Note, incidentally, that GIB's performance is still less than perfect on these problems.

The reason is that GIB's sample may be skewed in some way, or that SWO may fail to find a global optimum among the set of possible achievable sets.

## 8. Conclusion 8.1  Gib Compared

Other programs  GIB participated in both the 1998 and the 2000 World Computer Bridge Championships. (There was no 1999 event.) Play was organized with each machine playing two hands and the competitors being trusted not to cheat by "peeking" at partner's cards or those of the opponents. 19 Each tournament began with a complete round robin among the programs, with the top four programs continuing to a knockout phase. The matches in the round robin were quite short, and it was expected that bridge's stochastic element would keep any program from being completely dominant.

While this may have been true in theory, in practice GIB dominated both round robins, winning all of its matches in 1998 and all but one in 2000. The round robin results from the 2000 event were as follows: 20

| GIB        | W B   | MICRO   | BUFF   | Q- PLUS   | C HIP   | BARON   | M' LARK   Total   |    |    |
|------------|-------|---------|--------|-----------|---------|---------|-------------------|----|----|
| GI B       | 14    | 11      | 16     | 19        | 16      | 17      | 100               |    |    |
| W BRIDGE   | 6     | i       | 19     | 13        | 16      | 7       | 18                | 20 | 99 |
| MI CRO     | g     | 1       | 18     | 15        | 15      | 13      | 20                | 91 |    |
| l          |       |         |        |           |         |         |                   |    |    |
| BUFF       | 4     | 7       | 2      | -         | 12      | 20      |                   | 20 | 70 |
| O- PLUS    | 13    | 4       | 5      | 8         | 11      | 14      | 11                | 66 |    |
| l          |       |         |        |           |         |         |                   |    |    |
| BLUE CHIP  | 1     | 13      | 5      | 0         | g       | 11      | 20                | 59 |    |
| l          |       |         |        |           |         |         |                   |    |    |
| BARON      | 4     | 2       | 7      | 15        | 6       | g       | l                 | 14 | 57 |
| MEADOWLARK |       | 0       | 0      | g         | 0       | 6       | 18                |    |    |
| 0          |       |         |        |           |         |         |                   |    |    |

Each match was converted first to IMPs and then to victory points, or VPs, with the two competing programs sharing the 20 VPs available in each match. The first entry in the above table indicates that GIB beat WBRIDGE by 14 VPs to 6; the fourth that GIB lost to Q-PLUS BRIDGE by 7 VPs to 13. (This is GIB's only loss ever to another program in tournament play.)
In the 1998 knockout phase, GIB beat Bridge Baron in the semifinals by 84 IMPs over 48 deals. Had the programs been evenly matched, the IMP difference could be expected to be normally distributed, and the observed 84 IMP difference would be a 2.2 standard deviation