wrote:*Natty Bumppo <borf@...>*

Sword_4_hire <fastfredy0@ ...> wrote:

> 1) Is playing a singleton ace better

This is a "no brainer." The ace is better.

> then [than?] playing than [from?] offsuit

> doubleton KQ? How much better? How did

> you come to that conclusion?

It is infinitely better, because it gives

me two bites at the apple -- the ace itself,

and a king-high doubleton the loner has to

lead to, coming home, if he takes the first

three tricks.

> Where's the accounting? Where is the

There is no math (except for "two bites

> mathematics?

are better than one").Although you dont know how much better .. I agree with your qualitative analysis.> 2) Is playing a singleton ace better

See No. 1. Same answer. It's a "no

> then [than?] playing than [from?]

> offsuit doubleton KJ? How much better?

> How did you come to that conclusion?

brainer."

> Explain the effects of finessing the KJ.

The king-jack cannot be finessed because

no opponent is playing behind me.

If, however, the Interrogator means, by

"finessing," emasculating my doubleton

by leading away from it, no. In bridge

and spades you do not "lead away from a

king." In euchre sometimes you do, but

only to "promote a king" by forcing a

singleton ace; and that play is not

called for against a loner. It would

be not be a finesse, in this case, in

the first place; it would be a gift of

an end play to the maker.You clarified the question, but you did not answer it. The question is of little importance on its own, but a part of the complicated original question.

> 3) Is playing a singleton ace better

Probably not. (

> then [than?] playing than [from?] offsuit

> doubleton QJ? How much better? How did

> you come to that conclusion?

__Probably not__is a non-answer) This is a case of the undue

risk of forcing my partner into a squeeze

play. I don't need math or simulations for

this; I just know from experience (as do

T_Bolt and others) that queens very rarely

take tricks in euchre. The only doubletons

held by the loner that mine could defeat

would be A-10, A-9, K-10, K-9 and 10-9.

As for the 10-9, saving either my jack or

my queen is as good as saving both of them.

As for the former, it's a fat chance not

worth thinking about in light of the risk

of squeezing my partner, who may be able

to ruff my doubleton if she cannot ace it.

And, since I already have a doubleton, it

is unlikely that my partner will, too (in

that suit); so there is no big danger of

finessing her.

> 4) Maybe start easy. Is playing a singleton

Far worse. See No. 3. My nine and ten are

> ace better then [than?] playing than [from?]

> offsuit doubleton 10,9? How much better?

> How did you come to that conclusion?

absolutely worthless; and they give my partner

a chance to ace, the best chance to ruff, and

the least danger of being finessed. No math

or simulation necessary. The specific question

is another "no brainer," but I would like to

know what the other two cards in my hand are,

and what color they are, before I decide on my

lead. I know, without more, only not to lead

my ace.Although you dont know how much better .. I agree with your qualitative analysis.

> 5) Explain the probabilities of your

The probabilities are determinable by

> partner ruffing an offsuit lead when

> you have a singleton, doubleton, triple-

> ton. Explain how this effects [affects?]

> your decision. Explain how the probability

> of ruffing is affected by color of the suit

> you play and quantify your explanation. How

> does the probably of a low tripleton being

> ruffed effect [affect?] your playing an ACE

> first or from the tripleton? How much better

> is one strategy over the over? How did you

> come to that conclusion?

mathematics and do not require simulation.

I have not done the math on all these

questions (and the Interrogator apparently

has not, either, since he says only that

his answers are "proven by simulations" ).

And therefore I can't tell you the exact

probabilities of my partner's having a void

and a trump under any of the circumstances,

and so much for "quantification. " I can

tell you that (I've done the math on this),

if the suit is "green," the probabilities

are 20 per cent better if I lead from a

doubleton than if I lead a singleton, and

40 per cent better if I lead from a tripleton.

But so are the loner's. And the loner's

over-all probabilities are higher because

his hand is stuffed with trump; and if both

my partner and the loner can ruff, the loner

can probably overruff.

Not a high percentage for my partner in any

event. Finally, both my partner and my

opponent have greater probabilities of

ruffing if the suit is "next." It's a long

shot whatever I lead, but the odds are best

leading from a "next" tripleton. The odds

are low enough also that they elevate the

chances of my partner's stopping the march

with one of two aces. Therefore saving my

ace for last is the best strategy.

> 6) What is the probability of your partner

I don't know (well, you are honest on this one .. you do not know)-- I have not done the math

> having both ACES? How did you come to that

> conclusion? (Don't forget to account for

> the higher probability that the 4th seat

> has aces.)

-- but I do know that it is a question that

can be answered in a "closed form" probability

calculation, and that simulation is therefore

not necessary to answer it. I know also that

the probability is low and also that the

"likelihood" is even lower than the

"probability" because of the likelihood the

loner will have an offsuit ace. But, given

the low likelihood of my partner's winning a

trick by ruffing (see answer to No. 5 above),

the assumption that my partner does have two

aces is the best strategy because (a) it is

unlikely the loner has five trump (and if he

does, we're dead anyway), and (b) if my partner

does have two aces, we have all three outside

suits absolutely stopped if I withhold my ace.

> 7) If you lead an offsuit doubleton

This is a question for a mathematician

> rather than your singleton ace, there

> is a probability you will be finessing

> your partner's doubleton. Quantify this

> probability. Show proof. Compare this

> probability to the probability of your

> partner having 2 offsuit aces.

(and not for a simulation), and I do not

have the quantity or the proof. But I

can compare. (Again, you dont have the answer)And I have already done that.

See answers to Nos. 3 and 4 above. The

critical question is whether my doubleton

is worth guarding -- i.e., whether it is

headed by a king. If it is, I lead the ace.

> 8) If your partner had 2 offsuit aces,

As I said before, the probability approximates

> what is the probability he will not keep

> the correct one if you lead your offsuit

> ace.

50 per cent.

Now, there are my answers, to all eight

questions (and to many more, since many

of them were multipart questions).

We have seen no answers yet from the

Interrogator. All we have seen is

"proven by simulations. "The question, as you will recall is what is the best card to lead from the 1^{st}seat against a loners called by the 4^{th}seat given the first seat has an offsuit doubleton and a singleton offsuit ace in another suit.Based on experience I thought your answers were good and your qualitative descriptions were accurate. To be candid, the questions were posed to demonstrate the many facets to consider when answering a question like this. As can be seen, even with your experience you were not able to quantify a single answer. IF YOU CANT QUANTIFY A SINGLE FACET OF THE OVERALL QUESTION, THEN YOUR FINAL ANSWER MUST BE IN DOUBT.Ideally, a mathematical answer is the best one. Most euchre questions posed on this forum can not be answered that way. When I tried to answer this question I did 3 things:1) What were the facets that would effect the outcome.2) What were my qualitative answers3) How do I test the question to confirm my anticipated results? What were my results and are they different than what I anticipated? If so, why?

And here are some additional questions

for the Interrogator:

1) What did the lone hand used in the

simulations consist of?The simulation consisted of 500 hands. The contents of the 4^{th}seat lone hand varied. I could show every hand, but there is a time and effort constraint. If you list the 500 (or more) hands you used to answer the question, I will do the same. I can list and repeat every hand. I can recall every hand and replay every hand. Can you do the same?

2) Were more than one lone hand used?Yes, I imagine 500 unique hands were used. The hands were dealt randomly and if the 4^{th}seat had a hand that a good player would call a loner on, it was used. (In your use of a simulator the euchre lab you used sample sizes of 25ish, so I feel you should feel confident 500 would be adequate

3) If so, how were they chosen?500 unique hands (it is possible a hand or 2 were the same, but this is an unlikely event)If you are referring to the logic to determine when to call a lone hand then I will print an extract from my book on the subject if you print an extract from your book on the subject. Hmm that would be an interesting comparison. J

4) Did the simulator itself choose them?Yes. Cards were dealt out randomly and an algorithm used to determine if the hands fell within the parameters of the question.

5) How?Random number generator

6) If multiple lone hands were used,

was virtually EACH of all possible

leads, from EACH of the hands dealt

to the first defender, played hundreds

(or thousands) of times against EACH of

the lone hands laid out?9,000 hands that satisfied the criteria were used. Assuming you play an average of a hand a minute and assuming you are playing with aggressive loner bidders and assuming you played 1 hour a day it would take you roughly 3 yrs playing time to experience this simulation. (that assumes you wrote down the results)LOL @ this question. 500 lone hands * 5 leads * 1000 = 2,500,000No .I did not play 2,500,000 hands.Why would someone that has written explanations based 25 or so simulations wonder if I had done over 2,000,000? (granted, this question is more complicated than most I have seen)

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