2-card Poker: +EV Hands

Imagine a game of 2-card poker. It is exactly like hold'em, except there is only a pre-flop, and the best 2-card hand wins (pair > high card > all else). In an x-handed game, which hands are +EV (i.e. which hands win more than they lose)? I attempted to solve this problem myself, but I think my solution might be slightly off:

HANDED +EV
2 [J9, AA]
3 [QT, AA]
4 [K6, AA]
5 [KT, AA]
6 [KQ, AA]
7 [A3, AA]
8 [A4, AA]
9 [A5, AA]

Would someone verify if I'm correct using math and/or simulations? Thanks [img]/images/graemlins/confused.gif[/img]

[UATrewqaz]

Looking down to find AA in that game would be truly great...

[ QUOTE ]
Looking down to find AA in that game would be truly great...

[/ QUOTE ]

It would be even better when a fish called you with Q7s and managed to suck out anyway. [img]/images/graemlins/smile.gif[/img]

There are no suckouts. There is no flop. AA is the pure nuts.

[mulebennett]

[ QUOTE ]
There are no suckouts. There is no flop. AA is the pure nuts.

[/ QUOTE ]

Hence the joke... [img]/images/graemlins/tongue.gif[/img]

[RoundTower]

Is there betting in this game? I imagine the answer to your question depends on this.

[damaniac]

Essentially we could number the hands 1 to 169 or something right? So it's a lot like the numbers examples that appear in TOP, for example (though that was river betting, it is actually quite similar to this in that there are no more cards to come). To get the hands you just line them up in order of showdown strength, then what divide by N(number of players) to find out what hand is going to be best on average?

But even then you have to think of the hands that will call that are worse than yours, so the actual value of those hands isn't so straightforward. For ex, if you bet hand 51 out of 100, if hands 0-50 aren't calling, you have no value in betting.

[ohnonotthat]

How is this being structured ?

Is it identical to holdem with a small and big blind - i.e. no check-raising ?

If so, a simple ranking system would fail. Such a system would fail to take position, prior callers (or raisors) and the dynamics of tight vs. weak players.

We used to play a vicious form of 2-card poker when I was in H.S. but we played it with simultaneous declarations - identical to high-low stud declare except here the declaration was either "call" or "fold" (a chip for play, an empty hand for fold.

We had antes but no blinds and since position was irrelevant and there were no raises, unless I'm "missing the forrest for the trees" a simple ranking system would work fine here.

Oh, btw, pot-odds were also not applicable; the ante was 1 chip (usually a quarter) and losers all matched the pot while the winner collected, but he collected only the antes. The "match money" then remained for the next hand. Thus while the size of the pot in $$ would vary from hand to hand, pot odds never changed; you were always betting even money that your hand beat all other hands that chose to play.

Note that there would still be strategy but it would be based solely on your opponents tendencies - making this a perfect game for those proficient in the application of game theory.

If you always based your choice on the same [absolute] standards you got killed.

It might seem that reading tells would have been far more important than game theory but we were a bunch of idiot kids - usually drunk - so this was not the case.

There was one tell that worked on quite a few players though I'm not sure this is a tell in the typical sense of the word.

Alot of the guys would fail to take a chip off the table and place it in their lap (out of view to anyone) if they knew they would not be contesting that hand; ergo if a player looked at his cards then reached under the table WITHOUT GRABBING A CHIP FROM HIS STACK there was one fewer player to worry about.

It was not 100% reliable but there were no reverse tells; "all poodles are dogs but not all dogs are poodles" was the rule.

Translation: Some players would take a chip when they had no intention of calling but I never saw anyone leave a chip in their lap after a fold and use it to play the next hand.

It was a great game for anyone with half of a brain; it also produced lots of hilarious instances.

My favorite was when the game got 5-handed and a new player opened his hand to reveal TWO chips, rolled over A-2/suited (A-high flush and a likely winner 5-handed) and declared "both" - likely a sound play had we been playing hi-lo. [img]/images/graemlins/frown.gif[/img]

[tonypaladino]

This would be somewhat similar to 2 Card Guts

All players ante, each player is dealt 2 cards. Players decide all at once if they are in or out. (In some games you use a button and go in order) "Out" hands are mucked. "In" hands are turned face up and the best pair or high card wins. What makes this game interesting, is that on the next hand, all players who were "in" the previous hand, but lost, now have to ante an amount equal to the previous pot. This continues and the pot continues to grow with each hand, until there is only one person in for the hand who takes the whole pot.

I've played a similar game to this except with more hands rankings than just pairs and high cards.

From bottom to top these are the hand rankings:
High Card
Flush(Two suited Cards)
Straight(Two connectors)
Pair
Straight Flush(Suited connectors)

It's a game that I usually seem to win at but I don't really know why... Any suited connector, pair, or straight is playable, and when the pot gets pretty large I'll play flushes too.