David Sklansky (enthusiast) 10/24/03 03:25 AM
 \$200 Stipend to Expand A8 Result

With a one and two dollar blind we now know that A8offsuit in the SB, is better off moving in up to about 70 dollars more (even if the big blind saw his cards) than he would be folding. If we thus say A8 has a rating of 70 or so, what are the ratings for all other hands?

To make sure you understand, notice that 32 has a rating of one while slightly better hands have a rating of two. Thats because you are getting 3-1 if you put in one and 4-2 if you put in two.(Obviously the big blind would always call in this case). Fairly poor hands would be rated three, getting 5-3 odds. At the other extreme, two kings would have a rating of about 1000. Since it will pick up the pot unless the big blind has kings or aces and will win some of those hands too.

If someone can tell me the "rating" for all hands (I would assume with the help of a computer program), I'll send them \$200 and give them credit whenever I write about those results.

 Mangatang (enthusiast) 10/24/03 09:20 AM
 Re: \$200 Stipend to Expand A8 Result

Are these assumptions correct?

1. This is a no limit game where everyone folded to the SB (or it's a head-to-head match up between SB and BB).

2. BB will only call your raise. He will not re-raise.

3. BB has an unlimited stack (or at least big enough to cover up to SB's KK hand).

4. BB can always see your hand and will only call if his hand is better than yours.

Also, how do "we" know that A8o is worth a \$70 bet?

I'm just trying to fully understand the situation.

 Nottom (Carpal \'Tunnel) 10/24/03 09:35 AM
 Re: \$200 Stipend to Expand A8 Result

1) yes
2) you are all-in, so re-raising is pretty pointless
3) yes
4) after you push all-in you will reveal you hand so that you will only be called by a better hand (or on the extreme low end of the scall by a hand with odds to draw out on you)

A8 was solved in the previous thread, I'd suggest checking it out if you haven't already.

 Mangatang (enthusiast) 10/24/03 09:57 AM
 Thanks (N/M)

 karlson (enthusiast) 10/24/03 03:05 PM
 Re: \$200 Stipend to Expand A8 Result

Here is what I could come up with.
I noticed some slightly funny things in some other output, so these numbers might be barely off. I would expect that error to be no more than 1% or so.
BTW, kudos to pokersource for making the programming easy. Anyone doing any programming for poker purposes is probably best off starting off with their classes for hand evaluation and such.

22o 49.097373
32o 1.831860
32s 2.577355
33o 67.023645
42o 1.982895
42s 2.806653
43o 2.374371
43s 3.415791
44o 84.187055
52o 2.188207
52s 3.125558
53o 2.648645
53s 3.865458
54o 3.232330
54s 4.870879
55o 101.605019
62o 2.145689
62s 3.064287
63o 2.598784
63s 3.789969
64o 3.180263
64s 4.787757
65o 3.986211
65s 6.235193
66o 119.316820
72o 2.249071
72s 3.230863
73o 2.739177
73s 4.030750
74o 3.376566
74s 5.128923
75o 4.283982
75s 6.623716
76o 5.460449
76s 8.361698
77o 140.163654
82o 2.802784
82s 4.142291
83o 3.002894
83s 4.478709
84o 3.749197
84s 5.715560
85o 4.829605
85s 7.271507
86o 6.124065
86s 9.041014
87o 7.537942
87s 11.179617
88o 166.688882
92o 3.594775
92s 5.379643
93o 4.012116
93s 6.084035
94o 4.359892
94s 6.611112
95o 5.672884
95s 8.300009
96o 7.103121
96s 10.150592
97o 8.608650
97s 12.327652
98o 10.323988
98s 15.411158
99o 202.125049
T2o 4.848555
T2s 7.578143
T3o 5.501484
T3s 8.458991
T4o 6.274183
T4s 9.307921
T5o 6.949192
T5s 9.998652
T6o 8.609867
T6s 11.987398
T7o 10.253090
T7s 14.292145
T8o 12.223835
T8s 17.604507
T9o 14.930978
T9s 22.719979
TTo 256.815721
J2o 6.918703
J2s 11.204161
J3o 7.953932
J3s 12.109628
J4o 8.950459
J4s 13.032748
J5o 10.037694
J5s 14.134238
J6o 10.834186
J6s 14.809842
J7o 12.733956
J7s 17.316844
J8o 14.958200
J8s 20.810695
J9o 17.927646
J9s 25.981496
JTo 23.299660
JTs 36.628034
JJo 349.934987
Q2o 11.376900
Q2s 16.752437
Q3o 12.582989
Q3s 17.858401
Q4o 13.747946
Q4s 19.055679
Q5o 15.130340
Q5s 20.478763
Q6o 16.399874
Q6s 21.963309
Q7o 17.188395
Q7s 22.876650
Q8o 19.964644
Q8s 26.981677
Q9o 23.619890
Q9s 32.907071
QTo 30.036653
QTs 44.501932
QJo 33.204524
QJs 50.394333
QQo 550.087512
K2o 20.156245
K2s 26.980395
K3o 21.565057
K3s 28.660021
K4o 23.035466
K4s 30.475611
K5o 24.895185
K5s 32.657479
K6o 26.919787
K6s 35.300209
K7o 28.816285
K7s 37.796916
K8o 30.783568
K8s 40.437905
K9o 36.174856
K9s 48.564953
KTo 45.608339
KTs 64.095478
KJo 51.680575
KJs 74.338025
KQo 59.890903
KQs 89.067516
KKo 1290.323929
A2o 45.819455
A2s 59.197471
A3o 49.181824
A3s 63.478775
A4o 52.777483
A4s 68.020727
A5o 57.523826
A5s 73.895079
A6o 57.113411
A6s 72.267638
A7o 63.940106
A7s 81.074772
A8o 72.472249
A8s 92.302133
A9o 83.718586
A9s 107.386334
ATo 109.651660
ATs 144.726683
AJo 141.893786
AJs 193.397544
AQo 203.934890
AQs 297.477185
AKo 366.480212
AKs 658.056504
AAo Infinite

