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Some Meld Statistics
#11
TE, great, constructive posting.

Just a couple things to mention...

1. My setup didn't take into account Double Runs as I didn't declare a trump.

2. Is this the same adjustment meld calculation or a new spin on an old term. It's been a while since I looked at your adjusted meld concept.

3. I don't want to discuss too much about a new bidding system in a thread called Some Meld Statistics, but...
Lowering the Unlimited Meld Bid was what I was angling for -- for the same reasons you stated.
Setting the Unlimited Meld Bid to cap at 50+ meld, provides deflation while at a cost of actual meld clarity when dealing with meld above 50 (not really much of a loss, for useful gain).
I am spit-balling a different structure than you proposed, but I have flip-flopped back to idea that showing single aces around IS important.
As you mentioned, your bidding structure is cozy and nice when opening from the first seat, but the casualties begin when previous bids are made. More thought is required.

Progress is being made.
It's unbelievable how much you don't know about the game you've been playing all your life. -- Mickey Mantle
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#12
Ahh...yes, of course you can't have double runs in there. Wasn't thinking. So really, anything over 110-114 is quite unlikely. You can get to 110 with double aces and bits and pieces here and there.

The 'normal' form of computing adjusted meld is add 1 to your meld total for each ace. IF you start with a bid showing aces or are going to give a bid showing them, tho, you've already shown the first 4 in your hand. Don't use these to compute your adjusted meld.

And, yes, the complexities arise when there's been prior bidding. I brought it up, largely, to show why there's no necessarily simple answer to "how many hands do I deal, in this simulation?" It depends on the question.
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#13
(09-17-2013, 09:56 PM)mickmackusa Wrote:  I was curious to see just how much duplication there was, so I ran a few tests on the array of hands.

Hands Original Count = 100000
Hands Unique Counts = as low as 99988, as high as 99998.

Wow! ... You stored all the hands dealt and searched for duplicates?

(09-17-2013, 09:56 PM)mickmackusa Wrote:  In reality, if I played 100,000 games, isn't it possible that I would be dealt some hands that I had already had?
...
How many different variations of cards are there for a 20-card double-deck pinochle hand?

Interesting 2 questions ... Requires the term "variation" be defined.
For example, given a distribution S-H-C-D of say:

Hand1 = 8-7-3-2 ... is this the same as ...
Hand2 = 3-2-8-7

where the exact same ranks are found in each 8, each 7, each 3, and each 2 card suits?


(09-17-2013, 09:56 PM)mickmackusa Wrote:  ... when providing statistical data on the WWW, it is paramount that the facts be scrutinized and verified for absolute correctness.

Yes!

(09-17-2013, 09:56 PM)mickmackusa Wrote:  I should also reveal that:
1. My data was collected without any nomination of trump.
2. My meld calculating program includes "assumed" meld:

like a bonus 2 points for an assumed royal marriage when using a scorechart that doesn't recognize the Roundhouse:
TCTCTCKCQCTDTDTDKDQDTSTSTSKSQSTHTHTHKHQH
http://www.powerpinochle.com/forum/meld....p=&chart=0

or an assumed run (this is the only case where the meld can be an odd number):
ACTCKCQCJCADTDKDQDJDASTSKSQSJSAHTHKHQHJH
http://www.powerpinochle.com/forum/meld....p=&chart=0

Ooops!! ... My bad ... my current meld calculator does not include either of the above two examples for item 2 ... look for an update, if needed.

I did not declare a Trumps suit in my analysis either as that it is what I understood from mickmackusa's original post as assumed ground rules.

Without declaring Trumps, for all of the meld tables listed on this website except for NPA's, meld must be an even number. NPA's Meld Table uses 15 for a Single Pinochle ... this is why I adjusted the bin ranges from mickmackusa's post to include all of the values possible (mickmackusa used only Yahoo's Meld Table resulting in even numbers only).

The probability of a Quadruple Run is 2.828E-19. If you did hit it once in 100,000 it wouldn't change the results significantly. More than once ...

(09-17-2013, 09:56 PM)mickmackusa Wrote:  Thanks to FLACK for taking the ball and running with it.
His representation not only uses better technology to create the data, but is also more comprehensive in displaying data across multiple scorecharts.
(and the graph is visually appealing) *p.s. a couple of the red Yahoo bars seem to be a pixel higher than its competitors even when the %'s are the same (<15 & 26..35). Are my eyes deceiving?

One does what one can ... I see the same pixel delta ... I can only say Microsoft Excel does what it does ... or it could be in the SnagIt image capture program ... inclusion of the data table providing the numbers helps.

(09-17-2013, 09:56 PM)mickmackusa Wrote:  How many different variations of cards are there for a 20-card double-deck pinochle hand?
My data arbitrarily used 100,000 hands, but how many should be used?
Seems to me, that this magic number should be the backbone of all future computations.
I am not suggesting that all future computations iterate through every possible hand, because that doesn't seem realistic/natural.
I just want to identify the absolute best, most accurate procedure to garner statistical data.
[/size]

The first question requires definition of "variations".

The second question depends upon the problem being analyzed and how much error in the answer one can allow/tolerate as ToreadorElder pointed out. The expense of the runtime one can tolerate is also a factor.
Ta!
--FLACKprb
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#14
Bridge World uses a useful notation.
6-5-5-4 is used to denote any hand with that pattern.
6=5=5=4 is used to denote a hand with specifically 6 spades, 5 hearts, 5 diamonds, and 5 clubs. They use bridge suit rank ordering. We, unfortunately, have to define one because the rules don't define a ranking of the suits. Still, the notation is useful.

Is 3=2=8=7 identical to 8=7=3=2? No. Not identical. Equivalent if there are no pinochles involved, yes, but not identical.

BTW, Yahoo meld can be odd, without a run: triple pinochle is 45. And...how do you compute the quad run probability? There are exactly 4 combinations that are quad runs; there are 80C20 possible hands. According to

http://www.mathsisfun.com/combinatorics/...lator.html

80C20 is 3.5x10^18. That makes the quad run chance basically 1 in 10^18, rounding for simplicity, or so it would appear.

I wouldn't worry about the 4-runs hand. It's extremely rare, so it's not worth throwing in all the complexity. The purpose for creating the hands is to analyze meld distributions, to consider how to build a better bidding system, so the assumption must be that trumps are not specified. Heck, note that we'll deal hands with 9 card double ace runs, and a double pinochle. I wouldn't be showing meld; I'm gonna try to play that, at least for several rounds of bidding. But we're only asking about meld range frequencies; we're not asking to select the best bid to describe a hand.

I've run a number of poker simulations from time to time. To a degree, execution time is really the least of my concerns, in that I can run enough trials to create a large sample, plenty fast enough. Computers are just insanely fast for this sort of thing these days, unless the tool's just not well-suited, or the code's just *seriously* inefficient. But every desktop I have access to, is fast. Older laptops are a lot slower. Still...worst case for me, might be just start it up, then go grab a shower and one's morning beverage of choice. Smile
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#15
(09-20-2013, 01:21 PM)ToreadorElder Wrote:  Bridge World uses a useful notation.
6-5-5-4 is used to denote any hand with that pattern.
6=5=5=4 is used to denote a hand with specifically 6 spades, 5 hearts, 5 diamonds, and 5 clubs. They use bridge suit rank ordering. We, unfortunately, have to define one because the rules don't define a ranking of the suits. Still, the notation is useful.

Is 3=2=8=7 identical to 8=7=3=2? No. Not identical. Equivalent if there are no pinochles involved, yes, but not identical.

BTW, Yahoo meld can be odd, without a run: triple pinochle is 45. And...how do you compute the quad run probability? There are exactly 4 combinations that are quad runs; there are 80C20 possible hands. According to

http://www.mathsisfun.com/combinatorics/...lator.html

80C20 is 3.5x10^18. That makes the quad run chance basically 1 in 10^18, rounding for simplicity, or so it would appear.

I wouldn't worry about the 4-runs hand. It's extremely rare, so it's not worth throwing in all the complexity. The purpose for creating the hands is to analyze meld distributions, to consider how to build a better bidding system, so the assumption must be that trumps are not specified. Heck, note that we'll deal hands with 9 card double ace runs, and a double pinochle. I wouldn't be showing meld; I'm gonna try to play that, at least for several rounds of bidding. But we're only asking about meld range frequencies; we're not asking to select the best bid to describe a hand.

I've run a number of poker simulations from time to time. To a degree, execution time is really the least of my concerns, in that I can run enough trials to create a large sample, plenty fast enough. Computers are just insanely fast for this sort of thing these days, unless the tool's just not well-suited, or the code's just *seriously* inefficient. But every desktop I have access to, is fast. Older laptops are a lot slower. Still...worst case for me, might be just start it up, then go grab a shower and one's morning beverage of choice. Smile

6-5-5-4 could be:
ACACTCKCQCJCADKDQDJDJDTSKSKSJSJSAHAHAHJH
or
ACQCQCJCADADKDKDJDJDASTSKSQSJSAHAHKHQHJH
as the expression always resorts the suit order to be the longest suit to shortest suit.

6=5=5=4 is closer to my question because the suits are not organized by suit length.

My question about the probability of a matching hand goes beyond identical suit lengths and asks for an identical card for card match.
This isn't an important question; just one I couldn't answer myself.

p.s.

Yep, I forgot about Yahoo's Triple Pinochle value being an odd integer.

I wasn't trying to over-complicate the meld counting process by including the assumed melds.
Rather the opposite, I was trying to use a program that I had already written and tested/trusted.

regarding:
FLACKprb Wrote:Wow! ... You stored all the hands dealt and searched for duplicates?
This isn't that impressive.
Since I was processing and looping using arrays, it only cost ME one line of code
PHP Code:
sizeof(array_unique($hands_array)) 
It's unbelievable how much you don't know about the game you've been playing all your life. -- Mickey Mantle
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#16
well, I'm biased of course, but IMO adjusted meld is FAR more accurate as an evaluation tool. 16 with no aces isn't worth 20; 24 with 6 aces is definitely worth 30. I think it actually simplifies and clarifies when to give meld for a beginner, for the borderline hands. I surmise that the ranges you chose, actually reflect that you're used to giving 20 with 16...but is it any 16? Using adjusted, you'll probably want to shift your bins around, to 0-19, 20-29, etc. (I can often justify giving 20 on 19 adjusted.)

