Gedankenexperiment #2

[PDosterM]

Gedankenexperiment (Thought Experiment) #2:

Being able to tell when you have the nuts is, of course, an important ability. Everyone knows that an Ace-high flush can, under the right circumstances, be the nuts. If you hold A/images/graemlins/spade.gif5/images/graemlins/spade.gif you have the nuts when three or more spades are on the board, no straight-flush is possible, and there is no pair.

On the other side of the picture, if the best hand you can make is one pair, there are no boards that can make that hand be the nuts. Someone else could always have a set or even better depending on the board.

But these two concepts must meet someplace. Specifically, once the river has been reached, what is the lowest possible five-card poker hand that could, with the right board, be the nuts? You are free to hypothesize any initial two-card holding and any five-card board from the remaining cards.

[Warik]

I like this. I'll try.

The straight flush can be the nuts if there's no higher straight flush. Let's go down to quads.

Quads can be the nuts if the board isn't paired over the rank of your quads (i.e. H:KK B:KKQQ can be the nuts but H:KK B:KKAA might not be)... this would make H: 22 B:22345 the lowest quad hand that could be the nuts if and only if the 345 are not the same suit.

Moving down to a full house. A full house can be the nuts if the board if it's split. A pocket pair can't make the nut full house because that would require the board to be paired and thus someone could hold a pocket pair corresponding to the board pair. So H:AA B:AKK is not the nuts because someone could have KK.

So you'll need to have a split full house AND you have to ensure that the trip portion of your full house is the highest possible. i.e. H:KQ B:KKQA is not the nuts because AA beats you.

That would make the lowest nut full house H: 25 B:23455 as long as 345 aren't the same suit. 22 isn't possible and 33 and 44 are no good because you have 555.

Flushes... the A-high is the lowest nuts because you need a minimum of 3 suited cards on the board and AXs will beat any non-straightflush.

So now we're down to straights. H: 45 B:A23 XX would be the nuts as long as there's no flush possible, XX doesn't pair the board, and XX != 4 or 5.

Next we have sets... can a set be the nuts? Yes... if 1) no flush is possible 2) no straight is possible and 3) no higher set is possible.

555 won't work because to meet criteria #3 we'd be violating #2 and #3. 666? 777? 888? nope. 999? (23 67 9... 58 beats us). TTT? (23 79T... 68 does it). JJJ? (23 78 J... 9T does it). QQQ? (23 78 Q. That works). H: QQ B:2378Q looks like the lowest nut set. I'm not too sure about this one.

Two pair? Can't be the nuts ever because someone could have a set. Same deal with a pair.

So my official answer is that the lowest possible five-card poker hand that could be the nuts is:

H: QQ
B: 2378Q

Hand: QQQ78

if and only if there is no threeflush on board.

How'd I do?

[fluff]

I submit the following:

Hole cards: Q /images/graemlins/heart.gif Q /images/graemlins/diamond.gif

Board: Q /images/graemlins/spade.gif 8 /images/graemlins/diamond.gif 7 /images/graemlins/club.gif 3 /images/graemlins/heart.gif 2 /images/graemlins/diamond.gif

Edit: Well, I suppose kicker is important, and that can be minimized. Answer changed to minimize kicker.

[Warik]

We got the same solution and now I think it's right. Kicker, however, cannot be minimized because it would make a straight.

To reduce the kicker we'd have to reduce the 8. Can't make a 7 cause that pairs the board. Can't make it a 6 cause 45 will make a straight. Can't make it a 5 because A4 or 46 make a straight. Can't make it a 4 because of A5... and can't make it 2 or 3 because that pairs the board.

Q8732 looks like the solution. Anybody have anything lower?

[PDosterM]

Nice analysis. That’s what I come up with as well.

This problem interested me as I watched a player (live 4-8) contemplate for about a minute trying to determine if his set of Jacks was the nuts or not when a Jack was the high card on the board. Your analysis tells him to go directly to identifying what straight might be out against him. (There was one, and I had it.)

I have asked this question several times – just to strike up a conversation with a player – and so far, I haven’t come across anyone who had considered it.

Thanks.

[fluff]

You are correct.

The when I said minimize kicker, I meant with respect to the best 5 card hand.

For instance QQ with a board Q T 7 5 2 is also the nuts, with a set of Qs, but the 5 card hand is QQQT7 which has a higher kicker than QQQ87.

In fact, I'm certain that QQQ87 with no flush possiblity is the absolute lowest absolute nuts.

[Bozeman]

qq with q j 7 6 2, or similar board, no flush possible, will make three queens the nuts.

3 jacks or worse will never be the nuts because there will always be either an overcard, a pair, or a possible str8 on the board.

Craig

[Bozeman]

One error in your analysis, Warik:

To be the nuts, a FH has to have the top two different ranks on the board in it (and, as you said, the top rank paired). So 52 with 55234 is not the nuts because 54 beats it. I think 54 w 55234 is the lowest nut FH.

Craig

[Warik]

You're right. I was going to correct it but you beat me to it.

Your example with the jack kicker however is not the lowest possible three-queen set. I think 8 is the lowest possible kicker for that hand.

[Ed Miller]

It [a set of queens is the lowest possible nut hand] is mentioned in one of the books I read. I'm going to guess little Hold 'Em.

[CrackerZack]

I was bet into on the river at the Borgata a few weeks back when I had a set of queens that was the pure nuts. I raised, he called with T high busted straight and flush draw. If I had known this was the lowest possible nut hands I would've felt smart for about 2 seconds instead of trying to figure out 1.) Why he called 2.) Why he showed me his hand after calling.

[Festus22]

You seem to like useless holdem trivia. Here was a post I made about a month ago. Enjoy.

http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=holdem&Number=532158&Forum =All_Forums&Words=3555&Match=Username&Searchpage=3 &Limit=25&Old=allposts&Main=532158&Search=true#Pos t532158

[PDosterM]

Festus,

Yes. Nice set of questions that generated some thought and interesting posts.

I think I can get your question 4 answer for pot size in a 100-200 game up by yet another $1,000. At least where I play, if someone straddles, the cap doesn't take effect until 5 small bets are made. (The straddle doesn't count as the first raise.) That makes the answer $25,800.

[DrSavage]

Where I play if a straddle is restraddled then the preflop cap is 6, so it could be even more.

[PDosterM]

Sure,

As long as further straddles are allowed. My club allows one.

Are there places where it can go on clear to the button?