading the applications would be worth the pennies I'd pay out. Alas, I don't think it would make the players feel any better, and the do-gooders who consider poker winnings "ill-gotten gains" probably wouldn't accept this as my charitable effort

But that's not why I'm posting. Remember what I said about being a crappy typist? I typed 43 instead of 45, and built the rest of the equation on that, leading to the wrong number when I pasted it into the calculator. D'oh!

The correct postflop beat probability at a 10-seat table is:
9 * ((2*1) * (45!/29!))/(47!/29!) = 0.8326% = 120:1

[theben]

here are the real odds for the "mother of all beats":

Chance that Earth will experience a catastrophic collision with an asteroid in the next 100 years: 1 in 5,000

[larry364]

About a month ago, I also had the "sucker" straight flush and after I raised the original better he went all in. I decided he "only" had an A high flush, so I called and won.

[rfsch]

Thanks again Orpheus. I appreciate the correction and info.