As described in Section 5.2.1, * Loki*
makes use of a * field array* provided by the opponent modeling
module which is representative of the entire set of active opponents.
Unlike hand strength,
against multiple (two or more) opponents the *PPOT* and *NPOT*
values calculated with the * field array* are used without adjustment.
The correct calculation would be similar to
the one described in Section 5.2.1 (accounting
for each player adds an extra
iteration layer of approximately 1,000 subcases),
but, for potential, the value against one player is believed to
be a simple but reasonable estimate (high usefulness and low
computational complexity).

Calculating potential in the context of multiple opponents is complex due to
the many interactions; there is no easy reduction
to an approximate value similar to *HS*_{n}.
However, it is likely that the present estimates are typically optimistic
and the correct value would worsen with additional opponents.
For example, consider the situation where you have a straight draw
(4-5/6-3-T)
but you are unaware of any tendencies
of your opponents (* i.e.* uniform weight arrays). Each additional
opponent increases the chances that someone has a flush draw in hearts
(in fact, it increases the chances of any particular hand occurring).
This means that `intersection cards' like 2
and 7
are
worth less to you since the likelihood that they give you
the winning hand decreases, as does *PPOT*.
For another example, consider that you hold top pair
(K-T/6-3-T). Each additional opponent increases the
chance that you are up against a flush or straight draw so cards
like a 2, a 7 or a heart are more likely to give you a losing hand.
Therefore, *NPOT* increases with additional opponents.

But over-optimism is not always the case; multiple opponents can improve
your chances.
For example, if you have a straight draw with small
cards (4-5/6-3-K)
and your opponents are likely holding high
cards, then each additional opponent increases the chance that
the upcoming card is not high.
This will overall both decrease *NPOT* and increase *PPOT*, although
additional players also increases the size of the pot, which
increases the value of our draw.

These are only rough examples intended to demonstrate the complex interactions involved in multi-player considerations for hand potential. The actual effect of each additional opponent is dependent on the probability distribution of possible hands and its relationship to the probability distributions of the other players, as well as its relationship to your needed cards.