Posted 2014-December-10, 16:12
What I'm trying to explain is that because your expectation is > 50% already, your system has to do better than better than that to beat "play down the middle". You can, in fact, lose in the long run with a high variance, above average expectation system - if you're sufficiently above average expectation already.
It's a standard matchpoint decision:
- What is the chance that X is right over where you are now, and
- What is the expected win if you're right, vs the expected loss if you're wrong.
Throw away all the "doesn't matters" hands.
Here, the expected win from getting to the right contract, played the right way, giving the opponents different information that helps rather than hinders you, is <50% (not quite 100% - 50+%). The expected loss from getting to the right contract (that happens to be wrong this time), or played the right way (which happens to be wrong this time), or in the process giving the opponents information that helps them - is >50% (not quite 0% - 50+%). Sure, you get more smaller wins than your larger losses (or you wouldn't be in the right spot), but is it enough to get to what you'd get by playing down the middle? Note that in addition to those, there will be hands where you're forced into the wrong contract by system (because more often than not your system gets you to the righter contract, but this is one of the other hands), which will also win sometimes (< 50% of the time, for + <50% of the MPs) and lose sometimes (> 50% of the time, for - >50% of the MPs). Your card play advantage will eat into the losses and add to the gains, as will others that field-protect for you, but not enough to even balance that, never mind get it to 60-when-you're-right, 40-when-you're-wrong.
For me, the 50% cardplayer (shhh), it's a totally different question. If my system is 60% on the field, then I get 60% over the year. It'll be a bit pajama, and the variance will be high, but it will be well to my advantage. In addition, because I'm presenting the good card players with problems that a) the rest aren't getting, and b) they're not as familiar with as either I am, or as they are with "normal", they're likely not going to be as good card players as the usually are. That's not worth much (certainly not as much as the "they only play this to confuse us with their unfamiliar systems" people believe), but it is worth something.
Or as I said to the highest masterpoint holder in our unit, when he asked "but [EHAA] totally randomizes the results. Why would you want to do that?": "Say I flip a coin twice for all the matchpoints on these two boards; my expectation is 50%. Tell me that's less than what I would expect against you playing straight."
Question, just for the amusement:
You know that 6♣ is mildly odds-on (say, it's "9 without the Q" and some chances, so 55, 56%). You also know that the field, because of their system, is never going to even sniff at it - they'll all be in 3NT, which should be close to 100%. Do you bid it?
Now I tell you that you are a seeded pair in a field of 75 tables in a city where the sectionals draw 45, including a few from out of town. Still bidding it? Or are you going to bid 3NT with the rest of the room, knowing you'll take all the tricks and be solidly A+?
Does it make a difference if I tell you that while top on most boards is 50, this board is only going to be played at 16 tables, and your score is going to be factored from a 15 top to 50?
Does it make a difference if I tell you that the auction's at 3♥ now, and you could still be off two fast tricks in a suit (but the slam's about 75% if you're not), and if you try to find out, you'll lose the chance to play 3NT (and will sit in 5♣ for a clear, if potentially shared, bottom)?
These are the boards that are wins for your "better system"! And I know this all too well, having played Precision with 14-16 NTs and lots-a-gadgets for many years. These were the boards that greyed my hair - "I know this contract is better, but is it better enough to take the zero if this time it's wrong?"
[Edit: Aaaaand, while I'm typing, akwoo says what I am saying in a third the verbiage with double the comprehension.]
When I go to sea, don't fear for me, Fear For The Storm -- Birdie and the Swansong (tSCoSI)