HU Handrange BIG Surprise: Broadway vs PPs&SCs enumerate

Hi, I am new to the forum as a poster and I thought I wanted to share this surprise:

Assume the following theoretic conditions:

- 2 people play heads up without blinds, instead both can look at their hole cards for free, but they can only push or fold. Should they decide to push, they can both only push and call with an always equal pre-defined amount. Both players have an infinte amount of money available.

- Both stick to their handrange for an infinite amount of games which are always pushed and should the one player push with his predefined range the other player will always call with his predefined range:

Player One: classical Broadway, which is any 2 cards bigger than ten:
TT+, ATs+, KTs+, QTs+, JTs, ATo+, KTo+, QTo+, JTo

Player Two: any pocket pair bigger than 77 & any suited connector bigger than 54 suited:
77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s



Here comes the SURPRISE:

Broadway (~14,3% of all hands) vs. 77+,54s+ (~6,6% of all hands)
25,585,246,368 games 0.010 secs 2,558,524,636,800 games/sec

Board:
Dead:
{ TT+, ATs+, KTs+, QTs+, JTs, ATo+, KTo+, QTo+, JTo }
equity win tie pots won pots tied
49.124% 48.21% 00.92% 12334149208 234464490.00
{ 77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }
equity win tie pots won pots tied
50.876% 49.96% 00.92% 12782168180 234464490.00

The result does NOT base on a Monte-Carlo simulated approach, but on iterative enumeration, which means the result is definite (interative enumeration means there are no other combinations possible, the result is ALWAYS the same amount of games which are ALL possible combinations played out against ALL possible board combinations)

If you go down for the classical broadway versus player two's range and add 88 and 99 as pocket pairs like in low limit HU games, the player playing the calssical broadway +88&99 has even less equity:
49.017% vs 50.983% and winning percatenages of 48.10% vs 50.07%.

Hands up who is surprised by this post. Well...I was when I calculated it with Pokerstove! The equity difference is larger than 1.5% and the more you add PPs to the broadway the bigger the difference becomes.

I find this result spectacular. Usually it should be that the shorter the game becomes (and how can it be any shorter than heads up?!) that high cards strength counts. Of course on might argue that only 6.6% of all hands are played by Player Two.
Yes, but these hands so NOT high card strenth like. They are pocket pairs lower than the opponents PP range (down to 77 vs TT or even 88 which maeks it only worse), only 4 hands have at sort of high cards strength (AKs,KQs,QJs,JTs). EVERYTIME a push/call situation can only appear if both have a hand from their predefined range. Even though Player One's range APPEARS higher (15.2% and 14.3% respectably), when both Player have a Push/Call situation ONLY Player One's cards DO HAVE high card strength!!!

Now, to all of you thinkers: ISF, Sauce123, Massimo, JGB, Bigspenda, Hyper, Ville18, Kingnat, Dwarfman, Jyms, Ellipsejeff and much more that are in the forums: I do follow your posts regularly and thank you very much for your insights into poker which made me a better player, thanks for that! Now, can ANY of you guys explain me this paradoxon???
Because I don't get it....I always thought and learned (like ANY other player playing SH & HU) high card strenth is IT what counts when it gets short and shortest like in HU, but this result contradicts that statement!

Think about the result: NOT more money is won (can't be anyway with hot cold calculations like Pokerstove does it, there is ALWAYs a showdown therefore the theoretic push/call or fold condition without a moneychange), the amount of GAMES won is higher, therefore the equity and winrate of Player Two only playing 77+ and SCs is higher...

I am really interested in reading your explanations to this thread, I at least have NO explanation what so ever for this result.

Greetingz from Shoutgun...see you @ the tables

1) Pocket pairs occur less frequency and are ahead of all non-paired unsuited hands preflop. Thus, those that shove more are likely to be ahead, but they're never ahead by more than a few percentage points.

2) The change in EV comes from the domination of kickers, like AJ to AT etc. You failed to include several hands that are obviously shoves in hand 2's range, including AQs, AJs as well as AJo+. You should see a slight increase in equity but whenever you're talking about All-ins preflop with two people with wide ranges you're never going to have a large EV difference.

Originally Posted by elipsesjeff

1) Pocket pairs occur less frequency and are ahead of all non-paired unsuited hands preflop.

