Probability triples

To make a betting decision Loki-1 uses an evaluation function to
determine which of the three actions (fold, check/call, or
bet/raise) is more likely to be profitable. In fact, the
``best'' action can be considered as the action with the highest expected
value over all the possible scenarios.
However, Loki-1 provides too much information to the opponents if it
always takes the best action. Loki-1 is predictable and the
opponents exploit that predictability. We use *probability triples*,
a set of three probabilities representing the three types of actions,
to provide a randomized betting strategy for Loki-2 and
to represent the probabilistic nature of poker.
This representation isolates the expert knowledge
in a single function (probability triple generation routine)
and allows a computer oriented (i.e. easy to maintain and modify) design of
the evaluation function.

A *probability triple* (PT) is an ordered list of three values,
*PT*
= (*f*,*c*,*r*) such that
*f* + *c* + *r* = 1.0. Each value represents the likelihood that
the next action in a given state is a fold (*f*), a call (*c*), or a raise
(*r*), respectively. Probability triples are used in three places in
Loki-2: 1) as a stand-alone betting strategy, 2) as the reweighting factor
in the opponent modeling module, and 3) as the action generation
mechanism during the simulations.