Analyzing Games

            I was asked this past week about the process of analyzing a game.  I was caught a little off guard when I was asked in front of a room full of people.  My answer was probably a little jumbled.  But now, with some time to think about it some more, I think I can explain it better.  The real trick is not coming up with the payback of win frequencies.  What I'm really in search of is the proper strategy for the Player to play.


            For some games, this is not easy to do.  I'm not talking about a game like blackjack or video poker where the strategy is somewhat complex.  Determining the strategy is fairly straight forward.  There may be a lot of different strategy decisions, but the math is actually fairly simple and can be determined either via math model or a variety of computer techniques.  The challenges come in to play when there variables get harder to pin down.  The game of Ultimate Texas Hold'em has only a few strategy points.  You have to decided to Play/Check the 4x, Play/Check the 2x and Play/Fold the 1x wager.  But there are an absurd amount of possible hands at each point and just as absurd a number of possible resulting hands.  Throw in the community cards which makes it impossible to define a hand by simple the rank of the hand (The relative strength compared to the community cards must be considered) and UTH was not a lot of fun to work out the strategy for.


            The last part of the 'fun' is that most of my work is for games that don't exist yet.  We're playing with betting structures and paytables.  The work becomes very iterative.  We may find that the game pays 105% and now we need to make changes to it.  These changes might require starting the analysis all over again.  Compare this to analyzing an existing game and realizing you are dealing with static rules.  The rules are already determined and they are NOT about to change on you in the middle of the analysis.


            When I am analyzing a game under development, I frequently hear along the way questions about why I'm so worried about getting the strategy exactly right especially when it is something so complex that virtually no one could play it.  The probably is that 'virtually no one' means that there MAY be someone who does.  All analyses must assume that the Player is playing perfectly (or really, really, really close to it).   This becomes even more important as online casinos become a reality.  Players won't have to memorize strategy.  They'll be able to enter the information available to them (exposed cards, etc...) into a computer program which can play as perfect as, well, a computer can!


            A few weeks ago, my column was about a game called Asia Poker (a variant of Pai Gow Poker) where the Player is dealt seven cards and must break his hand down into three hands (4 cards, 2 cards and 1 card).  The original analysis (not done by me) assumed that the Player will play as the House plays.  For Pai Gow Poker, this is mostly true.  There are a handful of situations where the player would want to deviate, but the impact to payback is minimal and presumably it does not make the payback over 100%, so no one is too concerned.  But, in a 3-hand game, I always found it hard to believe that the House Way would be so correct for the Player.  Our preliminary analysis showed I was correct and we shaved the house advantage down by about 25-30%.  Since I wrote that column, we refined our analysis even further and cut the house advantage down by almost 50%.  This still leaves the game well below 100% so there is no concern there (although, when I started the process, I didn't rule this out).


            So far, we have not taken the perfect (or what we believe to be perfect) strategy and tried to put it into any form a human can use.  We're fairly certain that no human short of Rain Man would be able to play the game perfectly.  About 20% of the hands deviate from the House Way.  This may be neatly defined into a few rules or might be exceptions to the dozens of existing House Way rules.  Even if I were able to define the exceptions into a human useful form, I doubt the casinos will be too concerned.  Learning the House Way is difficult enough.  Learning variations from it will be mastered by very, very few Players.  Some people might learn some of the rules, but it's unlikely any one person will master them all.


            But the concern becomes more real if you are playing Asia Poker at an online casino.  Now, you can type your hand into a program and it will tell you the proper way to play the hand according to the expected value model we built as opposed to the House Way.  It can do this in less than a second, so there would be no issues about timing.  While I'm still fairly certain that very few people would use a tool if it were available, there is likely to be enough people who will that the casino may notice.  If the game were to go positive (payback > 100%) as a result of playing perfectly as opposed to play 'normal', you can be SURE that there would be Players who will do everything they can to take advantage of this.


            This is why a game analysis must assume perfect strategy.  A game like UTH would come dangerously close to the 100% mark if it were to be played online.  Should online casinos become that prevalent, I'm guessing that the blind payouts will be lowered slightly to help insure this doesn't happen.  UTH has the ability to do that, but not every game has a variable that can be changed in that manner to keep the payback from going positive. 


            Once the strategy has been determined, the rest is relatively easy.  The game simply must be simulated (or potentially every possible hand played) using that strategy to get all the relevant stats of the game.  While some games are more complex than others, this part of the job is always the easier half.