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6.3 Effective Hand Strength

The majority of betting decisions are made based on a variable which represents the strength of Loki's hand in the current situation. Basic hand strength (HSn) is the probability that it presently has the strongest hand. This alone is not fully adequate when there are more cards to come which can easily change the situation. For this reason, we compute the potentials PPOT and NPOT, which tell us Loki's probability of winning/losing given that it is currently behind/ahead. Using these values we can compute an estimate of Loki's chances of winning at the showdown (or of being the strongest after the next card, if it is the flop and we are using PPOT1). We define effective hand strength as

EHS = HSn + (1-HSn)*PPOT - HSn*NPOT. (6.3)

Observe that on the river EHS = HSn, since there are no more cards to be dealt.

However, there are some problems with including NPOT in the calculation. First, when we bet we do not know if our opponent will play. Second, in many situations where we compute a high NPOT, it is often a better strategy to bet/raise to force the opponent out of the hand. So when effective hand strength is used as a betting decision (as opposed to a calling decision) it is preferable to use a more optimistic version, EHS':

EHS' = HSn + (1-HSn)*PPOT. (6.4)

This is an estimate which means ``the probability that we are currently leading, or that we will improve to the best hand by the showdown."

The basic betting decision used in Loki is similar to Figure 6.2, with the exception that EHS' is used instead of HSn. A Make2 hand is defined as a hand with $EHS' \geq 0.85$. We raise when less than 2 bets have been made this round, otherwise we call. A Make1 hand is defined as a hand with $EHS' \geq 0.50$. We bet if no one else has, and call otherwise, except when it is 2 bets to call and we have not already called a bet this round. Finally, with EHS' < 0.50 we consider the strategies of semi-bluffing, pot odds and showdown odds (instead of resorting to Make0 as in Figure 6.2). These thresholds are an ad hoc but reasonable way to decide when to bet based on strength.

Figure 6.2: Simple Betting Strategy
% latex2html id marker 2093\footnotesize {\tt\begin{tabbing}
... \\
\>else \\
\>\>return Make(0,state) \\
\end{tabbing}} %tt

The lack of the ability to raise beyond two bets after the flop is a historical artifact, although not likely to be very limiting. Of course it must be addressed eventually, but it is a low priority function and hopefully will be superseded by a more general betting strategy.

next up previous contents
Next: 6.4 Semi-Bluffing Up: 6. Betting Strategy Previous: 6.2 Basic Post-Flop Betting   Contents
Denis Papp