An article from the April edition of ECU E-Magazine: “The confusing case of the “virtual opponent” by Tania Karali.

The current lockdown, however unfortunate it is, could be an opportunity to revise some chess and/or tournament rules.

In chess tournaments, it is often that unplayed games cause various irregularities. These may include a player waiting for his opponent who is not coming, non fulfillment of title norms, alteration of tie-breaks and, thus, prize giving etc. In an effort to minimize these consequences, the FIDE Handbook indicates how to deal with each case. In round-robin tournaments, for example, handling of the situation depends on whether the player who forfeited has already completed 50% of the total rounds. In this article, we will focus on swiss tournaments and the tie-breaks where the **“virtual opponent”** comes into play. These tie-breaks are Buchholz (sum of the scores of each of the opponents of the player) and Sobbeborn-Berger (sum of the scores of each of the opponents of the player multiplied by the player’s result against each opponent). For the sake of clarity, we will only refer to Buchholz. Calculating the “virtual opponent”’s score for Sonneborn-Berger is a very similar process.

(Note: The virtual opponent may also apply in the Progressive Score tie-break, but FIDE no longer advises using it, so it will not be discussed.)

First of all, let’s take a look at the relevant articles of the FIDE Handbook:

Art. C.02 13.15.2: For tie-break purposes a player who has no opponent will be considered as having played against a virtual opponent who has the same number of points at the beginning of the round and who draws in all the following rounds. For the round itself the result by forfeit will be considered as a normal result.

This gives the formula:

**Svon = SPR + (1 – SfPR) + 0.5 * (n – R)**

where for player P who did not play in round R:**n** = number of completed rounds**Svon** = score of virtual opponent after round n**SPR** = score of P before round R**SfPR** = forfeit score of P in round R

Art. C.02 13.15.3: For tie-break purposes all unplayed games in which players are indirectly involved (results by forfeit of opponents) are considered to have been drawn.

In our first example, player X did not show up for the first round of a 7-round tournament and was, eventually, excluded from the remaining rounds. Player A is the opponent who got stood up. After 7 rounds, player A has a Buchholz tie-break of 28.5 points from the opponents who were not involved in unplayed games. But what will his Buchholz score be for the first round? 0 points? No, that would be totally unfair. For the first round, we will consider that player A was paired against a “virtual opponent”. This “virtual opponent” had 0 points before the tournament started and made a draw in all the remaining rounds (apart from the first one where he forfeited). So, after 7 rounds his score would be 3 points. Indeed, according to the formula,

**Svon = 0 + (1 –
1) + 0.5 * (7 – 1) = 3**

so player A’s total Buchholz score is 28.5 + 3 = 31.5 points.

In our second example, we will consider player B who played against player A in the second round. At the end of the tournament, the sum of player B’s opponents is 26.5. Will this be his Buchholz score? No, because one of his opponents (player A) has an unplayed game, which is now considered as a draw (Art. C.02 13.15.3). Thus, player B’s Buchholz score is 26 points.

In our final example, player C started with a score of 3/3, did not play in the fourth round, but played all the remaining rounds. His score from his actual opponents is 25.5. The score of his “virtual opponent” in the fourth round is

**Svon = 3 + (1 –
0) + 0.5 * (7 – 4) = 5.5**

so his Buchholz score is 25.5 + 5.5 = 31.

Hopefully, this article has helped in shedding some light on this confusing topic. A more detailed presentation, written by IA Prof. R Anatharam, can be found on the FIDE website: