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## Re: [EuchreScience] Natty answers the questions

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• Natty Bumppo wrote: ... This is a no brainer. The ace is better. It is infinitely better, because it gives me two bites at the apple --
Message 1 of 25 , May 1, 2007
Natty Bumppo <borf@...> wrote:

Sword_4_hire <fastfredy0@ ...> wrote:

> 1) Is playing a singleton ace better
> then [than?] playing than [from?] offsuit
> doubleton KQ? How much better? How did
> you come to that conclusion?
This is a "no brainer." The ace is better.
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
> mathematics?

There is no math (except for "two bites
are better than one").
Although you dont know how much better .. I agree with your qualitative analysis.

> 2) Is playing a singleton ace better
> then [than?] playing than [from?]
> offsuit doubleton KJ? How much better?
> How did you come to that conclusion?

See No. 1. Same answer. It's a "no
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
> then [than?] playing than [from?] offsuit
> doubleton QJ? How much better? How did
> you come to that conclusion?

Probably not. (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
> ace better then [than?] playing than [from?]
> offsuit doubleton 10,9? How much better?
> How did you come to that conclusion?

Far worse. See No. 3. My nine and ten are
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 dont know how much better .. I agree with your qualitative analysis.

> 5) Explain the probabilities of your
> 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?

The probabilities are determinable by
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
> 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.)

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

This is a question for a mathematician
(and not for a simulation), and I do not
have the quantity or the proof. But I
can compare. (Again, you dont 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,
> what is the probability he will not keep
> the correct one if you lead your offsuit
> ace.

As I said before, the probability approximates
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 1st seat against a loners called by the 4th 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 CANT 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 answers
3)      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 4th 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 4th 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 = 2,500,000
No .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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