Try this Argument!
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Try this Argument!

by John Probst, London, England UK


Editor's note:

This article arose out of an email correspondence involving Max Bavin, EBU Chief Tournament Director, Hermand De Wael of Belgium, David Martin, John Probst and David Stevenson of England

Note that there is another article also following from this correspondence.

Max Bavin wrote
If you arrow-switch 1/4 of the boards, you will be comparing with all the other pairs an equal number of times (actually, you have to make it more than 1/4, because some of the switches will cancel each other out: hence Herman's figure of 1/3).

If this were an all-play-all competition, this would be ideal and we'd all be in total agreement. However, it isn't an all-play all competition.

The point is that we don't actually want equal comparisons (as distinct from equal balance) when it's not an all-play all event.

Some pairs don't play against each other. As compensation for this, we want them to have to compare scores more frequently with one another.

So, in a Mitchell movement, we don't want to switch 1/4 (or 1/3) of the boards - it needs to be something less than this in order that the pairs who dont play each other (i.e. the ones sitting in the same line) compare scores quite frequently.

Herman De Wael wrote
I understand this, but I would like to receive some indication that this is the huge difference between 1/3 and 1/8. Please David ?


This is the difference Herman. Let's have one more go. Sit me NS at table 1 in a line of geriatric LOLs, and have an average line sitting EW. generally speaking I'm going to get a top on every board I play in the same direction as the LOLs. In fact I'm going to have 56 comparisons and I'll score 7 on each board (ACBL scoring) over 8 boards for 56 match points in a normal Mitchell. The LOLs are all going to tie with each other and will score 3/7 on each board for a total of 24/56. In effect my action against the geriatrics is 56-24 = 32 matchpoints.

The important thing to note is I can't do anything about the matchpoints they did score because I didn't actually get to rip them to shreds. In fact those 24 matchpoints can only represent my interest against the EW pairs. (YES ITS THAT MUCH) and is represented by my head-to-head with each of the EW pairs in turn.

When we arrow switch, then I arrow switch a board and so do all the LOL's. Their arrow switching costs me because they promptly get a top for their opponents against me. Suddenly, just because they have switched I'm scoring 6/7 on all 7 of the boards I played the normal way round. In other words the LOLs have ganged up a whole board against me.

Not only that, on the board I arrow switched I whack out a huge score and the damned geriatrics get another matchpoint they didn't deserve. I've just lost another 7 matchpoints off my score, against them.

So there I was with 32 matchpoints of action against them and the bloody arrow switch has cost me near enough half my edge over them (ie 14 points). Indeed if you arrow switch another round I'm going to lose another 12 match points to them and they'll be close to beating me.

Of course the EW players are grateful for the arrow switch because they benefit by gaining a point off me when the LOLs give them their top, and the board I switch on gives them another sodding matchpoint. In fact the other line grabs the sodding 14 matchpoints and the LOLs have just stuffed me for another 14 against EW.

The nett effect of that is I've been stuffed 25% by the LOLs (which is just a straight forward loss compared to EW who had no part in it at all) and another 25% by the other line grabbing another 14 points which is another 25%. All in all my nett loss against the other line is HALF my action. (1/4 from the LOLs and 1/4 from the other line).

So my 56 comparisons are divided into 42 favourable comparisons and 14 which are negatively biased against me. Which means nett I only get half the action I used to have against the geriatric LOLs, and the other half of the action is now with EW.

Stick with 1 in 8 Herman - it works. Otherwise check on Probst's rule for imperfect arrow-switching and employ it. Your score will go up by about 4%.


Gopher Editor's note:

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