Hi Jeff,

some words to Pokerstove. Pokerstove is a hot/cold calculator, that means that all hands are simulated through showdown. No one is allowed to bet, raise or fold. Now some words to enumeration: any possible combination of both players predefined cards are outplayed versus any possible board combination. The possible combination of clashes of player 1 and 2 vs any possible board is more than 25 Million different combinations. But 25,585,246,368 is the maximum number of n! (n factorial) with regards to both players hands and all possible boards combinations that can occur as iterative combinations.

Now, do me one favor: check the hands with Pokerstove yourself and SEE that result for your self, the enumeration takes less than a second on my very fast computer.

Problem for 1) is that with Pokerstove calculations Pokerstove really STICKS to the hands that are to be enumerated as n! (n factorial) combinations versus all possible board combinations - see hot/cold explanation.

Here one example:

Player One will only push Pocket Pairs bigger than pocket Tens, Player Two lowers his range to all Pocket Pairs bigger than 77.

The result is once again enumerated, NOT simulated.
The result is that Player One has dominant equity:

2,208,872,160 games 0.050 secs 44,177,443,200 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 62.993% 61.68% 01.32% 1362371700 29056578.00 { TT+ }
Hand 1: 37.007% 35.69% 01.32% 788387304 29056578.00 { 77+ }

You see in the brackets that Player One only plays TT, JJ, QQ,KK,AA
and Player Two 77,88,99,TT,JJ, QQ,KK,AA

Player Two has a wider range here and therefore should both player have their range, Player One has dominant equity because he ALWAYS has at least TT for the calculations. Simple as that.

Now back to our ORIGINAL situation the problem is that HERE Player One has at least TT for the pocket pairs and Player Two goes as low as 77 as in the above example other cards exluded.

The nice thing about pokerstove is that ALL calculations can be recalculated by yourself with Pokerstove, enumeration will lead to the exact same result with the exact same amont of game down to the last game, THAT is why the result is definitive and recalculatable.

Now back to the second part of that sentence:

Originally Posted by elipsesjeff

Thus, those that shove more are likely to be ahead, but they're never ahead by more than a few percentage points.

Pocket Pairs bigger than TT (TT, JJ, QQ,KK,AA) that are played out vs ANY suited connector BIGGER THAN 54s (AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s) are a MASSIVE favourite, 75% vs 25% FOR the Pocket Pairs and AGAINST the Suited Connectors
Again, Pokerstove ASSUMES that ONLY these hands are "clashed" against each other (once again, Pokerstove is a hot/cold calculator), it employs in its calculation the requencydistribution and mesures this n! (n facotiral) versus all possible board combinations, which are in this case more than ONE BILLION COMBINATIONS:

1,869,835,968 games 0.010 secs 186,983,596,800 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 75.275% 75.01% 00.26% 1402639668 4883634.00 { TT+ }
Hand 1: 24.725% 24.46% 00.26% 457429032 4883634.00 { AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }

As you can see, what you wrote does not fit the result. The nice thing is, as I said that you can REPEAT and RECALCULATE that with Pokerstove yourself, your will come ENUMERATED to the EXACT SAME RESULT. ALWAYS!

Originally Posted by elipsesjeff

2) The change in EV comes from the domination of kickers, like AJ to AT etc. You failed to include several hands that are obviously shoves in hand 2's range, including AQs, AJs as well as AJo+. You should see a slight increase in equity but whenever you're talking about All-ins preflop with two people with wide ranges you're never going to have a large EV difference.

Well Jeff, THAT is what I did NOT include in the calculations. As you can see, Pokerstove ALWAYS puts in the handrange that has been calculated.

Opern Pokerstove, Copy-Paste the line under here for Player one:
TT+,ATs+,KTs+,QTs+,JTs,ATo+,KTo

and als copy-paste the line under here for Player Two:
77+,AKs,KQs,QJs,JTs,T9s,98s,87s,76s,65s,54s

Then click on the button in Pokerstove of Player 1 and you will see that he plays exactely 25 hands and ONLY these 25 hands ALL the time, THESE are his range. Click OK, otherwise Pokerstove will loose the setting. The occurence of hands which are his "get hands dealt frequency" is here14.3%, which means he will be able to play 14.3% of his dealt hands always sticking to this range.

Then click on the button in Pokerstove of Player 2 and you will see that he plays exactely 18 hands and ONLY these 18 hands ALL the time, THESE are his range. Click OK, otherwise Pokerstove will loose the setting. he occurence of hands which are his "get hands dealt frequency" is here6.6%, which means he will be able to play 6.6% of his dealt hands always sticking to this range.

Now, make sure you have "Enumerate All" as calculation setting for Pokerstove. Click on "Evaluate" and you will get EXACTELY this result down to the last number down to the last game:

25,585,246,368 games 0.010 secs 2,558,524,636,800 games/sec

Board:
Dead:
{ TT+, ATs+, KTs+, QTs+, JTs, ATo+, KTo+, QTo+, JTo }
equity win tie pots won pots tied
49.124% 48.21% 00.92% 12334149208 234464490.00
{ 77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }
equity win tie pots won pots tied
50.876% 49.96% 00.92% 12782168180 234464490.00

Now, again: EVERYTHING you thought of I thought of before, too! But that is NOT the case and THAT is why it is worth to take a second look at this Paradoxon. Please anyone reading this, check it yourself with Pokerstove and be perplexed like I am.

One more info, should it make you take this paradoxon more serious:
I used to teach econometrics and statistics for Master students on a private university. No need to brag here about myself but the point is I crunch numbers for a living. If it perplexes me it SHOULD perplex YOU also, because in Poker we are crunching numbers to make some decent money out of it!

So someone, give this some thought again please, I am getting crazy about this, there IS NO sufficient explanation for me so far.

TY for PokerStove Tutorial.

1) Pokerstove isn't entirely hot/cold. It calculates equity based on the occurances of each type of hand. For example:

AKo happens more often than AA, which happens more often than AKs. This is what I mean when I say pocket pairs occur more frequently than any suited cards, connected or not, because more combinations exist in the deck of 52 cards.

2) The fact that you included 54s in your shoving range but not 55 or 66 or AKo for that matter is why I said your range is wrong.

Putting random hands into a Poker EV calculator then want a detailed explanation of why %EV is similar between two players with wide all in ranges preflop isn't time well spent.

Heh, glad to see professors do useless things outside the classroom as well zing!

Holy hell this thread delivers, what it delivers, however, I am not as sure of.

Originally Posted by elipsesjeff

2) The fact that you included 54s in your shoving range but not 55 or 66 or AKo for that matter is why I said your range is wrong.

Hey Jeff...you nailed it on the point! Exactely! The range SEEMS to be completely wrong! But the result is NOT. Remember that Sklansky used to write before the time of computer calculations about the value of hand rankings? Then there was a simulation study conducted by Darse Billings, Aaron Davidson, Jonathan Schaeer, and Duane Szafron from the Department of Computing Science of the University of Alberta in Edmonton, Alberta (Canada) that changed the value of the Sklansky groups according to their results - and according to THEIR results Suited Connectors are supposed to have MORE "SPECIAL" value, page 12:

hxxp://spaz.ca/aaron/school/AIJpoker.ps.gz

Now, I read Sauce123 NL Shorthand guide to crack games and he wrote to call in ANY position with at least 2 people already in the hand a raise with suited connectors:

Originally Posted by sauce123

6. Call a raise in ANY position if the following conditions are present:
a) you are holding an SC or a PP
b) there are two or more people already in the pot
c) your hand is not strong enough to 3bet (not in the top 1/2 if their opening range from that position)

So THAT'S how I came up and thought to myself...hmm..hm....what about the blinds? so I wrote down Sauce123's ranges for ALL positions Pokerstove style:

UTG: 22+,AQs+,AKo
HiJ: 22+,ATs+,KQs,AQo+
CO: 22+,ATs+,KTs+,QTs+,JTs,T9s,98s,87s,AJo+,KQo
BTN: 22+,A2s+,KTs+,QTs+,J9s+,T8s+,97s+,86s+,75s+,65s,54 s,ATo+,KQo,QJo,JTo

You can just copy-paste that into pokerstove by the way.

Now, I thought about which ranges would be profitable against these positional ranges to CALL from the BLINDS.

So I thought...and checked...and thought...and checked....

