[Echognome]

I used to be an academic, so this conversation pained me. I entitle it "Principle of Restricted Mathematics."

I was kibitzing the following hand on BBO:

Scoring: IMP

1♣(16+) - 1♥(8-11 any)
1NT - 2♠(ask)
3♣(max) - 4♦
4♠ - 5♣
5♦ - 5NT
All Pass

---

T1: ♠4 - 7 - 6 - 8
T2: ♦A - 7 - 5 - 3
T3: ♣5 - 2 - K - 4
T4: ♦J - 4 - ?

So a conversation began about finesse versus drop. And someone made a comment about the inferred spade length affecting the odds so I looked up the odds on Richard Pavlicek's website and posted them assumed 8 and 10 vacant spaces. (Actually if we infer 5-3 spades, that's not quite right, but an aside). One of the kibitzers claimed that Q7 dub was 25% so the finesse was obvious. I said that the assertion was wrong and a bit of an argument broke out, but didn't last.

Anyway, here are some excerpts of the conversation that followed in private...

Kibitzer - "you're missing the Q, 7, 4 and 3 in a suit... if W plays the 7 under the A, then it's only 25% he now holds the queen, regardless of spade length"

Gnome - "suppose west had opened 3♠. you don't think that would change the odds?"

Kibitzer - "of course it does... that would make a first round finesse a possibility... but you still deny looking at the spots played and the spots you're looking at as declarer"

Gnome - "i don't think they are as relevant as you do. if trick 1 went 3 and 4 from both hands you think it'd be different from 3 and 7? from 4 and 7?"

Kibitzer - "if, as the west hand, you played the 3 or 4, then it's a case of deciding from bidding... spots on the dummy were JT98... the 7 by west dictates one of two holdings, unless showing himself a doubleton.... Q7 or stiff 7... there is only a 25% chance that the 7 can be from Q7 doub..."

Gnome - "the 7 can be from Q7 or stiff 7. that's all we know by the point of the decision. you are saying that you think stiff 7 is 3 times more likely than Q7. i simply think that's wrong"

Kibitzer - "it has been proven mathematically, and not by me, I might add, that I'm right... you're more than welcome to test it yourself... have you never heard of the Rule Of Restricted Choice?"

Gnome - "i think you're misapplying it and you are also not accounting for vacant spaces at all"

Kibitzer - "YOU do the math... prove me wrong... I'll tell EVERYONE you're right"

Gnome - "ok. Q7 is a sixth of the 2-2 breaks (40/6 = 6.67%) and stiff 7 is a quarter of the 3-1 breaks onsied (25/4 = 6.25%)"

Kibitzer - "WRONG,... he laid down an honor first"

Gnome - "this is not accounting for spaces"

Kibitzer - "YOU are not account for spaces... there are only 4"

Gnome - "vacant spaces from OTHER suits!"

Kibitzer - "oh Christ almighty... you have 9 cards in a suit... no opp's bidding... figure the odds... HONESTLY"

Gnome - "point number 1, i'm telling you the odds first off NOT accounting for vacant spaces. point number 2, the *entire point of the argument* was that we should adjust our odds based on inferred spade length"

Kibitzer - "look... go to bridgeguys.com, look up the "rule of restricted choice"...

Gnome - "i know very well what restricted choice is. it's an application of bayes rule."

Kibitzer - "I didn't develop it... I'm not anywhere near good enuff to make rules (well.. some I have)"

Gnome - "i am not sure you know how to apply it, but i'm confident i understand it"

Kibitzer - "is your degree in math?"

Gnome - "one of them."

Kibitzer - "to me, spot cards and the card count make it very simple... I'm sorry if I'm FAR too old to remember how to explain it... I quit teaching 25 years ago"

Gnome - "right. but i think you're misapplying it. think of it this way. at the time of the decision, we know west has 7 stiff or Q7 exactly. what are the odds he will play the 7 from either holding? 100%! therefore restricted choice DOES NOT APPLY."

Kibitzer - "ok... I'll try this one more time... you have 4 spots missing in a suit... right?"

