Until enough data has been accumulated for a category (20 points,
this value was selected arbitrarily),
we weight the frequencies with hard-coded
defaults^{7.1}*d*[*c*][*a*], and mix the observed frequencies with the defaults,
using linear interpolation:

(7.3) |

However, each player will play the earlier rounds more
than the later rounds (* i.e.* more pre-flops than flops, and so on).
Assuming that a player's style does not change drastically between rounds,
we can take advantage of data gathered in prior rounds and
use only one set of defaults and a recursive definition
of frequency. To this end, we must first adjust the notation to
consider the round. Given that the definition for the category *c* is composed
of a round *r* and number of bets to call *b*, we can also define *c* as
(*r*,*b*) where *r*=0 for the pre-flop. Now we can recursively
define the new frequency function *f*'' based on the reduced
set of defaults *d*'[*b*][*a*]:

An alternative approach would have been to use * Loki*'s own frequencies as the
default behavior for opponents, however the majority of human players on
IRC were observed to play much looser than * Loki*. The default
frequencies were therefore based on a typical IRC player (and
do not involve any additional computation).