 Nottom (Carpal \'Tunnel) 10/24/03 04:45 PM
 Re: \$200 Stipend to Expand A8 Result

I'd hate to try and apply a Sklanski theory problem to real life, but ...
Let's say I'm playing in a Party \$50 game (1/2 blinds), its folded to me in the SB (OK you can stop laughing now) and I have a stack of 60. If I don't mind the massive varience going all-in with any hand rated 60 or better would be +EV correct? In fact since my opponent could call me with worse hands and fold better hands, this might even be EV with hands rated less than 60, correct?

 David Sklansky (enthusiast) 10/24/03 04:46 PM
 The Sklansky-Karlson All In No Limit Holdem Rankings

That's what these results will be called from now on. Assuming they are right of course. A cursory glance looks good. Am I right in assuming that you took into account that lessor hands will be called by two card holdings that are slightly worse? And that you took the two cards of your hand out of the deck? (Considering AKs outranks QQ it seems you did.)

Please let us know your full name Karlson. And where I should send the \$200.

Also would someone be so kind as to reorder these results from highest to lowest. I would also appreciate if someone would double check some of these results by hand.

Believe me, these are far from trivial results. The can be used as major weapons in tournaments.

 Nottom (Carpal \'Tunnel) 10/24/03 04:54 PM
 Re: The Sklansky-Karlson All In No Limit Holdem Rankings

Would you advocate actually using any of these results in a tourney situation? It seems like there is a lot more variance here than most touney players would like. Unless the player is already using your "system" it seems like this wouldn't be too useful until you are late in the tourney and feel that your opponents are better players than you post-flop. I wonder what these results would look like from other positions at the table ... hmmm ... is this the basis for an improved more detailed "System".

 Boris (old hand) 10/24/03 05:05 PM
 Re: The Sklansky-Karlson All In No Limit Holdem Rankings

Why is AKs ranked higher than QQ while AQs is ranked lower than JJ?

