New heads up poker game - best strategy?

[dfan]

At a recent home poker game, a few of us were early and sat down at the table. It happened that 4 of us were on one side of the table and the host, we'll call him Jim, sat on the opposite side. A joke was made about the four of us teaming up against Jim, and Jim (who is forever telling us what a gifted player he is) said jokingly, "Hell you could all combine your cards and I could still beat you." We laughed and said something to the effect of "yeah right!" After a bit of bantering he made the following serious offer: He would play me heads-up, with me getting dealt 8 cards from which I could choose my 2 card starting hand. He would play his regularly dealt hand but I had to give him 2 to 1 on the money. For example, if he bet $25 and I called and lost I had to pay him $50.

I accepted his challenge and we played. This was 1/2 NL, and we each had a stack of $180.

Here are the questions:
1) Which side of this proposition would you take - mine or Jim's.
2) What strategy would you use if you were me in this game? (starting hand selection, how much to bet preflop (most important), etc.).
3) What is Jims best strategy?

BTW, we played two sessions of this. I'll post how I came out and what my strategies were after I hear the comments of others.

[jay_shark]

1) I would take yours . You can do a lot of damage with 8 cards , but I guess it depends on the relative difference in skill level .

2) Ideally in heads up you would pick cards that are higher in rank as drawing cards become less valuable . Middle and high pocket pairs are extremely valuable and should have preference over almost all non -paired hands .

3) Jim's best strategy is to not play the game .

[BrianBigNFun]

I assume that the hand has to be chosen preflop and cannot be changed after the cards come out?

[riverspecialist]

the rules werent totally clear. it sounds like u get 8 cards, pick 2 and discard 6.
anyone who plays heads up would obviously take jims side. starting hands dont really matter that much in heads up no limit and you couldnt play a strictly "high card" strategy because it would be to readble. getting 2:1 on ur money is a better edge.

if u somehow meant u get and 8 card hand from which u can only use up to 2 of at showdown, then you have the better deal.

A more fair game would be to shrink the 8 card hand to 4 and u get to keep them all until showdown like in omaha.

another one would be to keep the original game of being dealt 8(keep2) and also u always get to be all time button.

curious to hear the results u got

[dfan]

[ QUOTE ]
the rules werent totally clear. it sounds like u get 8 cards, pick 2 and discard 6.

[/ QUOTE ]

Sorry about the ambiguity. Yes, that was the rule.

[holdem2000]

It would take me a while to rigorously pick an opinion, but intuitively I think Jim has an edge in this game. Jim gets to bully you to a ridiculous extent... if he's 35% to win a pot it's +EV for him to be allin. If you bet the pot (that is, the amount of your stack you put in is equal to the pot) on the turn, he's being offered 4:1 on his money... you can't take him off of a real draw. Worse, if he's any better than a 2:1 dog he can just push his draw and actually want you to call.

If the stacks were a bit smaller it might be +EV for him to push blind every hand.

[Galwegian]

I think I would take Jim's side. Choosing 2 from 8 cards means that he can choose the best from 28 possible starting hands (I know these are not independent, but still 28 is a lot). I suspect that (given the stack sizes that you specified) if he just jams every single hand, that he will be +ev. I will work out some math later on this - don't have the time right now. One way to think about this would be to model this with a [0,1]-game (as in Mathematics of Poker). Let's suppose that the largest number wins (I know this is the opposite to MOP) Now suppose that Jim gets dealt 28 uniformly distributed random numbers between 0 and 1 and can choose the largest of these to play against against your single uniformly distributed random number. His hand will be better than yours more than 97% of the time. That is a big edge! I'll try to work this out fully later

[jay_shark]

Galwegian , did you mean to say Jim's friend ?

Jim's friend gets to choose 2 of 8 cards . Jim is the guy with the ego who thinks he can win with any two cards . A common mistake people make in heads up .

[Todd Lapham]

I'd take your side. It'd be nice to know 6 dead cards as well.

[rufus]

The holdings that are 66% or better against a random holding are:
Pocket Pair Ace through 8 and AK suited - that's a total of 52 good pocket holdings. The chance of getting two particular cards in an initial holding is 52 choose 6 divided by 52 choose 8 = 8*7/46*45 = 56/(46*45). Based on this, I'd guess the 8-card player is getting the best of it almost all of the time, and his strategy, is basically going to be all-in all the time (times where there is no premium hand are effective pseudo-bluffs).

Against this range of 'power' hands, the single-hand player can reasonably call with A-T paired - about 1 time in 22. (Since the 8-cards player is going to be basically raising all the time, there's no reason to give away information by raising.)

The one time in 22 that the simple holding player calls, he's looking at a toss-up about 2/3 of the time, and getting an average return of 1.66 or so the remaining third of the time. So the calls are worth about 1% of a stack per hand.

So, if the stacks are larger than about 100 blinds, the 8-card player might want to use smaller raises than all-in, which complicates the game a little, but below that, a first order approximation of the value of the game to the 8-card player is:
blind size - stack size/100
where the blind size is whatever the 2-card player has to put in, and stack size is the size of the smaller stack.

So, I would say that the 8-card player's strategy should probably be something along the lines of:
Bet about 70 times 2-card players blind all the time (looking for premium hands A-8 paired AK suited in the 8-cards).
The 2-card player should respond by pushing/calling with paired tens or better, and, if not all-in should also bluff at some rate based on the stack/pot ratio.

In response to a 2-card player push, the 8-card player calls with paired aces, kings or queens, as well as some weaker hands based on the raise/pot ratios.