Hi Dear Mr. Wolff
Very instructive hand with the theme of elopement which would gladden Ottlik
Regards
AVRR
PS : kindly see my post pertaining to yesterday’s deal (posted belatedly few minutes back)

Hi AVRR,

Obviously, if one player who plays bridge all his life for at least 50 years he may or may not see one actual bridge elopement, although the theory of such lends itself to the beauty of our great game.

And besides one can only dream of making a small slam while both opponents get to take the last trick.

Add to the pleasure, by playing it against one’s worst enemy.

Hi Bobby,

Sorry to be slow and responding to yesterday’s hand, but I am still struggling with the logic.

With 4 outstanding heart cards, there are 16 possible heart suits on either side (including the void). If we look at what East could have after the ten (from West) Ace and 8 have been played, those 16 hands whittle down to just 2 possibilities AJ8 and A8. A8 is the only doubleton -because East has played both cards, and of the 4 tripletons possible, we have to remove the 3 possible tripletons that have a 10. This leaves West with two options, 10 singleton, or J-10 doubleton.

At the moment of truth, West has one more card than East – who is more likely to have a specific card?

Ginny: Without going into all of the possibilities, what you are forgetting is that W is forced to play the 10 if that’s his only heart, but if he has J10 he will presumably play the 10 half the time and the J half the time. 50% of the time the suit will break 3-1 and 40% 2-2, but only half of the time when it is 2-2 with W holding J10 will he play the 10. And yes at the critical point, W is known to have one more unknown card than E, but that adds very little to the chance that playing W for the J10 is the right line of play. I believe our host stated almost all of this in better language than my poor effort, but perhaps this different language will help in understanding this very important principle.

Hi Ginny,

You do have a convincing argument, but so did Terrence Reese, when he outlined what has become to be known as restrictive choice.

Wherein when one chooses from equals (J10) one or the other, since he plays one of them it tends to show he is more likely not to have the other one, and although that theory was at first rather severely argued against (for similar reasons to the ones you gave), but, for my experience now for many years, perhaps 50+, the results, and I individually can, at least say, that it is not delusional, but that it seems absolutely clear cut and thus without doubt that he is as right as anyone can be.
IOW, it works and in NT.
The similar circumstance though if it occurs that when a player can have an extra card such as J108 and falsecards an honor the restrictive choice law does not apply, since that extra card takes the forced nature of a singleton play away from the options available.

Hi again Ginny,

However I should have further said, for the opening lead of the 10 of hearts, it does not apply since although the jack is an equal, the opening lead is normally conventional, but subject to deception, while in mere course of the play, where everyone knows they are equal and partner is not to be considered, the jack may well be held with the 10, but at the time, (and in this case the ten may, in itself, cost a trick) only the declarer’s choice later would insure the result, fooling partner would not matter.

Hi David,

I, of course, did not see your post until now.

Thanks for your strictly on point discussion which, at least to me, is the most accurate description of the sometimes difficult to understand but critical knowledge, necessary for the aspiring player to both understand and, then and most importantly, practice.

Gentlemen,
I can see what you say as bridge logic and when I went through my spreadsheet as West, I was left with multiple open slots where Bridge Logic alone allows for multiple options – before the play of the 8 of hearts. However, once the 8 of hearts is played, EAST must have started with AJ8 or A8. There are no other options.

If West had played the Jack on the first trick, the same possibilities hold. EAST must have started with the A,10,8 or A,8.

Because we can whittle both hands down, due to the highly limited quantity of cards, we can reduce the choices completely. At crunch time, there is one heart card left and East has 1 less chance to have it than West.

If we take the thinking further, we destroy the idea of playing for the drop with 9 cards in a suit if the ten is played and the jack is still out?

Lastly, if West has just the Jack, he would be forced to play the jack on the first heart trick. If he had the Jack, Ten, he would play the Jack 50% of the time.

Hi Ginny,

I, for at least one, do appreciate your determination to get your logical point across about, when East follows (with the eight) West has more room in his hand for the key card, either the jack or the ten, depending on whether West played the other one.

At least what I have believed for all these years, this theory, Restricted Choice, transcends arithmetical statistics into restricted choices and since whatever honor West played originally makes the finesse coming back about a 2 to 1 favorite simply because West didn’t play it (the human element) on the first round.

In some ways but not all, the reasoning might be similar to, on this hand, if and when a good player on lead chooses the 10 of hearts for his lead, it almost seems automatic for the declarer to play the honor from dummy in case the lead is either from 10x or a singleton 10, but experience will tell the declarer that no good player on the auction given would ever lead a singleton 10 of trump, because of the unnecessary risk that the defense, having to play 1st and 3rd instead of the cat bird 2nd and 4th all bridge players seek. Therefore, at least to me, I have learned, early on, the hard way (wondering why I was out thought).

Of course, on this hand it is quite different, but humanity does enter into it, the choice by a random very good player to play either the jack or the ten, by TR’s innate arithmetical genius, he is unlikely to the tune of 2 to 1 to possess the other same strength honor.

So Ginny, I am just one in many who can explain how I view it, and no where near the one another to choose to explain, but I can give a valid testimonial that, if you play enough hands (unlikely) but now keep a running total of how often it works, you will be surprised with your success by what David and I have tried to explain.

I do suggest that if you have a mathematical guru to turn to and in addition, he can understand the playing of cards and other casino type arithmetic, let us know, if you have time, what you heard.

Again thanks for your concern and since I think in the next couple of hundred years, (it is possible some of us will not still be around) science will concentrate on the human brain and will find that, of all our working organs, it has been the least one to reach anywhere near its full potential, at least up to 2018.

Finally a commercial: Since bridge, particularly the high level kind, should be taught in our schools, which they already do, subject to rave reviews by the students, teachers and believe it or not, the parents of the students, in 11 European countries and all of China (200 million students there).

But in spite of that suggestion our parent organization, ACBL, is not interested in trying to promote such a thing and convince the US Educational department just how valuable it can be.

Good luck and do not be a stranger to our site.

Thanks Ginny for your points. I have myself
been uneasy with “restrictive choice”. West has to play something, and when he (in a gender neutral fashion) does, it tells you what he had, not what he didn’t have, except if that inference can be made by other means. Yesterday Iain, an outstanding bridge logician, compared this to the “Monty Hall” problem, but the way I see it, this bridge example is a different sort of problem-I would like to hear more from him, or Bobby, or someone who can explain it more convincingly. My own personal experience (more limited than most) is that it doesn’t seem to work; or maybe that’s just recall bias. On the other hand, restricted choice as a concept is an important one, and an example of a lesson that would be investigated if bridge were thought in schools-we are behind you on this one!

Joe,
let’s say there are 100 such deals and 50 times it’s 1-3 with Ten singleton and 50 are 2-2 with Jack-Ten doubleton. So the Ten will have to appear on the first round in all the 50 deals that are 1-3, whereas you may expect the Jack on the first round in 25 of the doubleton cases. Hence, of the 75 occasions where the Ten appears, 50 represent a singleton. When you see the Ten come out, the likelihood it’s a singleton is two-thirds

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