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