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Here is a puzzle on Poker

The other day I was down at Bullets Poker Club, in the Mobius Strip, playing Texas Hold 'Em. It was a pretty tight crowd and I couldn't get much action but this was one of the more interesting hands of the night.

I limped in on the button with suited connectors (8s, 9s). The flop came down Ac, 7s, 6s. A rock in ealy position raised it up to about triple the big blind. Everyone folded round to me but I stayed along for the ride. He had a pretty sizeable stack and didn't hesitate to go all in when a red Ace hit on the turn. this put me in a tricky spot, my fear was obviously that he'd been slow playing rockets.

If that were the case, the only way to win the hand, would be to land a straight flush on the river.

My two questions for you are:

1. What are my odds of hitting that killer straight flush?
2. Out of interest, what are my odds of making any straight or flush at the river?

Joseph Bolas wrote:Here is a puzzle on Poker

The other day I was down at Bullets Poker Club, in the Mobius Strip, playing Texas Hold 'Em. It was a pretty tight crowd and I couldn't get much action but this was one of the more interesting hands of the night.

I limped in on the button with suited connectors (8s, 9s). The flop came down Ac, 7s, 6s. A rock in ealy position raised it up to about triple the big blind. Everyone folded round to me but I stayed along for the ride. He had a pretty sizeable stack and didn't hesitate to go all in when a red Ace hit on the turn. this put me in a tricky spot, my fear was obviously that he'd been slow playing rockets.

If that were the case, the only way to win the hand, would be to land a straight flush on the river.

My two questions for you are:

1. What are my odds of hitting that killer straight flush?
2. Out of interest, what are my odds of making any straight or flush at the river?

I bet you're asking us that because you don't know.

Kai Laddiman wrote:I bet you're asking us that because you don't know.

I wouldn't set you all a puzzle if I didn't have the answers

Joseph Bolas wrote:My two questions for you are:

1. What are my odds of hitting that killer straight flush?

Well, if you're convinced that he has pocket aces, then there are 44 unknown cards and two of them make your straight flush. So 1 in 22 to make the straight flush against his four of a kind. If you assume that you don't know his hand (probably better here as he is beating you with almost anything) then its 46 unknown cards and two of them still make your straight flush, which means your odds have decreased to 1 in 23.

Joseph Bolas wrote:2. Out of interest, what are my odds of making any straight or flush at the river?

Again there are two situations. If you really believe that he has four of a kind then there are 44 unkowns and your outs are 2s, 3s, 4s, 5s, 10s, Js, Qs, Ks, 5d, 5c, 5h, 10d, 10c, 10h, which makes fourteen. So you're looking at 7 in 22. If you're not absolutely convinced that he has aces then you're looking at 46 unkowns, but an extra out, the As, making 15 in 46.

I'm not sure this is right though.

Jon O'Neill wrote:

Joseph Bolas wrote:My two questions for you are:

1. What are my odds of hitting that killer straight flush?

Well, if you're convinced that he has pocket aces, then there are 44 unknown cards and two of them make your straight flush. So 1 in 22 to make the straight flush against his four of a kind. If you assume that you don't know his hand (probably better here as he is beating you with almost anything) then its 46 unknown cards and two of them still make your straight flush, which means your odds have decreased to 1 in 23.

Joseph Bolas wrote:2. Out of interest, what are my odds of making any straight or flush at the river?

Again there are two situations. If you really believe that he has four of a kind then there are 44 unkowns and your outs are 2s, 3s, 4s, 5s, 10s, Js, Qs, Ks, 5d, 5c, 5h, 10d, 10c, 10h, which makes fourteen. So you're looking at 7 in 22. If you're not absolutely convinced that he has aces then you're looking at 46 unkowns, but an extra out, the As, making 15 in 46.

I'm not sure this is right though.

The answers I have, were based on the fact that you did not know what he had, so your answers of 1 in 23 for question one and 15 in 46 for question two, were correct .

Just to say I have seen a straight flush - Christine made one, with the board showing queen, jack, ten and nine all of clubs, Christine was holding the king of clubs. I suppose you'd have to feel a bit sorry for someone if they were holding the eight of clubs in this situation, as that would be a lower straight flush! So just one card away from the perfect royal flush.

Martin Gardner wrote:Just to say I have seen a straight flush - Christine made one, with the board showing queen, jack, ten and nine all of clubs, Christine was holding the king of clubs. I suppose you'd have to feel a bit sorry for someone if they were holding the eight of clubs in this situation, as that would be a lower straight flush! So just one card away from the perfect royal flush.

I've had a few straight flushes before, but I have also once had a Royal Flush on Pokerstars.

Joseph Bolas wrote:I've had a few straight flushes

Why are poker players so homophobic?

Phil Reynolds wrote:

Joseph Bolas wrote:I've had a few straight flushes

Why are poker players so homophobic?

That's the second time you've made this joke, are you trying to tell us something?

Martin Gardner wrote:That's the second time you've made this joke, are you trying to tell us something?

Yes - I like to tell the same jokes repeatedly.

Joseph Bolas wrote:If that were the case, the only way to win the hand, would be to land a straight flush on the river.

You've had the maths done for you by this point obviously (even though you'd also done it yourself!)... I'm just here to say that I really really hope you did fold?

Phil Reynolds wrote:Why are poker players so homophobic?

I've kissed two men whilst very drunk at house parties, and I'm quite the poker player too.
And yes, I know it was a joke, but my kissing men wasn't.
It's a very serious matter, and leaves you with an odd taste in the mouth and in the heart immediately afterwards.

Matt Morrison wrote:I've kissed two men whilst very drunk at house parties

An interesting admission, though probably not that unusual. As the joke goes:

Q. What's the difference between a straight man and a bisexual?
A. About four and a half pints of lager.

Until I met the man who is now my partner at the age of 40, my relationship history for the preceding 25 years consisted largely of intense emotional, and sometimes physical, friendships with straight men.

Aha! Ok that makes a bit more sense - needless to say I had absolutely no idea (and why would I) that you were gay!
Congratulations on eventually finding happiness (not that you said you were happy, but I guess you are!), hopefully we can all achieve that in our own ways.

Matt Morrison wrote:needless to say I had absolutely no idea (and why would I) that you were gay!

Well, I suppose some of my recent posts in other threads (like suggesting that Alistair Appleton would make a droolsome presence in Dictionary Corner) may have given the game away, although you probably marked all those as read when you rejoined the board. And having set up my profile so that you can link to my website by clicking the little globe symbol over there on the right, it is possible (though admittedly unlikely, assuming you have a life) that you might have already checked me out - but, as you say, why would you. Even I find my website boring these days.

Congratulations on eventually finding happiness (not that you said you were happy, but I guess you are!), hopefully we can all achieve that in our own ways.

Thank you - that's nice of you. Yes, the past seven years have been happier than I had any right to expect. Good things do indeed come to those who wait.

Matt Morrison wrote:

Joseph Bolas wrote:If that were the case, the only way to win the hand, would be to land a straight flush on the river.

You've had the maths done for you by this point obviously (even though you'd also done it yourself!)... I'm just here to say that I really really hope you did fold?

If this was the case in real life, I would've folded. I think it would be tough to call in that situation (but I might be wrong).