What are the Odds?

There are a lot of ways to shuffle a 52 card deck. Way more the a trillion or quadrillion. Something on the order of the number 8 followed by 67 zeroes.

80,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. More or less.

Think about that.

When a new dealer was coming in at my table last night, I asked him to deal me a flush. Or any winning hand, really. At the moment it seemed like a flush would be good enough. My JJ had lost to 86s held by a player with a short stack and ‘fuck it’ attitude who wanted to stick it all-in pre-flop. My AA had lost to a guy with a slightly larger but still short stack who stuck it in with T♣8♣ after a flop of JT♠7. Three other times my opponent rivered a straight. AKs < AJs. Death by a combination of paper cuts and a couple of Saturday Night Specials.

But I am resilient, and through the miracle of having put more cash than normal in my pocket, I’m deep stacked again. It is a purchased deep stack, not my preferred way to get one.

With QQ♣ in early position, I raise. After two callers, another player re-raises to nearly 4x the amount I had bet. For purposes of this blog, I’ll call him “Phil.” We are good friends. And as badly as my session is going, his is going well. Or at least it was going well, until he redistributed a chunk of his profits from earlier in the session. He still has me covered.

I’ll make the hand history brief…

I check/call after a flop of K94. I check again when the T gives me the 2nd nut flush on the turn along with a 1-outer to a straight flush. Phil bets again.

Unless one of two things happens here, I’m good! Either he has the ace of hearts, in which case I’m toast, or he has a set (most likely kings, but tens and even nines could be in his pre-flop 3-bet range) and improves on the river to a full house.

What are the odds of all of the following being true?

  • Phil and I are both deep stacked
  • Phil has the ace of hearts – with 52 cards in the deck, that’s about (1/52) x 2, or 1/26. In other words, about 25-to-1 against
  • I have the queen of hearts – same 25-to-1 against, although we know I have it
  • All hearts come on the flop, including specifically the king. A monotone flop occurs approximately 1% of the time, so that’s 99-to-1 against. But only one in four of those will have a king, meaning it’s another 3-to-1 against
  • Another heart comes on the turn. At this point there would be 45 cards remaining in the deck, including eight hearts, which we can sorta round to 4.5-to-1 against

That all adds up to something over 800,000-to-1, which the nerdiest readers of this blog are sure to point out is mathematically flawed. Well, leave a comment if you must; I’ll be sure to ignore it.

Those are really long odds, and here I was with the 2nd nuts. It felt like it was my turn to win a big pot. Or light my bankroll on fire. How long can I run bad? Surely the last thing I want to do is let Phil improve to a full house if he has a set here, without charging the maximum price.

Ahem, make that the next-to-last thing I want to do, because when I announced all-in, and he snap called and fast rolled two red aces, my definition of the last thing I want to do quickly changed.

running bad

Odds are for dummies. #TheyAlwaysHaveIt

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