 tewall (veteran) 10/24/03 07:17 PM
 Hands Sorted

AAo 10000
KKo 1290.32392
AKs 658.056504
QQo 550.087512
AKo 366.480212
JJo 349.934987
AQs 297.477185
TTo 256.815721
AQo 203.93489
99o 202.125049
AJs 193.397544
88o 166.688882
ATs 144.726683
AJo 141.893786
77o 140.163654
66o 119.31682
ATo 109.65166
A9s 107.386334
55o 101.605019
A8s 92.302133
KQs 89.067516
44o 84.187055
A9o 83.718586
A7s 81.074772
KJs 74.338025
A5s 73.895079
A8o 72.472249
A6s 72.267638
A4s 68.020727
33o 67.023645
KTs 64.095478
A7o 63.940106
A3s 63.478775
KQo 59.890903
A2s 59.197471
A5o 57.523826
A6o 57.113411
A4o 52.777483
KJo 51.680575
QJs 50.394333
A3o 49.181824
22o 49.097373
K9s 48.564953
A2o 45.819455
KTo 45.608339
QTs 44.501932
K8s 40.437905
K7s 37.796916
JTs 36.628034
K9o 36.174856
K6s 35.300209
QJo 33.204524
Q9s 32.907071
K5s 32.657479
K8o 30.783568
K4s 30.475611
QTo 30.036653
K7o 28.816285
K3s 28.660021
Q8s 26.981677
K2s 26.980395
K6o 26.919787
J9s 25.981496
K5o 24.895185
Q9o 23.61989
JTo 23.29966
K4o 23.035466
Q7s 22.87665
T9s 22.719979
Q6s 21.963309
K3o 21.565057
J8s 20.810695
Q5s 20.478763
K2o 20.156245
Q8o 19.964644
Q4s 19.055679
J9o 17.927646
Q3s 17.858401
T8s 17.604507
J7s 17.316844
Q7o 17.188395
Q2s 16.752437
Q6o 16.399874
98s 15.411158
Q5o 15.13034
J8o 14.9582
T9o 14.930978
J6s 14.809842
T7s 14.292145
J5s 14.134238
Q4o 13.747946
J4s 13.032748
J7o 12.733956
Q3o 12.582989
97s 12.327652
T8o 12.223835
J3s 12.109628
T6s 11.987398
Q2o 11.3769
J2s 11.204161
87s 11.179617
J6o 10.834186
98o 10.323988
T7o 10.25309
96s 10.150592
J5o 10.037694
T5s 9.998652
T4s 9.307921
86s 9.041014
J4o 8.950459
T6o 8.609867
97o 8.60865
T3s 8.458991
76s 8.361698
95s 8.300009
J3o 7.953932
T2s 7.578143
87o 7.537942
85s 7.271507
96o 7.103121
T5o 6.949192
J2o 6.918703
75s 6.623716
94s 6.611112
T4o 6.274183
65s 6.235193
86o 6.124065
93s 6.084035
84s 5.71556
95o 5.672884
T3o 5.501484
76o 5.460449
92s 5.379643
74s 5.128923
54s 4.870879
T2o 4.848555
85o 4.829605
64s 4.787757
83s 4.478709
94o 4.359892
75o 4.283982
82s 4.142291
73s 4.03075
93o 4.012116
65o 3.986211
53s 3.865458
63s 3.789969
84o 3.749197
92o 3.594775
43s 3.415791
74o 3.376566
54o 3.23233
72s 3.230863
64o 3.180263
52s 3.125558
62s 3.064287
83o 3.002894
42s 2.806653
82o 2.802784
73o 2.739177
53o 2.648645
63o 2.598784
32s 2.577355
43o 2.374371
72o 2.249071
52o 2.188207
62o 2.145689
42o 1.982895
32o 1.83186

 Re: The Sklansky-Karlson All In No Limit Holdem Rankings

I think it's primarily a function of the number of dominating hands that BB could hold given the cards that SB holds:

-AKs could face 6 (3 AA + 3 KK) whereas QQ could face 12 (6 AA + 6 KK);
-JJ could face 18 (6 AA + 6 KK + 6 QQ) whereas AQs could face 24 (3 AA + 6 KK + 3 QQ + 12 AK).

 karlson (enthusiast) 10/24/03 07:55 PM
 Re: The Sklansky-Karlson All In No Limit Holdem Rankings

Yes, I took the cards out of the deck, and yes, the BB could call as a slight underdog.

I have specific data such as which hands will call the raise and their odds of winning, if people find any particular result fishy. I'll try to post the AQs / JJ data at some point.

My name is Victor Chubukov. I'll put my coordinates in message for you, David.

For those that think they may know me, I'm a student at Berkeley and semi-regularly play in the 15/30 at Oaks Club.

 karlson (enthusiast) 10/24/03 08:16 PM
 Re: The Sklansky-Karlson All In No Limit Holdem Rankings

I don't have a great answer to this question.

I think the danger of running in to AK may be the key. AQs will win about 43% of the time that it's called, and AKs, 46%, if that helps.

 Re: The Sklansky-Karlson All In No Limit Holdem Rankings

Not to be a dick, David, but it seems it should be the Karlson-Sklansky ratings, wouldn't you agree?

 Re: The Sklansky-Karlson All In No Limit Holdem Rankings

Hi Karlson,
Could someone point me to the thread that originated this line of inquiry?

I'm still trying to figure out the exact scenario being analyzed and why it's important enough to offer a reward for the answer.

