In practice, hand strength alone is insufficient to assess the quality of a hand. Hand potential assesses the probability of the hand improving (or being overtaken) as additional community cards appear. Consider the hand 8-7 with a flop of 9-6-2. The probability of having the strongest hand is very low, even against one random opponent (11.5%). On the other hand, there is tremendous potential for improvement. With two cards yet to come, any , 10, or 5 will give us a flush or a straight. Hence there is a high probability that this hand will improve substantially in strength, so the hand has a lot of value. We need to be aware of how the potential affects hand strength.

This example describes positive potential (*PPOT*): the probability
of pulling ahead when we are behind. We can also compute the
negative potential (*NPOT*): the probability of falling
behind given we are ahead. Both of these can be computed by
enumeration in real-time.
We have 1,081 possible subcases (opposing hands for which
we have weights) on the flop and 990 on the turn.
For each subcase we can either do a two card look-ahead
(consider the 990 combinations of the next two cards
on the flop) or a one card look-ahead (45 cards on the flop
and 44 on the turn).
For each subcase we count how many combinations of upcoming cards
result in us being ahead, behind or tied.
The total number of cases to be considered is:

*PPOT*_{2}and*NPOT*_{2}(two card look-ahead on the flop): 1,070,190*PPOT*_{1}and*NPOT*_{1}(one card look-ahead): 48,645 on the flop and 43,560 on the turn

The potential for A-Q/3-4-J
with
uniform weighting is shown in Table 5.1. The table shows what
the result would be after seven cards,
for cases where we are ahead, tied or behind after five cards.
For example, if we did not have the
best hand after five cards, then there are 91,981 combinations of cards
(pre-flop and two cards to come) for the opponents that will give
us the best hand. Of the remaining hands, 1,036 will leave us tied
with the best hand, and 346,543 will leave us behind. In other words,
if we are behind we have roughly a
*PPOT*_{2} = 21% chance of
winning against one opponent in a showdown.
Additionally, if we are currently ahead and that opponent
plays to the showdown, we have roughly a
*NPOT*_{2} = 27% chance of
losing.

If *T*_{row,col} refers to the values in the table (for brevity
we use B, T, A, and S for Behind, Tied, Ahead, and Sum) then *PPOT*_{2} and
*NPOT*_{2} are calculated by:

Figure 5.2 describes the algorithm for two card look-ahead
from the flop. The parameter *w* is, as for Figure
5.1, for the weight array of the opponent
(opponent modeling is discussed later), and can simply be a uniform
set of weights.
The ** HandStrength** calculation is easily embedded
within this function, and the one card look-ahead function ** HandPotential1**
is essentially the same as ** HandPotential2**.
In this function, the inner loop is executed
times and so the
*Rank* function is called

times. However, there are many redundant calculations. There are only possible unique calls in the inner loop to

calls to

calls to

on the flop (17,251 on the turn).

In Table 5.1 we compute the
potential based on two additional cards and it produces

(5.7) |

(5.8) |