The Neuberg Formula - Introduction

Article by Max Bavin
Chief Tournament Director

Consider the following situation. The last table to finish play for the evening are just about to start their final board. Everyone else has finished, and the scoring has been completed save for the final board.

Pair 'X' currently have a top on the final board - but there is still one result to come.

What do you think the chances are that Pair 'X' will still have a top once the last table have finished?

Well, there are three possibilities. Let us say that it is an 11-table complete movement, so a top on a board is 20 match-points.

The three possibilities are:-

	the final table will beat pair 'X's result, so pair 'X' will score only 18 points out of 20.
	The final table will get the same result, so pair 'X' will score 19 points.
	The final table will get a worse result, so pair 'X' will indeed score their complete top and get 20 points.

So, if all three outcomes are equally likely, pair 'X' would have a normal expectancy of 19 points out of 20 in such a situation (the average of 18, 19 and 20).

However, demonstrably not all three outcomes are equally likely. After all, pair 'X' have already beaten 9 out of 9 other results, so it must be heavily odds-on that they will beat the 10 th and final result as well - not certain, but very likely.

So, their normal expectancy in such a situation must be closer to 20 points than it is to 19. We will return to this question later.