And then I found his Rule No. 6 that states to call in ANY position (therefore also the blinds) with PPs and SCs IF at least 2 people are in the hand.

So I put up a CROSS-MATRIX and used combinatoric to combine any of the positions against his Pre-Flop positional Rules.

I experimented with DIFFERENT ranges and THIS range is the one I came up with that was ALWAYS profitable.

It is SO striking, that I thought to check how that does heads up, because if BOTH blinds can play these tanges, how would a range play versus either a Big Blind that play like UTG, HiJ, CO or Btn which I used AGAIN Sauce123's ranges. Then I got results that were stunning:

Small blind ALWAYS pushes with his handrange PP 77+ & SC 54s+

Against a BB that plays dead-tight like UTG:
13,643,638,272 games 0.080 secs 170,545,478,400 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 51.026% 50.19% 00.84% 6847453044 114348826.00 { 77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }
Hand 1: 48.974% 48.14% 00.84% 6567487576 114348826.00 { 22+, AQs+, AKo }

Against a BB that plays rock-tight like HiJ:
16,890,166,656 games 0.010 secs 1,689,016,665,600 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 51.193% 50.39% 00.80% 8511719508 134799340.00 { 77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }
Hand 1: 48.807% 48.01% 00.80% 8108848468 134799340.00 { 22+, ATs+, KQs, AQo+ }

Against a BB that plays tight like CO:
24,424,304,256 games 0.005 secs 4,884,860,851,200 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 52.723% 51.76% 00.96% 12641993620 235153018.00 { 77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }
Hand 1: 47.277% 46.31% 00.96% 11312004600 235153018.00 { 22+, ATs+, KTs+, QTs+, JTs, T9s, 98s, 87s, AJo+, KQo }

Against a BB that plays semi-tight like BTN:
38,163,831,552 games 0.010 secs 3,816,383,155,200 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 55.481% 54.46% 01.02% 20782805552 390914548.00 { 77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }
Hand 1: 44.519% 43.49% 01.02% 16599196904 390914548.00 { 22+, A2s+, KTs+, QTs+, J9s+, T8s+, 97s+, 86s+, 75s+, 65s, 54s, ATo+, KQo, QJo, JTo }

You see that the LOOSER the range gets, the MORE equity THIS STRANGE amd WRONG LOOKING range has.

STILL...even against a DEAD TIGHT Big Blind that only calls pushes against the Small Blind with the dead-tight UTG range from Sauce123's SH-NL thread, it HAS POSITIVE Equity.

"How the f...is that possible??" I asked myself. So I experimented with it and simulated that EVEN if ALL players would stay in the hand (like in the loosest Micro NL game imaginable), then BOTH BLINDS would still have MORE (MORE!!!!!!) equity than the UTG Player with this strange range!!! Look at 10 Million simulated games:

9,909,598 games 19.337 secs 512,468 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 17.434% 16.86% 00.57% 1671018 56628.92 { 22+, AQs+, AKo }
Hand 1: 16.616% 15.94% 00.68% 1579623 66968.67 { 22+, ATs+, KQs, AQo+ }
Hand 2: 15.182% 14.48% 00.71% 1434441 70013.42 { 22+, ATs+, KTs+, QTs+, JTs, T9s, 98s, 87s, AJo+, KQo }
Hand 3: 14.025% 13.36% 00.67% 1323556 66295.00 { 22+, A2s+, KTs+, QTs+, J9s+, T8s+, 97s+, 86s+, 75s+, 65s, 54s, ATo+, KQo, QJo, JTo }
Hand 4: 18.358% 17.75% 00.61% 1758998 60201.92 { 77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }
Hand 5: 18.385% 17.78% 00.61% 1761655 60200.08 { 77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }

Guys, I SERIOUSLY think we have a problem here. Against a RANDOM range (because you calle the range "random") the result would look like THIS:

10,382,336 games 19.758 secs 525,475 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 21.139% 20.52% 00.62% 2130357 64322.92 { 22+, AQs+, AKo }
Hand 1: 20.095% 19.32% 00.77% 2006364 79948.42 { 22+, ATs+, KQs, AQo+ }
Hand 2: 18.661% 17.85% 00.81% 1853214 84220.58 { 22+, ATs+, KTs+, QTs+, JTs, T9s, 98s, 87s, AJo+, KQo }
Hand 3: 16.988% 16.19% 00.79% 1681380 82345.42 { 22+, A2s+, KTs+, QTs+, J9s+, T8s+, 97s+, 86s+, 75s+, 65s, 54s, ATo+, KQo, QJo, JTo }
Hand 4: 11.556% 10.98% 00.58% 1140017 59748.25 { random }
Hand 5: 11.562% 10.99% 00.58% 1140612 59807.42 { random }

So the RANGE I defined is NOT random, it has MORE (MORE!!!!!) equity than the super tight UTG or any other range. Aaaaaahhhhhh!!!!!

I get crazy about this, this CAN'T ( CAN NOT!!!) be! NOT possible!!

So YES yes yes yes Jeff, YOU NAILED IT! It looks soooooo f....wrong and THAT's WHY I am posting this, but the result IS NOT. So why on god's green earth is that so?

Originally Posted by elipsesjeff

Heh, glad to see professors do useless things outside the classroom as well zing!

I am not entirely sure that the thread is useless, see Spenda's quote:

Originally Posted by bigspenda73

Holy hell this thread delivers, what it delivers, however, I am not as sure of.

THAT's also nailed on the point: I am ALSO not sure what it MIGHT deliver, that's why I posted it! I THINK that it MIGHT deliver that there is MORE to the combination of PP's & SC's than we THINK there is....if THAT's so...then some comon knowledge about "getting short" and "high-card-value" make no sense any more and the sauce123 knows more than WE know about THIS combination than any other poker player so far. Again, my mental mess was caused by Sauce123's SH "getting Saucy and beat SH NL mid- and high-stakes games".

Now, on the TOP of this website I read the word "Community". Isn't THIS what community is about? Developing ideas together to become a better player? I think this thread MIGHT deliver something VERY know to this UNIQUE combination. WITHOUT AKo or other so called "high-card strength" related cards that we celebrate so much for Shorthand. I THINK this thread might deliver that there is SOMETHING wrong to to the way we perceive "high-card strength". This "strange" combination value that mentally originated from Sauce123 so to say might deliver us a key to new insights.

IF we can make something out it to "add value" to our poker games.

I think it might DELIVER that...

Originally Posted by Warpe

"Really, if there’s one thing I’ve learned without question about poker, it’s that poker screws with people’s brains and drives them batshit." - Ed Miller

Yup...this paradoxon drives me brain mad like batshit..quite fitting!

This is a very interesting thread and it's making me think a lot...

Joined: 01 Jan 2008
Posts: 3
WPP: 1124

Excellent WPPs!

The reason your range does so well is that it is very rarely dominated and dominates even the tightest of ranges frequently. I'm going to break you range in two and show why this is...

22+ vs. SCs >54. 63:37

The SCs have 37% equity here which really is suprisingly large. I think this is because it is often a coinflip, and when it isn't, SCs are the best hands to have when facing an overpair.

AQs+,AKo vs. SCs 60:40

SCs have 40% equity here. This is again not suprising because most overcards vs. undercards are ~60:40

77+ vs 22+ 63:37

Not much to say here...

77+ vs. AQs+,AKo 59:41

Interesting. I was expecting this to be closer, but the opposing range is unlikely to hit more than pairs/ 2 pairs.


I know this has seemed like a random ramble, but the point I am trying to make is that your range will very rarely be dominated and when it is, it has a comparatively large amount of equity.

One slight observation I have to make is that in the example that you gave stated that there were no blinds. Obviously, if this were the case there would be no need to play anything other than AA, as Sklansky states in Theory of Poker. As we need to win the blinds more often, having a wider range than the 6% that you have chosen is actually beneficial.

What it has shown is that playing SCs against a fairly narrow range is more profitable than I had thought. That could mean that 3betting SCs/ shoving with SCs makes sense!

Thank you sir, great thread!

Damn, I was going to post something super long and Warpe summed up exactly what I was going to say, but only shorter.


The reason why I said this is a complete waste of time, is because this scenario has never, nor will ever, exist. If you didn't already know the percentages of hands then I guess this could help you out.

Finally, PLEASE stop typing in CAPS because when you do IT every OTHER word its REALLY annoying. It makes YOU look like a complete ASS by assuming we DONT know when to place EMPHASIS correctly.