Sincerely,
AA

 Nottom (Carpal \'Tunnel) 10/24/03 09:10 PM
 Re: The Sklansky-Karlson All In No Limit Holdem Rankings

The "Important No Limit Math Problem" also posted by Sklanski. In that he asked, how big a stack could a player in the SB push all-in (after all other players had folded) in a game with 1-2 Blinds, flip over his cards to show the BB and still be making a +EV play

 Re: The Sklansky-Karlson All In No Limit Holdem Rankings

Hi Nottom,
Thanks much.

Sincerely,
AA

 Boris (old hand) 10/25/03 04:01 AM
 ty

 Phat Mack (old hand) 10/25/03 07:57 AM
 Re: checks: A8o, T8s, QTo.

I would also appreciate if someone would double check some of these results by hand.

I've checked a couple, and they looked real solid.

Am I right in assuming that you took into account that lessor hands will be called by two card holdings that are slightly worse?

I would have to know the criterea for including marginal hands to get a precise check. For example, in the famous A8o problem, I selected all hands with a greater than .5 EV against A8o. I came up with 134 hands ( out of 1225). These included A8s but not the other A8o's. I think A8s's were excluded from the original problem.

At any rate, A8o had an avg. EV of .32455 against the 134 hands. x = 73.457, which was very close to 72.472.

Using the same methodology, T8s yielded an x = 20.98 vs. 17.6. (T8s's EV against 700/1225 hands was .4186.)

QTo produced an x= 32.01997083 vs 30.036653.

 Phat Mack (old hand) 10/25/03 08:05 AM
 PS

Sims were done in Hold 'em Showdown. Calculations were performed as per Almost Perfect Simple Solution

 karlson (enthusiast) 10/25/03 09:54 AM
 Re: checks: A8o, T8s, QTo.

The T8s will be called by quite a few hands that are not favorites. These are small pocket pairs (through 55, 66 is slight favorite) and the other T8 hands. I have it being called by 733 hands and still at about 42% when it is called.

A8 will be called by 141 hands, including two that are underdogs (the ones with the 8 of the suit of our A). That may account for the slight discrepancy.

 ZeeJustin (veteran) 10/25/03 07:23 PM
 Re: Hands Sorted

Late in a tournament, there's an all-in raise, and you are either in the big blind, or know for some reason that if you call, no one else will. Is it safe to say that this is the order of hands that you should play? I.e you should be more likely to call the raise with AQs than TT?

 muck_nutz (journeyman) 10/25/03 08:46 PM
 Re: checks: A8o, T8s, QTo.

I'm not sure I follow why you think T8s will be called by 55 in the open hand situation. The 33 > AK, AK > JTs, JTs > 33 non transitive example is well known enough that at least some people are going to realize that you fold 77 [ignoring dead money] to a "revealed" raise by JTs (but you call with 88).

 karlson (enthusiast) 10/25/03 09:31 PM
 Re: checks: A8o, T8s, QTo.

Quote:

Why would you do that?

 tewall (veteran) 10/25/03 09:48 PM
 Re: Hands Sorted

I don't think that's necessarily so. The first list is a list of hands that make a profit raising the BB even if the BB knows the hand that's raising it by order of how large the stack can be before the bet is no longer profitable. This list is acting against an unknown, and therefore, random hand. What BB can call with could well be different because what SB would raise with is not random.

 muck_nutz (journeyman) 10/25/03 09:52 PM
 Re: checks: A8o, T8s, QTo.

It wasn't important to my comment. You wouldn't ignore the dead money in real life. So, back to my question. Why do you think if you jammed with T8s I would think my 55 was a favorite? Or are you assuming that dogs which are getting the right price are going to call? I thought you were making a subjective assumption that some people would call with hands which were not getting the right price. Is that incorrect?

 karlson (enthusiast) 10/25/03 10:17 PM
 Re: checks: A8o, T8s, QTo.

The BB is an expert. He will only call with hands that are getting the right price. 55 is a call against T8s even thought it is a slight underdog because of the blinds already in the pot. We are not making any subjective assumptions.

Hope that clears up any confusion.

 muck_nutz (journeyman) 10/25/03 10:40 PM
 Re: checks: A8o, T8s, QTo.

Yea, that is as I hope it was.

 Phat Mack (old hand) 10/26/03 06:03 PM
 Re: question

Do your numbers represent the total amount bet, or the amount in addition to the \$1 called?

