What strategy would you choose for this game?

You can choose your hand under the following conditions:

.At most only one Broadway card A-10

.You can’t select the same hand twice in succession

.Suits are randomly selected by the computer.

I'm not sure if there is any lesson here if there are responses but maybe a bit of fun for some.

Is every other player also faced with the same choice, or do they get dealt random hands in the normal fashion?

It's heads-up and both have to choose but maybe the other player getting dealt random might be worth looking at. Anyway, for now let's assume both choose.

Just to be clear are you asking how we would construct our ranges from both positions given the rule?

Random seems more interesting as it could be a way to simulate capping your range early in a hand.

If both players get to choose it seems more fair but not sure what we could learn from it.

Also what are the stack and bet size restrictions? Raked or unraked?

I came up with a strategy for both players having to choose ignoring such factors as stack size, position, etc.

If you want to do A chooses and B dealt random, which may be more interesting, ok by me.

Same for speificying deep or short stack or xxx.

I assume you used preflop/all in equity or am I just not seeing something in the rules to simplify this....

Yes, to make it simple I just assumed no further betting

Unless I'm missing something the best strategy in the game where both choose and there is no further betting is for each player to alternate between 99/88, always choosing the same. Neither has any incentive to deviate because no hand can beat 99 under the rules, or beat 88 if 99 was chosen previously.

I guess one player could choose something that isn't 99 but has a lot of equity, like T9s, so he can play the next hand with an advantage of knowing the opponent can't have 99, but then the opponent could just quit and take his win rather than be at a disadvantage for the next hand.

With no further betting against a random hand, I'd still alternate between 99/88. The game is only interesting with further streets of action, and is probably best with a FL/PL structure. NL just doesn't work, IMO.

It might be interesting as an all-in preflop game if a certain number of hands are forced to be played. Then the optimal strategy would involve mixing other hands with 99, I think.

Assuming that we're playing HU NLHE 100bb deep, I'd imagine the optimal opening range to be:


Jam with this range. Next hand choose 88 if you were called by 99 and jam again.
If opponent folded the last hand vs a jam, just choose any two and open fold.

If we're playing PL however, it gets a bit more complicated. I'd imagine the optimal open range to look more like:



It would also be optimal to have a limping range.

If we're deeper we'd mix our strategy even more. If we're very short, we'd pretty much only play 99.

I agree with both Brownie and ZKesic.

It should be apparent that 99 is the best hand under the rules followed by 88. If at the start both players choose 99 then it would shift to 88 vs 88 and then back to 99 vs 99 etc. making for a very boring game.

If a player decided to make things a bit interesting, he might choose T9s when his opponent is playing 99 as that is the best hand vs 99. Then he has the edge in the following hand, but it then becomes the tie game T9s vs 99 followed by 99 vs T9s, etc.

If there was future betting so a player doesn’t have to show his hand if his opponent folded, the strategy could be more complicated I suppose.

Under these rules:
Players must continue to play indefinitely.
Players choose their hands by the rules set in your OP
There is no betting beyond an initial ante.
Both players know what the other chose last round.

The mirror strat you suggested doesn’t quite work.

Round 1, A chooses 99, B chooses T9s
Round 2, A chooses T9s, B chooses A9s

B retains the option to play 99 next and A can’t counter with T9s. I think the equilibrium strat requires a mixing in the first round. Choosing 99 as a pure strat seems to be losing.

Yeah, I forgot about (actually didn't think of) the A9s gambit.

FWIW, J9s does significantly better vs T9s than A9s does, so if this game does indeed require a mixed strategy, J9s would presumably be played at some frequency.