Originally Posted by badgers

This is a very interesting thread and it's making me think a lot...

Thanks, no I am not the only one bashing my head...

Originally Posted by badgers

I know this has seemed like a random ramble, but the point I am trying to make is that your range will very rarely be dominated and when it is, it has a comparatively large amount of equity.

The point is the uniquw COMBINATION of Pocket Pairs AND Suited Connectors that struck me. Yes, they are MUCH stronger than I also expected. So that IS worth the time looking into this matter!

Originally Posted by badgers

One slight observation I have to make is that in the example that you gave stated that there were no blinds. Obviously, if this were the case there would be no need to play anything other than AA, as Sklansky states in Theory of Poker. As we need to win the blinds more often, having a wider range than the 6% that you have chosen is actually beneficial.

That is the point. In the end, there ARE blinds and the equity only exists in this theoretic cube, on the table we could still use this surprisingly in SB vs BB. Of course the high card value MUST hold true and it DOES if one manipulates the range of the Big blind to another range that is also as tight but with HIGHER value SUITED cards:

If we choose HIGH-VALUE suited cards, then if we go down for the calling range of the BB to pocket pairs 22+ and any Suited card bigger than Ten we get this result:

16,328,530,944 games 0.010 secs 1,632,853,094,400 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 51.666% 50.82% 00.84% 8298652688 137677032.00 { 77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }
Hand 1: 48.334% 47.49% 00.84% 7754524192 137677032.00 { 22+, ATs+, KTs+, QTs+, JTs }

ONLY if we heigthen the range to say pocket 44+ and suited cards bigger than Ten we get an EVEN status:

14,520,337,920 games 0.010 secs 1,452,033,792,000 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 49.606% 48.73% 00.87% 7076204564 126703092.00 { 77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }
Hand 1: 50.394% 49.52% 00.87% 7190727172 126703092.00 { 44+, ATs+, KTs+, QTs+, JTs }

The ONLY possible range to make profit heads-up versus the Pocket Pairs 77+ and suited connectors bigger than 54s+ is THIS one:

Any pocket pair 77+ and ANY suited cards Ten or higher:

11,910,786,624 games 0.005 secs 2,382,157,324,800 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 45.897% 44.93% 00.96% 5351946848 114789000.00 { 77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }
Hand 1: 54.103% 53.14% 00.96% 6329261776 114789000.00 { 77+, ATs+, KTs+, QTs+, JTs }


THIS would be 18 cards vs 18 cards and HERE we can see that High card value DOES count.

BUT: see how THIS range does vs. the broadway:
24,194,855,520 games 0.060 secs 403,247,592,000 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 44.991% 43.21% 01.78% 10455296268 430218282.00 { TT+, ATs+, KTs+, QTs+, JTs, ATo+, KTo+, QTo+, JTo }
Hand 1: 55.009% 53.23% 01.78% 12879122688 430218282.00 { 77+, ATs+, KTs+, QTs+, JTs }

NOW pushing any card 77+ and ANY suited card higher than ten gives us 55% equity. Not bad.

Our PP 77+ and SC 54s+ does like this, we had that above already:

25,585,246,368 games 0.010 secs 2,558,524,636,800 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 49.124% 48.21% 00.92% 12334149208 234464490.00 { TT+, ATs+, KTs+, QTs+, JTs, ATo+, KTo+, QTo+, JTo }
Hand 1: 50.876% 49.96% 00.92% 12782168180 234464490.00 { 77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }

Now, as you can see that the difference between OPTIMUM calling range (77+ and any suited cards higher including a ten) and PP&SC defined pushing range is just 5%. Well...5% is a lot BUT I expected the numbers to be completely different!

THAT is what drives my brain "batshit" insane. The difference is SO small, that it should NOT be that small and it should NOT have a positive equity vs. the broadway. This is WHY this is so stunning and I will ALSO change my game according to this! Also note, that to ANY of the writen ranges you get WORSE equity when you add OFFSUIT high cards!!

Take the optimum calling range: 77+,ATs+,KTs+,QTs+,JTs
add just ONE offsuit high card like AKo to this range and you LOOSE equity! So this result leadsme to to thinking forget pushing AKo for example. yes, I know that in high-stakes HU you push it happily. But how many times have you been called happily and lost? And how many times was it a PP or SC?

