I was clarifying why AKs makes more nuts than AQs. Specifically because AAKQX board....

And good catch on the T5, of course it can make TT543 nuts occaisonally.

What is the potential argument for ATs making more nuts than AKs?

The difference in the straight flush possibilities when having a flush.

I have calculated it before and it was ATs

I do not have the program that I wrote to calculate it anymore so I cannot show my work

Any hand with an Ace in it.

And why by the ways there is so far no discussion of the fact that in order to have the nuts at the river you need to survive all prior streets of activity that clearly makes many of the hands considered unlikely to see the river often enough compared to other stronger candidates . Seriously this depends on how many opponents and what style they have etc. So for me this thread is a non tractable thread that cannot produce any results unless statistical analysis of accumulated data over millions of hands played in fr or 6max but in any case the same format can offer any light !


What chance has some T5s to see river. And even ATs . You need to have something at flop to keep you going . And this is where hands like AKs will be surviving more than ATs or JTs etc.


If that were a simple issue as in deal all 5 cards and then check which hand has the nuts more often then yes a solution with enumeration could exist if you created a program to do it. But poker is not played this way and it wont matter.

And of course realize that the supervast majority of hands are won by non nut hands at river .

Because that wasn't the question.

This post is not about how to play poker. It's a simple question, deal the cards out, what hand ends up with the nuts most often? "Why" or "How did we get to the river" is not part of it.

Well, in that case, it seems just as stupid as asking, "what hands are least likely to be the nuts on the river most frequently?", or, "what day of the week is (on average) the air most humid?".

The question is a question, but the answer bears no useful information and is uninteresting. I don't see why it deserves to be in the theory section, unless there is some actual point to the whole idea behind the question.

I don't think it's a particularly *interesting* question but it's more related to poker theory than many things that get posted to this forum. Poker Theory isn't "how to play poker", at least not exclusively. It's anything related to poker that can be solved or approached theoretically or mathematically. It's similar in nature to "can you construct hands where KK is drawing dead" or "Can you construct a hand where you have the nuts but less than 50% equity" or similar questions.

The idea that every question in this forum needs to be "useful" or "have a purpose" is missing the point, I think. Many people enjoy just thinking about things, without those things having an immediate application to playing poker.

I'm guessing that in your calculation you didn't consider AK to be the nuts on a AAK board. Because that happens far more often than straight flushes.

Actually you aren't considering AAK boards vs straight flushes; you are considering AAKT boards vs straight flushes.

I think what he's getting at is that on an AAK board, a program could have a mistake where it doesn't consider AK to be the nuts, because it thinks AA is the nuts (both of those are possible nut hands on that board)

Right, but if he is then it's also making a mistake on AAT boards where AT is the nuts, so the amount not considered isn't just any AAK boards, it's the amount of AAK boards minus the amount of AAT where the other cards are below T.

There are still probably more of those than straight flushes though I guess.

I keep thinking the answer is QTs without any data to support my thought. If you include 2nd-nut hands that any poker player would still consider the nuts(example: TTQ43) it makes the case stronger perhaps?

The ability of QTs to make more straight flushes than A10s is my reasoning. AKJs, KJ9s, J98s, 9876s, whereas A10s can only make two(nut) straight flushes(KQJs, 9876s)[2345s wouldn't be the nuts]

So, QTs can make 4 nut straight flushes and A10s can only make 2. This same effect applies to just bare straights. And without doing the work, I think this is enough to make up for all the nut-flushes A10s can make.

lol, if I'm not even close. Just a feeling without looking it up.

i really, really doubt it. but i haven't done the math or anything (nor would i know how to in a way that wasn't extremely exhaustive), just doesn't seem right to me

.

My guess is A10s -> AKs .... all have the same nut-straight possibilities and all will be the nut-flush on a non-paired board.

It'd definitely be nut-flush or nut-straight hands.... full houses are never nuts (unless top full house).

Ace-rag suited is probably the best **** hand.... A10-AK and you'll be getting all jacked up over it... but having A2s and hitting nut flush is pretty nice

My bet would be on A10ss-AKss

I can answer this pretty easily with propokertools PQL queries - for example:

select count(nutHi(player, river)) as nuts
from game='holdem', player='AKs'
Results:
Trials NUTS
618407 25419 (4.11%)

I will run 10 million trials each and post results here later today.

PQL results for a random hand - 10 million trials each. I will post vs some non-random ranges later to see how different that looks.