It might be most useful to express the numbers as a ratio to the dead money in the pot, as opposed to the bet in a specific \$1, \$2 NL game.

 karlson (enthusiast) 10/26/03 06:41 PM
 Re: question

The \$1 in the SB is not included.

Divide by 2 if you want the ratio of the bet to the dead money.

 Phat Mack (old hand) 10/26/03 07:51 PM
 Re: question

Divide by 2 if you want the ratio of the bet to the dead money.

I think I'm missing something. There's \$3 in the pot: in the A8o example, moving in with \$70 would be 70/3 the dead money. In a \$5-\$10 game with \$15 dead money, I would move in 70/3 * \$15 = \$350. Correct?

 karlson (enthusiast) 10/26/03 09:23 PM
 Re: question

Yeah, that's right.
Just a question of terminology....to me, there's only \$2 dead money in the pot and there's a \$1 bet to you.
I think you have the idea.

 magic_man (journeyman) 10/27/03 01:18 PM
 Improving the System?

In Mr. Sklansky's articles on "The System" and "Improving the System", he challenges others to improve upon his "groupings" even more...can we use these results to do just that?

~Magic_Man

 Nottom (Carpal \'Tunnel) 10/27/03 01:26 PM
 Re: Improving the System?

Does anyone happen to have a link to the articles on "the system"?

 magic_man (journeyman) 10/27/03 01:32 PM
 Re: Improving the System?

It used to be at the link below, but it's not working now for some reason. Maybe it will come back:

http://www.cardplayer.com/?sec=afeature&art_id=13194

~Magic_Man

 tewall (veteran) 10/27/03 02:27 PM
 Re: The Sklansky-Chubukov All In No Limit Holdem Rankings

So shouldn't it be the Sklansky-Chubukov No Limit Rankings? By the way, it's a good thing "karlson" is with a "k" and not a "c"! I'm not sure David could stomach that.

 Nottom (Carpal \'Tunnel) 10/27/03 02:49 PM
 Re: Improving the System?

I had checked there before I posted and couldn't find it. I also noticed that there were none of Mason or Davids articles from before a couple months ago listed in the archives.

I did however find this thread on these boards.

Summary of Davids Bellagio Seminar

 rockoon (journeyman) 10/29/03 08:02 PM
 Re: \$200 Stipend to Expand A8 Result

Quote:

With a one and two dollar blind we now know that A8offsuit in the SB, is better off moving in up to about 70 dollars more (even if the big blind saw his cards) than he would be folding. If we thus say A8 has a rating of 70 or so, what are the ratings for all other hands?

To make sure you understand, notice that 32 has a rating of one while slightly better hands have a rating of two. Thats because you are getting 3-1 if you put in one and 4-2 if you put in two.(Obviously the big blind would always call in this case). Fairly poor hands would be rated three, getting 5-3 odds. At the other extreme, two kings would have a rating of about 1000. Since it will pick up the pot unless the big blind has kings or aces and will win some of those hands too.

If someone can tell me the "rating" for all hands (I would assume with the help of a computer program), I'll send them \$200 and give them credit whenever I write about those results.

It is interresting to note that the "optimal" (maximizing EV) all-in amount is different from the "maximum" (break-even) all-in amount and that the two functions are not linear to each other. Considering the pocket pairs:

(all values in units of the big blind)

22 - 3.1, 24.6
33 - 3.4, 33.3
44 - 3.8, 41.5
55 - 5.0, 49.9 <- the "opimtal" amount peaks here at 5*BB
66 - 4.8, 58.2
77 - 3.6, 68.0
88 - 3.5, 80.2
99 - 3.2, 96.3
TT - 3.4, 120.3 <- smaller peak here, TT kills str8s
JJ - 3.0, 160.2
QQ - 3.0, 239.6
KK - 3.0, 477.5
AA - INF, INF

While the "maximum" amount keeps rising, the "optimal" amount rises then falls and does a dance near the end. The values for pocket aces are undefined. Aces EV is the money in the pot.

These values were derived from the A8o puzzle where the small blind hold's one of these pocket pairs instead.

 JonCooke (newbie) 10/30/03 03:53 PM
 Re: \$200 Stipend to Expand A8 Result

Next job, David.
And this is even more crucial for the heads up stage of one table satellites.

With a stack size of n, blinds 1-2.

Lets constrain betting to fold or all-in.

For various values of n:
What range of hands should go all in?
Given that range of hands going all in, what should the opponent call with?

This is a game theory excercise. I've got some approximations for n=20 using TTH. Does anyone have a spreadsheet with Hand A/Hand B/Odds that they could send me? Then I'll tackle the whole problem.

