Restricted Choice Pt 2
Since my readers have anticipated the mathematics that were going to be Part 2 of this piece, I’m going to redirect the discussion a little. As Bob and Colin pointed out to me, in Frank’s scenario it is actually correct to play for the drop. Had he seen the jack, he would have been 100% to finesse.
So overall, the opponents’ agreement to do something non-random has actually hurt them, and in the long run Frank will have better than 1.84:1 odds when he has to play this combination against them.
But now we get into murkier waters. What if they don’t quite always play the queen from the doubleton queen-jack? Now we’re almost into Game Theory, and the analysis is certainly beyond me…
And as Ulrich asks, can they have this agreement — that they will play the queen 100% of the time except occasionally they won’t? Let me digress for a moment, since I’m reminded of two situations from my bridge past. In the first, we were told by the opponents that their carding was random — no signals or discards meant anything. The director, when summoned, informed them that this was an illegal agreement (obviously it’s very easy to cheat!) but it’s not clear to me how that ruling can be enforced.
The second case was closer to the Frank Vine story. Linda and I were playing in the World Mixed Teams in Rhodes a few years ago, and we sat down against an Irish pair with very complex pre-announced carding and opening lead methods. It took several minutes explanation before we felt we understood their agreements. Then on the first board, they made an opening lead that didn’t follow those agreements!
We all have some familiarity with the rules about psychic bidding. The danger is that partnerships become aware of their own tendencies, and are more prepared for psyches than their opponents. The same psyches repeated too often become partnership agreements, and are frowned upon (at least in the ACBL), since now the pair is basically playing ‘controlled psyches’. Some years ago, playing against a pair known to psyche frequently, I sat down and was presented by them with a list of ‘things we have tended to do in the past’. ‘Ah,’ I said, ‘ so I can assume that you won’t do any of those in this set.’ But of course they did, and we ended up in a committee, and things went down a rathole from there.
However, I’m not sure I’ve ever seen much discussion of psychic carding. Certainly, books on defense talk about falsecarding as a perfectly legitimate tactic, especially in situations where it doesn’t matter whether you deceive partner. I remember years ago as declarer trying to get a count on a hand to find a queen, and watching Fred Gitelman on my left carefully signal to show three cards in a suit. Was he giving his partner true count, or playing head games with me? I went for the latter, and I was right :-) Fair enough, and definitely part of the game as far as I’m concerned. But to me, having a specific unusual carding agreement and then deliberately violating it crosses a line. It’s analogous to psyching a conventional bid, which is illegal.
Linda’s comment is interesting here — in these days of voluminous play records, it should be easy to gather stats on what card people play from QJ doubleton, but I would guess with her that the queen is played significantly more than 50% of the time. And because of that, I confess that I myself tend to play the jack from that holding (don’t know whether she’s ever noticed that…).
Finally, a piece of advice from a very wise lady, Mary Paul, who has won both the Open and Women’s Canadian team titles, and played in many world championships. Mary once told us that if you’re in a slam and someone leads the jack of trumps, they always have the queen-jack doubleton. No-one ever leads the stiff trump jack against a slam, and they never lead the queen from the doubleton either. That’s one we’ve watched out for, and trust me, Mary’s absolutely right.
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I don’t think it’s illegal to psych a conventional bid. The ACBL does bar psychs of certain calls (strong, forcing, artificial 2C, or conventional responses to conventional openings) but that’s just zonal regulation of conventions, not illegal agreements according to the laws of contract bridge.
ACBL does bar psychs of conventional bids – contract bridge rules say nothing other than to permit a player to make a psychic call “provided that such call is not based upon a partnership understanding.
The WBF basically says that psyches are completely okay as long as there is full disclosure to the opponents about any and all tendencies and that insufficient disclosure is illegal:
http://www.worldbridge.org/departments/systems/psyches.asp
The interesting side of this is the game theory – if I get a chance I’ll try to talk about it a little.
There are some interesting pieces to the story here:
First – why did LHO feel that it was extremely important (in the middle of playing a hand) to point out their carding agreement?
For the less ethical amongst us that makes the play easy – you have a 100% two way shot. You play for the drop and if RHO shows out you get the committee to reverse it based on the fact that LHO went out of his way to make you play the wrong line.
——
From the mathematical side:
With odds are now 6.78 : 6.22 (approximately 1.1 : 1) – in order words 52% to 48% or 4% better to play for the drop.
If 8.5% of the time he psychs and plays the J (17 / 200) times or *not very often*) the odds now change in favor of the drop.
So now you are in to how often is *not very often*?
If you want to look at the game theory of these positions, these are mixed-strategy Nash Equilibria.
The action set of the players is finite (play the Q from QJ, play the J from QJ) so the set of strategies is compact (play the Q from QJ some percentage of the time) and there will always be at least one mixed-strategy equilibrium
Carding agreements are one thing, but following suit preceding declarer’s critical guess is another. I might be missing something, which unfortunately is quite likely, but leading the J from QJ doubleton, what Terrence Reese used to refer to as “the old chestnut”, is just one example of what are many poker elements in bridge.
If someone would call me over officially and ask, “May I do this or that while defending a game or slam (or even part score)”, the answer is an unqualified yes, assuming that what is done is not necessarily known by partner and not alerted. If a defender does lead a conventional something or other, the only responsibility that his partner has — is to, in a relatively low key way, explain that we do conventionally lead the Q from QJ (or the opposite) but since partner is not involved in having to know which — the leader can do whatever he wants. Of course, in my sponsor days I once led the Jack of trumps from QJ doubleton and my partner, “Yes Miriam” followed with her K from Kxx, saying proudly to me later that “Bobby weren’t you proud of me for not finessing you”.
As a final note, I will add that when poison gas labs are used by some notoriously very good players, your subject might come up, but my guess is that their discussion would only be the emphasis put on the answer, assuming they are playing against really novice players. For example with the jack led, the answer may be “Oh yes we definitely deny the queen with our jack lead and found that discipline has worked very well for us”. Of course, we are talking about bridge in the very poor levels and is probably not worth discussing. It is just an example of those who do not miss an opportunity to better their scores. Following through and possibly to the quick, going back some years to my being in appeals meeting control, if opponents would bring these culprits before a committee, they would be subject to a suspension, but as far as I know — that situation has never occurred.
In summation, psychic carding usually is not subject to scrutiny, but I suppose it could be exposed if used to “shoot fish in a barrel.”