Look at THIS one:

Say you get EVERY time AKo you PUSH it vs Pocket pairs bigger than 77+ and any suited connector bigger than 54s:

1,623,264,192 games 0.005 secs 324,652,838,400 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 49.379% 47.99% 01.39% 778943544 22607526.00 { AKo }
Hand 1: 50.621% 49.23% 01.39% 799105596 22607526.00 { 77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }

That makes AKo a LOOSER.

Now have a look at THIS one:

Instead of the Offsuit AKo we take the suited AKs versus our new PP&SC range:

547,937,280 games 0.005 secs 109,587,456,000 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 52.098% 50.24% 01.86% 275273840 10189736.00 { AKs }
Hand 1: 47.902% 46.04% 01.86% 252283968 10189736.00 { 77+, AKs, KQs, QJs, JTs, T9s, 98s, 87s, 76s, 65s, 54s }

Ahhh....suddenly AKs is a winner.

So one more AGAINST high-card strength. I think I will forget about high-card strength if it is NOT suited. The difference is massive here. Think about how many hands per year a good player mutlitables. I don't know about you guys, to me 3% is A LOT on multitable volume.

Originally Posted by badgers

What it has shown is that playing SCs against a fairly narrow range is more profitable than I had thought. That could mean that 3betting SCs/ shoving with SCs makes sense!

YES SIR!! It does! ONLY IF we would have the information that a player includes these hands into his pushing range and defines his pushing range according to THIS post, then the ANTI-CALLING range so to say is
any pocket pair bigger than 77+ and any suited cards Ten+, which are ALSO exactely 18 cards. Acutally that is why I included 54s to make it 18 cards also, so now you have my COMPLETE background of thinking. But then again YES, it really shows that there is more to SCs. I would like to see the SPECIFIC hands that were won in the enumeration for PP's&SC's. But that are more than 25 Billion hands to go through...ahh...ok. Maybe not.

Originally Posted by badgers

Thank you sir, great thread!

Thank you FTR, the posts and the great videos here actually made me a better player, so I thought I join the community and participate a bit and do not just follow the posts as a passive reader.

By the way, I posted this thread in HU, because I think the people reading here are the ones most likely to understand it and are also most likely the only ones that will read this anyway, the HU has the least posts and threads, so I thought it might be right here!

Originally Posted by elipsesjeff

Finally, PLEASE stop typing in CAPS because when you do IT every OTHER word its REALLY annoying. It makes YOU look like a complete ASS by assuming we DONT know when to place EMPHASIS correctly.

Sorry. Bad habit.

Wow, thanks for being so thoughtful to really write this all down and thoroughly explain it .

I'm sorry to say all I did was skim this but from reading it two thoughts come to my head.

1. This should make you realize the profitability of being aggressive, as you are never far behind or very ahead.
2. However, just because ranges are even doesn't mean that you immediately win half the pot, there is a flop turn and river!! Position and postflop skills often is a bigger factor than equity.

Originally Posted by IowaSkinsFan

1. This should make you realize the profitability of being aggressive, as you are never far behind or very ahead.

Writing this post throughly made me realize this even more!

Originally Posted by IowaSkinsFan

2. However, just because ranges are even doesn't mean that you immediately win half the pot, there is a flop turn and river!! Position and postflop skills often is a bigger factor than equity.

That is where I gave much thought yesterday to the ISF theorem. Actually, it is the best sentence I have ever read somewhere so far. It sounds really simple but it is nearer to the truth than anything else I could come up with. Ingenious! Bluff TAGs because you have more fold equity and can "ping" their range more predictable, be tight against LAGs, they might hit more due to their range, especially the much hated random 2 pair - more often than we expect due to some sick variance or when the universe decided to conspire against us - otherwise value bet them, they might pay u off.

Actually I had to think about another sentence from a SH guide:

Originally Posted by ilikeaces86

"In a raised pot if you can beat Aces (=2 pair+), you have the nuts."

What do you think about that one for post-flop skilled play? It says "I have the nuts". It does not say most of the time. For HU, that is probably true 95% of the time. But for 6 max (even this is another posting category)? Hmm...I would truly like your opinion on that sentence.