Gnome - "yes"

Kibitzer - "Q, 7, 4, 3"

Gnome - "yes" so we know the holdings are (7, Q43) , (74, Q3) , (Q7, 43) , (Q74, 3) at that point

Kibitzer. "agreed. east plays the 3, under the ace, west plays the 7. that leaves 2 spots unaccounted for there's only a 25% chance that west has the Q7 doubleton. if he has Qxx of anysort, the finesse will always fail... brings us back to making the winning play 75% of the time

Gnome - "but we observe the 4 next. And yes if Qxx is offside, then it doesn't matter. If Qx is onside doesn't matter"

Kibitzer - "right... so the winning play is to take the hook"

Gnome - "no!"

Kibitzer - "75% of the time"

Gnome - "winning play is the drop!"

Kibitzer - "NOT when you see the 7 appear"

Gnome - "ok. so let me put it another way. suppose the 3 appeared on the left and the 7 appeared on the right would the odds change?"

Kibitzer - "back to drop. the appearance of the 7 is what changes the odds"

Gnome - "but we haven't changed the relevant holdings!"

Kibitzer - "oh, indeed we have"

Gnome - "he would still play the 3 from Q3 and from 3"

Kibitzer - "yes, but the 3 makes playing for the drop more advantageous than the finesse... you're not understanding what I'm saying about the "spot" cards, even though I know a 7 isn't ... considered a "spot"... if he'd had Q7, he'd have won the trick with the queen against most good players... guaranteed

Kibitzer - "take that hand to your professor... the one who teaches ratios, etc... he doesn't have to be a bridge player to tell you"

Gnome - "why would i go to a professor when i was a professor?"

Kibitzer - "I taught algebra, trig, geometry & calc... I know of what I speak... sorry... don't wanna argue... I'm done with that... just realize, please, given the spots you're looking at, ... when you're playing bridge and have 4 missing, if someone plays the 2nd highest card under your A, then there's only a 25% chance left that they hold the other missing honor, i.e. ... queen... it's not hard to figure unless you just love to argue for arguing's sake"

Gnome - "you assume that people always play their lowest spot. but even despite that! the relevant holdings are a singleton 7 and Q7 doubleton. how can you say that that those holdings are 75% and 25% respectively?

Kibitzer - "ok... please take into consideration, I'm asking once again, that you've made the discovery play of an honor... the person in one particular position plays the 2nd highest spot ... you're missing... there's only a 25% chance they hold, regardless of position, the missing honor. I don't know whether you're aware of this... but if you hold a 7 card fit, the odds are that the suit will break 4-2..."

Kibitzer - "well... I only have a few measly thousand masterpoints... but I've found that the odds I've been taught re: bridge work well... I'll give ...you a game if you'd like, sometime, and we can see "

[rogerclee]

Getting into arguments with online BBO kibs = no-win line.

[finally17]

poor gnome.

you didn't fail, you can't fail at something for which you have no hope of succeeding. by his own admission the guy has been playing for decades under these beliefs. good of you to try though.

and roger, it's not just kibs. unfortunately it can be decent players you enjoy playing with as well. if i ever use as my primary argument "i've been playing for decades i know what i'm talking about," i hereby give whoever is reading this permission to go buy one of those cattle punches the bad guy in No Country for Old Men uses, and put me out of my misery.

good title for the conversation tho. shoulda been the title of the thread.

why am i still up?

[paulg]

I think this illustrates well gnome's academic background.

At which point would the rest of us have marked the kib as an enemy so that we win the argument ... and at which point would he have done the same to us?

p

[gwnn]

Paul, I don't mark people as enemy, only if they are amazingly rude. I much rather write some sort of humorous player note.

[Ant590]

This reminds me of when gnome taught me symmetric relay...

[barmar]

This XKCD comic seems appropriate:

http://xkcd.com/386/

[awm]

So what Gnome is missing, is that on the first round of diamonds, LHO might've played the queen. Since he would play the queen half the time, he should be less likely to hold Q7 and play the 7 rather than hold singleton 7, making the finesse a favorite.

On the other hand, this analysis also misses that RHO had two chances to play the queen. If he holds 4-3 doubleton he would play 3-then-4 half the time, whereas if he holds Q43 third, he has six possible first and second plays and would only play 3-then-4 one sixth of the time.

So we are back to the drop.

Remember, you have to apply to both hands:

(1) The principle of restricted choice.
(2) The principle of restricted intelligence.

[barmar]

Is there any chance that RHO gives count religiously? That makes the finesse right.

