I would also expect that all or close to all hands should play,
getting at least 3:1 odds, favourable implied odds, and a free
pass to the showdown. 32o wins just under 33% against a random
hand, and of course worse against the best of two random hands,
but it still might be near the playable region. I haven't done
any math to support that intuition, but I fully expect that an
optimal strategy is *far* from easy to describe. You have to
compute the EV for every possible flop and turn, and the outcome
for every possible board. The opponent hand distribution can be
pre-computed, and updated as board cards are revealed by zeroing
the impossible cases. All in all, that's a pretty big job, but
should be quite doable with today's machines.

- Darse.


On 4-Mar-07, at 10:46 AM, Darse Billings wrote:
>
> I just did a quick read of the rules. If I haven't misunderstood
> how the game is played, an optimal strategy will involve many hands
> that call the raise with draw odds, and then recover some equity
> by betting after the flop (favourable implied odds from +EV hands
> against the opponent's known distribution). With the exception
> of big pairs and perhaps some potentially dominating hands (e.g.
> AK), the preflop all-in is not a very powerful action, because a
> mere 60-40 advantage reduces the leverage considerably, and must
> abandon the implied odds from optionally flat betting one unit on
> the flop and turn.
>
> The good news is that it is not a difficult game to solve, because
> the EV can be computed for each case against the known distribution.
> I suppose the game designers did this when defining the game, to
> ensure a guaranteed profit against optimal play (and much better
> against typical humans, who are much weaker than they imagine).
> However, there have been many promotions in the past where the
> house failed to do the math properly, and ended up taking the
> worst of it, so it might be worth looking into.
>
>
> On 4-Mar-07, at 3:33 AM, JRWashington wrote:
>
>> Hi,
>>
>> I am interested in a program which optimally solves the wager works
>> casino game of Texas Hold'em shoot out, I am also interested in the
>> variance but not as much as the ideal strategy. My expectation is
>> that the optimal strategy would be all in or fold. The rules and the
>> bot behavior can be found
>>
>> http://casino.virgingames.com/GameDetails.do?menu=STRP&gameid=0068-0
>>
>> Bottom line is there are 2 possible pot states, you are effectively
>> always the small blind as one of the bots will always raise, leaving
>> either a 3 unit pot or a 4 unit pot.
>>
>> The you have the option to go all in, or fold, the bot will always
>> call your all in. An all in is worth 8x your ante so makes either a
>> 19 unit pot or a 20 unit pot and seeing 5 cards.
>>
>> The eval example would almost seem to do everything you need, apart
>> from, picking the stronger of the bots hand to play with.
>>
>> I am willing to pay upto $50 (by paypal most likely) for the house
>> advantage with an all in or fold, a proper strategy table/or
>> application for an all in or fold strategy, and the source code with
>> compilation instruction and code comments.
>>
>> If the optimum strategy is not all in or fold (eg it is call and play
>> down the streets), then, I will pay $100 if you are prepared to solve
>> that - and provide the same as above - application, HA and source with
>> comments, as it looks like more work.
>>
>> Many Thanks,
>>
>> John.
>>
>