- bachfan of ProPokerTools fame

Hand	River Nut %
TAs	4.343116789953018
JAs	4.242516609768383
QAs	4.139867466439645
KAs	4.084431336897797
A9s	3.528580974213432
A6s	3.410878770524322
TJs	3.3973464221030287
A8s	3.3410039053393215
A7s	3.3090012167724634
A5s	3.2616597736522395
TJo	3.246038377303518
A4s	3.1023485299779243
QKs	3.015350526732977
QJs	3.000333315986652
KJs	2.980597743068052
TQs	2.950436597715041
TKs	2.9496971187866285
A3s	2.944184546394309
A2s	2.7806564350708083
QJo	2.755209403510006
TQo	2.6983060349429526
QKo	2.321733316094645
T9s	2.2536388720471177
KJo	2.2259680615281594
TKo	2.1622596760483352
T9o	2.083802243034237
KAo	1.992877117595469
AA	1.9438074443395854
QAo	1.8787450012553664
JAo	1.7771762545174596
KK	1.766171872352324
98s	1.7443818577333088
TAo	1.7147010882681275
87s	1.7116914000772976
76s	1.6871830384488056
65s	1.6720420175564712
J9s	1.6506331975487682
98o	1.6298134624788712
87o	1.5936283624866425
T8s	1.584529079152431
76o	1.5642855907706952
65o	1.5386005777042124
J9o	1.497992348414609
54s	1.4817342256029005
T8o	1.4542415386542775
K9s	1.3914775014728558
54o	1.3622279149268655
K5s	1.3576558059530837
K4s	1.3379597166090418
K3s	1.321884698749019
K8s	1.3148611487354394
K2s	1.311802745845678
97s	1.2981535981816603
86s	1.2639039574440583
K7s	1.2578495686740516
75s	1.2515143797410198
64s	1.230965215088948
K6s	1.2292001894981985
Q9s	1.2291749118067674
QQ	1.227309086641568
97o	1.1664719332585842
86o	1.147410919834386
75o	1.1202503601692397
64o	1.1045322622184854
53s	1.0621355814119973
J8s	1.001121787591242
JJ	0.9908037781429723
Q9o	0.9730280199363589
TT	0.9561380228598674
T7s	0.9400847306831837
53o	0.9305627525444053
J8o	0.8974790097412075
T7o	0.8520567108267805
43s	0.8369289685694427
A9o	0.754941003488073
43o	0.752944692103469
99	0.7202963943801168
Q8s	0.7182876928548908
A8o	0.7125996348076745
88	0.7114887962985804
77	0.7042652134992669
96s	0.6938886253812592
66	0.688442455506356
A7o	0.678801124420493
85s	0.6755325108133728
55	0.6734746560406711
44	0.6666149957311551
33	0.6593786483162586
74s	0.6584814314610438
22	0.6557415368435942
A6o	0.6475838783562906
63s	0.645860569208766
Q7s	0.6382346141850028
A5o	0.629713231542285
A4o	0.6161335321256487
K9o	0.6146757389537583
A2o	0.6062251962790585
Q6s	0.6048871477040091
96o	0.6026372720387809
A3o	0.6006229347815236
Q5s	0.5920095558243503
85o	0.5828022367651792
Q4s	0.5764463826425201
74o	0.5724844864351146
K8o	0.5701772672785179
Q3s	0.5677536732462877
Q2s	0.564720103720106
63o	0.5574811355905612
K7o	0.5340017218896319
Q8o	0.5161955324136962
K6o	0.5086246215617335
J7s	0.5025533978602874
K5o	0.4874058093446486
Q7o	0.4753265620461639
52s	0.4741666864681236
K4o	0.4690205823099986
K3o	0.4597697244439257
K2o	0.4539407200239095
T6s	0.44932901577701995
Q6o	0.4429262986043172
42s	0.43952327698475935
J7o	0.43919421649985896
J6s	0.4330360446285566
Q5o	0.42442664326785234
Q4o	0.4076484979585646
J6o	0.40731315898671655
J5s	0.4021245158834986
T6o	0.40016968664692315
Q3o	0.39988358236822014
Q2o	0.3947781391979772
J4s	0.3876398029032711
J5o	0.3866472743166749
J3s	0.3834108739850074
52o	0.3809524760712447
T5o	0.37813068245860254
T5s	0.3779278613313533
J2s	0.37150796344554965
J4o	0.3713453609818976
J3o	0.3638007381658168
T4o	0.36118132998348906
T4s	0.36082681761376756
J2o	0.35444571031802247
42o	0.35311782585846
T3o	0.3512072224394233
T3s	0.3492401301463377
T2s	0.3476977338119803
T2o	0.34662999722584237
32s	0.28213691099526106
32o	0.23858485576188715
95s	0.20667202338828916
84s	0.19076675732707576
73s	0.1810881859094765
62s	0.1765621339785756
95o	0.15983341721810426
94s	0.14685195113359586
94o	0.14418180544011538
84o	0.14394634423751457
83s	0.13730994891173964
73o	0.13709555440494994
72s	0.13547459846297402
83o	0.13371456407028248
93o	0.13353847129665855
92o	0.13335166153895878
92s	0.1325143988705352
93s	0.13173399305355446
82s	0.129927928977796
82o	0.1293231528622855
72o	0.12879587853188698
62o	0.12705408933959014

Does your program recognize card removal? ie. that AK is the nuts on a AAK84 board? I can't imgaine those results if it did.

It does. All possible hands are dealt besides our own on the river, and if any beat us, we do not have the nuts.

PQL Query:
select count(nutHi(p1, river))
from game='holdem', p1='AK', board='AsAhKs8s4c'
Results:
Trials COUNT 1
601474 601474 (100.0%)

Ok cool. I'm never folding ATs preflop again

Very nice bachfan. Lol at AA. The results follow the general consensus.