This is a hand from my 1987 World Championship test which gives a good
illustration of how COBRA thinks and bids.

It also illustrates the complexity of COBRA's precise rules.  The
computer will almost certainly reach the slam, although I'm not sure
whether I have the final auction right.

Board 25: North dealer, E-W vulnerable.

        K
        AT4
        AT87432
        93
92              J843
J7652           KQ
5               Q96
KQT42           J765
        AQT765
        983
        KJ
        A8

The humans were in 3NT down two, 4S down one on a heart lead, 4S making
on a club lead, and 5D making.  

COBRA's auction:

W   N   E   S
    1D  P   1S
P   3D  P   4C
X   4H  P   4S
P   6D

6D is a good contract, but it goes down on a club lead with the bad
splits.  

North has 11 HCP
+7 for diamonds three cards beyond minimum biddability
+1 for four aces and tens
-1 for stiff king
=18 points.

South has 14 HCP
+4 for spades two cards beyond minimum biddability
+3/4 for three aces and tens
-1 for KJ alone
=17-3/4, round up to 18 points.

North opens 1D, showing 13 or more points.  (1C requires 14 HCP as well
as 18 points.)

South gains two points for two honors not in a solid top sequence in
partner's bid suit, making 20, and bids 1S.

North gains one point for king in partner's bid suit, but loses one for
singleton in partner's bid suit.  He bids 3D, showing a hand 3-5 points
above minimum (16-18) and rebiddable diamonds.

South now knows there is a diamond fit; KJ is adequate support for a
rebiddable suit.  He gains no points for ruffing value because his trump
length is the same as his shortest side suit.  He gains an extra half
point for each ace and loses a half point for each queen or jack outside
trumps, for a net gain of 1/2.  This raises his hand value to 20-1/2,
rounded down to 20.  (The fractions which were rounded earlier were lost.)

South then deducts three points because he is considering a slam try in
a suit and his hand has no singleton or void.  This leaves him with 17,
still enough for a possible slam (34 points are required); thus he
cannot rebid 3S, which is not forcing.  He bids 4C, showing first-round
control in clubs, agreeing diamonds as trumps, and making a mild slam
invitation.  (Partner is not required to cue-bid in response to a mild
slam invitation.)

West doubles; the human Wests all doubled club bids when given the
chance.

North now knows about the diamond fit.  He does not gain any points for
ruffing values because he is not dummy, but he gains 1-1/2 for two aces
and the ten of trumps, and one point for one honor not part of a solid
top sequence in a suit partner has (implicitly) raised.  With 20-1/2
points, rounded down to 20, he accepts the slam invitation and bids 4H,
also a cue-bid and mild slam invitation.

South could now bid 6D, but I believe he bids 4S, showing rebiddable
spades.  He can insist on slam, but 6S may be the correct slam.  (A
grand is theoretically possible, but Kx Axx AQxxxx xx is the only hand
consistent with North's bidding on which it is a good contract.  Adding
even another ten would make the hand too strong for North's 3D rebid.)

North has nothing further to show, but he does have extra values, so he
rebids 6D.