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What is the minimum preflop range I have to play to have on every 5 Card board the nuts in my range?

E.g. On a: As 4s 5s Kc Qs Board I would need 2s3s But I guess there is no board where you need any 27o to represent the nuts.

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what if the board is 7s 8s 9s 2c 3d: if you have Ts and 6s you have the nuts, because nobody can have Js Ts (you have the Ts). But if you have Js Ts, you also have the nuts. Should Ts 6s be part of the "range" you want to find? – TacticalCoder Jan 12 '12 at 1:12
my definition of "nuts" in this context: a hand you are sure nobody has a stronger hand. So on 77225 72 are nuts, but you still dont have to have 72 in your range to have the nuts on 77225 – MartinK13 Jan 12 '12 at 1:25
silly me. Of course. My example was poorly chosen: but now at least I know you're not talking about the "exclusive nuts". Back to the drawing board : ) – TacticalCoder Jan 12 '12 at 1:28
but then what do you need to have on, say, an AAAAK board? You have the nuts (you are sure nobody has a stronger hand). Or on a 99932 board. Nuts is any hand with a 9 but you don't "have" to have 92o, nor do you need to have A9o. Which would be "correct" to have here? – TacticalCoder Jan 12 '12 at 2:53
if I understand your question correctly, is it safe to assume that the range you're after does not include any offsuit card? For example any time you could represent the nuts on a board where AKo would be the nuts (e.g. Qc Js Td 6s 2h) then if AKs is in your range AKs is "better" than AKo because it helps to "minimize" your hypothetical range? – TacticalCoder Jan 12 '12 at 3:30
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2 Answers

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To have every nut hand in your range:

22+, 32s+, 42s+, 52s+, ATs (pocket pairs; suited 0, 1, and 2 gappers; ATs)

22+ covers all nut 4-board-card straight flushes, and the combination of {32s+, 42s+, 52s+, ATs} (ATs is a special case for KQJ) covers all 3-board-card straight flushes. Since it includes one of every rank, it covers quads with 3-of-a-kind on board. Since it includes all of the suited broadway hands, it covers all nut flushes when there are no straight flush possibilities.

You'll need 22+ to cover quads when the board is paired, that also covers all full houses.

Since straight flushes are covered, straights are as well.

Any time a straight flush, quads, a flush, or a straight is not possible, the nuts is a set, and your pocket pairs have that.

This range covers 16.1% of starting hands.

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I think OP's question is not about how to potentially get the nuts on every board, but is about what his minimal range has to be so that his opponent can think that OP may potentially have the nuts. For example if the board comes 5s 6s 7s 8s Kd the hero does not need to play 100% of his hands to potentially have a 9s in his hand... – TacticalCoder Jan 12 '12 at 2:58
If he does not have the 9s in his hand, his opponent could have the 9s, in which case his opponent would know he does not have the nuts. – Chris Marasti-Georg Jan 12 '12 at 3:04
"If he does not have the 9s in his hand, his opponent could have the 9s"... Once again I think that is not OP's question at all. OP's question would be "If on any board an opponent doesn't have the nuts, what range should I play so that I could potentially have the nuts". At least that's how I'm understanding OP's question. – TacticalCoder Jan 12 '12 at 3:19
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@user988052 I agree with you. His question states "What is the minimum preflop range...". If that is what the OP means then he would need a 100% range, or precognition about what the board will be, prior to it coming, before he can narrow his choice of starting hands. – Toby Booth♦ Jan 12 '12 at 15:25
@ChrisMarasti-Georg Good point with boards that "blocks" certain hands from my range. But it is still wrong that you need a 100% range. Since the 5th card can block only 1 hand at a time, so you only need 2 different hands containing this single card. To make it more clear: imagen a 100% range, missing only 2s7d. There is no board where did not have the nuts in your range – MartinK13 Jan 12 '12 at 17:50
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I'm pretty sure that based on your nuts definition you have preflop range of 100% because on preflop you can't imagine what is nuts and what not and on preflop you dont see any common cards then you must call every hand to look on board and do some calculations.

This is based on that you must have nuts in range then 72o is nuts possibility too. For example in board 7s 7h 7c 2d 2s

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I dont want to have every nut hand for every board in my range, biut a least ONE nut hand for every range – MartinK13 Jan 12 '12 at 17:51

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