But I guess this is a separate issue.

[jdonn]

If this guy bumped into gnome in person, I'm sure he would go with whatever gnome said.

[matmat]

jdonn, on Mar 29 2008, 10:52 AM, said:

If this guy bumped into gnome in person, I'm sure he would go with whatever gnome said.

yes, knowledge is much clearer and more acceptable when delivered from above.

[hotShot]

Using suitplay we find that after trick 2 we have:

x [space] - Qxx [space]18.65
xx [space]- Qx [space] 20.35
Qx [space]- xx [space] 20.35
Qxx - x [space] [space]18.65

After east putting the 4 on the table, options 2 (east did not drop the Q) and 4 (east was not single) are out, we are left with with:

x [space] - Qxx [space]18.65
Qx [space]- xx [space] 20.35

So finesse would be 47.8% and drop 52.2%.

Whoever holds the ♦Q can see dummies JT98.
Opps were silent during the bidding.
Play was one round of ♠ and ♣.

This is not much extra information.

[vuroth]

Gnome, you make me wish my stats prof hadn't spent the whole term mumbling into the board in a thick unintelligible accent. I might have wound up a better bridge player....

[han]

Teaching only works well if both parties know who the teacher is.

[inquiry]

hotShot, on Mar 29 2008, 11:18 AM, said:

\CODE]x   - Qxx  18.65
Qx  - xx   20.35
[/CODE]
So finesse would be 47.8% and drop 52.2%.

This is very close to the odds of playing for 1-1 spilt missing Kx in a suit (52.00 versus 48.00).

But I am surprised no one discussed the play in spades at trick one. Who has the spade Queen, ten, nine?

We can not be certain, but it looks like WEST. So unless East is playing some huge game at trick one, vacant space theory does actually favor playing the finessee over playing the drop (we have three "known" spade cards with WEST TT9 versus none with EAST).

I am always uncertain of how to calculate these things.... so maybe gnome can help out.... lets assume first for 100% that the play at trick one marks WEST with QT9, and next marks WEST with T9 (east withholding the queen to cover jack later).

In the first case, is the math, 13 vacant spaces in EAST's hand versus 10 in west, or do the calculations taking into account all non-essential cards played....

If at trick 4 the vacant space theory takes into account first three tricks... IN CASE one (WEST has QT9 of spades), the vacant space is 10 in west, 13 in EAST, or 55% the finessee in on (changing odds from 52.2% quoted above for drop, to 45% for the drop). If we subtract the three played cards, vacant space becomes 7 to 10 for east and west, and the odds for the "finessee" improve a little more... to 57.15%.

Now it might be reasonable for EAST to insert the 8 from Q8(x) to keep the queen over the jack. If we assume that is likely, the odds for 11 versus 12 vacant spaces is very very close, rather you calculate it as 11 versus 12 or 8 versus 9 is precisely 50% each for drop and for hook.

Ok, i admit, i am rusty on when to apply vacant space (is is 10 versus 13 since no significant cards had been played, or is it 7 vesus 10 because some cards have been played, significant or not). All in all, the person arguing with gnome was, well very confused. His logic and his explaination was, well, extremely warped. However, there does seem to me to be a reason to hook. IF EAST has spade queen, hook versus drop are equal chances, if EAST lacks spades queen, hook is significantly better odds than drop.

Maybe i am all confused too, since my conclusion (hook not drop) conflicts with everyone elses but the fellow who was clearly confused. Gnome mentioned 8 vs 10 on assumed spades (not sure where he got 8 and 10 from, i can see 7 and 10 or 8 versus 9). He must have discounted 8 versus 10 because math favors hook then i think... see why i stay confused?).

[sceptic]

Quote

Kibitzer - "is your degree in math?"

Gnome - "one of them."

Professor in comedy?

[matmat]

vuroth, on Mar 31 2008, 09:25 AM, said:

Gnome, you make me wish my stats prof hadn't spent the whole term mumbling into the board in a thick unintelligible accent. I might have wound up a better bridge player....

where he taught he _was_ the one with the weird accent...

[kfay]

This is hilarious. Pretty sure it wasn't very amusing at the time. Frankly, I'm impressed you were able to keep such a level head, I would have abandoned the conversation after about the 5th line.