This section contains the experimental results of using Probability Triples as a stand-alone betting strategy (Section 4.2.1) and as a reweighting factor in opponent modeling (Section 4.2.2). Both the individual effect of each enhancement and their combined result are discussed. In the experiments, B stands for the use of the PT generation function as a betting strategy and R stands for the change of the reweighting system to use PTs.
Figure 4.3 shows the results of playing ten Lokis against themselves in a homogeneous environment (only one type of player) with the B and R enhancements individually and combined (B+R). The players were eight Loki-1 players against two enhanced Lokis. Loki-1's performance is the baseline for the comparison. The B feature represents a sb/hand improvement, the R feature represents a sb/hand and B+R represents a sb/hand improvement. The B+R results show that the effect of these enhancements is nearly additive since these features are almost independent of each other. Note that each enhancement is a win by itself and in combination with the other one.
A second series of experiments was conducted to see how well the new features performed against a mixture of opponents with different styles. For this set of experiments, opponents with different playing styles were used. In each experiment there was a pair of players from each of the four categories: tight/passive (T/P), tight/aggressive (T/A), loose/passive (L/P) and loose/aggressive (L/A). In each pair, one of the players was a basic Loki-1 player and the other was a Loki-2 player with either new betting strategy (B), new reweighting system (R) or both features (B+R). Figures 4.4, 4.5 and 4.6 show the absolute improvements per type of player obtained by adding B, R or B+R respectively. Since ten players are required to play a tournament, we actually used two pairs of tight/passive players and reported the average over the results of both pairs.
In each mixed experiment, the enhanced player always outperformed the corresponding un-enhanced player. The absolute individual improvement varies greatly from one style of player to another. For example, the L/A player enhanced by R in Figure 4.5 had a 0.11 sb/hand improvement going from -0.033 sb/hand to 0.077 sb/hand, while the T/P player enhanced with R went from -0.031 sb/hand to 0.023 sb/hand showing a 0.054 sb/hand improvement. On average the B enhancement produced an improvement of 0.045 sb/hand, the R enhancement of 0.070 sb/hand and B+R of 0.096 sb/hand. These experiments showed that both enhancements win, regardless of playing style.
Loki-2 with B and R was also tested under more realistic conditions against human opposition. Loki-2 plays in an on-line poker game running on the Internet Relay Chat (IRC) poker server (irc.poker.net). Human players and other poker-playing programs connect to IRC and participate in games conducted by dedicated server programs. No real money is at stake, but bankroll statistics on each player are maintained. Since there is no control over the quality and type of opponents, the performance of the program depends strongly on which players happen to be playing and the variance in these games is very high. However, Loki-2 is a consistent winner increasing its bankroll at a rate of 0.11 sb/hand in 25,703 games (Loki-1's winning rate on IRC was 0.08 sb/hand).