Looking to do my first real analysis PAPro, I decided the simplest sim I can do would be a study on the effects of rake on a zero sum table. This was to be a very simple test, just to see how much money was left on a Limit table after all but one player had busted.
I set up a standard Low Limit ring game, $.5/$1 Blinds with a standard
PokerStars Rake. 9 Players were at this table each with $50, for a total of $450 dollars in play. There were to be no rebuys and no new players would sit, so ignoring rake, this was truly a Zero Sum game. I used the normal randon distribution of bots to fill this game, to best simulate a normal SSH game.
So I started the game and let it run. 3,333 hands later we had a clear winner, Fred. Fred had almost tripled up for a grand total of $145.75. Thats $304.25 that went to the house, or 67.6% of the money in play. That works out to only $0.091 per hand.
Looking at Fred's Play, He looks to be a LAA player with 49% hands played (Not VP$IP mind you), 16% Pre-Flop Raise, 1.9 Aggression, and 53% Went to showdown and Won money (This seems to be something akin, but not the same as, WSD and W$SD) Overall. But with 7 or more players he is 41%/11%/1.4/49%, putting him somewhere between LAA and LAP. But obviously he is a fish that was getting lucky. As you can see on the following graph, his stack continued to grow fairly well (RED LINE), at a win rate of 4.37bb/100. But, the Blu line indicates the relative strength of his preflop cards, which is showing that he had superior hands dealt to him the majority of the session. The Green line shows the overall luck factor (what everybodie's final hand would have been), and while this indicates he wasn't flopping as well as everybody else, His superior cards were winning since the winning hands had probably already folded.
While this little study doesn't represent anything new or earthshaking, it does give a little insight into some of the features Of PAPro. It also shows that fresh blood at a table is critical for the games survival, long term and short.
If the same set of players remain at a table for a long period of time, then the house's edge over the good players' ability to take money from the weaker players grows. Look at it this way, each player has a certain EV vs another player. Good aggressive players have a huge edge over the semi-loose, semi-aggressive players, but not as much over the almost as good players, and the total randomness of the true guppies makes them hard to keep a good EV. You may even have a -EV vs certain players, either they are just better than you, or you can't adjust to their game. These are small edges vs each player that add upto your expected Win rate for that session. If this EWR is less than the expected effect of rake, you will end up a losing player. The introduction of more fish to the table will add new money to the table and it will up your expected win rate.
Zero Sum and The effects of Rake.
Linear Mode