At what value of n is the allin or fold strategy no longer optimal?

 bigpooch (old hand) 11/01/03 05:14 AM
 Re: The Sklansky-Karlson All In No Limit Holdem Rankings

David:

Karlson's numbers don't seem correct. Consider KK:
The number quoted is 1290+ but look at this calculation:

Assume (with a benefit to the KK!) that KK wins about
19% of the time vs AA:

There are 50C2 = 1225 possible hands:

AA (6): EV = (x+2)(0.19)-x(0.81)
KK (1): EV = (+3)(1/2)
other (1218): EV = +3

Thus, for the EV to be >0,

6((x+2)(0.19) - x(0.81)) + 1(1.5) + 1218 (+3) > 0
solving yields x as approximately 983. It should
be a tiny bit less since KK doesn't quite win 19%
of the share of pots versus AA.

Cheers,

"bigpooch" a.k.a. "mangler"

 karlson (enthusiast) 11/01/03 06:23 AM
 Re: The Sklansky-Karlson All In No Limit Holdem Rankings

Thank you very much for pointing this out. I am surprised that no one (myself included) tried this simple calculation by hand. I checked some other ones, but I used intermediate results that were incorrect.

So I did find an error in my code. I will have new numbers posted tomorrow sometime. The correct value for KK is 954.

If anyone has conclusive proof that these numbers cost them a place in a tourney, I'll make sure to reimburse him or her.

Victor.

Edit: By the way, the numbers for most hands should not change much, since my mistake was effectively making the BB call with one extra hand. For KK, this was quite significant.

 bigpooch (old hand) 11/01/03 12:35 PM
 Re: The Sklansky-Karlson All In No Limit Holdem Rankings

Victor:

I just thought intuitively there was something wrong with
that specific number for KK as it is only about 220-1
against the BB holding AA. After your new table is
constructed, it seems more useful to consider a modified
game: suppose the SB states that I have "the hand XY or
better" and then the BB must decide. This seems a much
more useful practical question especially in a NL cash
game or tournament. So even if someone were using your
older numbers for the purposes of a tournment or in a
cash game, I would think the play still had +EV.

Cheers,

"bigpooch" a.k.a. "mangler"

 karlson (enthusiast) 11/02/03 03:39 AM
 Re: The Sklansky-Karlson All In No Limit Holdem Rankings

As promised, I have revised rankings.

They looked ugly when I posted them, and I don't want to clog up the thread, but you can see them at
http://www.decf.berkeley.edu/~chubukov/rankings.html

Let me know if there are more issues.

 rockoon (journeyman) 11/04/03 02:16 AM
 Re: The Sklansky-Karlson All In No Limit Holdem Rankings

Quote:

Victor:

I just thought intuitively there was something wrong with
that specific number for KK as it is only about 220-1
against the BB holding AA. After your new table is
constructed, it seems more useful to consider a modified
game: suppose the SB states that I have "the hand XY or
better" and then the BB must decide. This seems a much
more useful practical question especially in a NL cash
game or tournament. So even if someone were using your
older numbers for the purposes of a tournment or in a
cash game, I would think the play still had +EV.

Cheers,

"bigpooch" a.k.a. "mangler"

I did some research along this line. I did not take into account dead money in the pot or blinds posted. Just a consideration along the lines of two players each get dealt a hand. The first player begins with the entire range of hands and asked the question, what hands can't profitably play? I called this list Grade F.

Then I took the remaining list of hands, the ones that could profitably play, and asked the question, what hands can't profitably play against this list? I called this list Grade E.

I kept doing this until I got down to the 3 hands AA, KK, and QQ.

Grade B: JJ, TT, AK, AQs
Grade C: 99, 88, 77, 66, AQo, AJ, AT, A9
Grade D: 55, 44, A8, A7, A6, A5, A4, A3s, A2s, KQ, KJ, KT, K9s
Grade E: 33, 22, A3o, A2o, K9o, K8, K7, K6, K5, K4, K3, K2, QJ, QT, Q9, Q8, Q7, Q6, Q5, Q4s, Q3s, Q2s, JT, J9, J8, J7s, J6s, T9, T8s, T7s, 98s

The grades are structured such that if you opponent may hold Grade D or better, you can only profitably go even money against him when you hold grade C or better (the next higher grade)

"AK" is taken to be either "AKs" or "AKo" and so forth.

 clovenhoof (member) 11/17/03 11:33 PM
 Shouldn't it be Karlson-Sklansky? (n/m)