And, yes, insofar as the meld test goes, I'd suggest using adjusted meld there as well, or at least having it as an option.
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#17
(09-20-2013, 10:07 PM)ToreadorElder Wrote:  well, I'm biased of course, but IMO adjusted meld is FAR more accurate as an evaluation tool. 16 with no aces isn't worth 20; 24 with 6 aces is definitely worth 30. I think it actually simplifies and clarifies when to give meld for a beginner, for the borderline hands. I surmise that the ranges you chose, actually reflect that you're used to giving 20 with 16...but is it any 16? Using adjusted, you'll probably want to shift your bins around, to 0-19, 20-29, etc. (I can often justify giving 20 on 19 adjusted.)

And, yes, insofar as the meld test goes, I'd suggest using adjusted meld there as well, or at least having it as an option.

I must defer this decision to my supervisor.
If rakbeater feels Adjusted Meld is the way Power Pinochle is going to go and he will be adopting the method in his upcoming literature and teachings, then I will update the programs.
It's unbelievable how much you don't know about the game you've been playing all your life. -- Mickey Mantle
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#18
Adjusted Meld is not the way Power Pinochle is going at this time. I've been focused on teaching beginners, and in every situation, beginners have enough problems learning/understanding/remembering meld, biddable hands, trick taking, bidding, scoring and how to play hands...all at once. Adding adjusted meld at the beginning is too much and too confusing for the average beginner in my experience.

A goal of mine is for this website to have the tools available for any potential pinochle player to use to learn how to play and then join an online game and feel comfortable. Using a new bidding system, adjusted meld, or anything that isn't generally accepted will not be working towards that goal.
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#19
Bringing this back up. I'm NOT trying to replace or critique what we said before. I'm building towards some different analyses.

First things first...some simple meld frequencies. Notes:

1. This never attempts to set a trump suit. Therefore, all marriages are 2 points per, and there are no runs. I'm going to work on the conditions where you could go ahead and count the run, but that's kinda tricky.
2. I'm using the Pagat chart (Pogo, PlayOK). Triple pino is 60; quad pino is 90.
3. THIS sample (25M deals, so 100M hands) is using regular meld ONLY, not adjusted meld.

Here's my numbers. I'm breaking the low totals into several bins. The last column shows the percentage of time that meld range was achieved.

max 0 1.518888
max 4 15.560815
max 8 17.220658
max 14 30.056984
max 20 19.410532
max 25 5.570019
max 30 3.582645
max 40 3.87179
max 50 2.097852
max 60 0.287614
max 70 0.245246
over 70 0.576957

One point to note is the degree of risk you take, when you have some monster hand but the only meld is a basic run. You've got a 17% chance that you won't make the board.
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#20
Round 2 of the tests. Same testing, same sample size. I did change the bins because I wanted a bit more resolution, for the 2 new additions:

raw meld adj meld support
max 0 1.517 0.001 0.001
max 4 15.556 1.448 0.253
max 8 17.212 13.728 4.105
max 12 19.378 18.090 14.097
max 16 19.409 17.355 18.080
max 20 10.692 19.479 17.284
max 25 5.575 13.870 16.225
max 30 3.584 6.473 14.818
max 40 3.871 5.213 9.249
max 50 2.097 2.899 3.676
max 60 0.288 0.596 1.228
max 70 0.245 0.192 0.254
over 70 0.577 0.656 0.729

NOTE: the MIN on the bins is 1 more than the max of the bins before. So the Max 20 bin is the 17-20 bin.

raw meld is the usual meld total.

adjusted meld counts 1 point per ace. It's what I prefer for bidding...16 meld +4 aces = 20 adjusted meld, and therefore I'll give it.

support counts 2 points per ace. This becomes a likely slightly conservative estimate of the total points your partner will contribute, between aces and tricks. I'm only counting 2 points per ace because they won't always cash...and to keep things in integer math. Smile Support can be useful to a potential *declarer* as an estimate of how much total help partner can provide.

Support is tricky, as the more extreme your shape as declarer, the more uncertain dummy's aces are. And it doesn't count any possible ruffs dummy can provide, or the small chance he'll actually have a run in your suit. Still, it's useful:

1. I've advocated for some time that if you never hear a meld bid or aces bid from partner, expect 15 support. The numbers suggest support of 14 or less should be about 27% of the time or so; that puts the odds of 15 support at about 3 to 1 in your favor.

2. In a shutout bid situation:
60 - ?
60 - pass - pass - ?

Partner is not limited in the first case, and not greatly limited in the second case. (Jumping to 70 is RISKY; I generally won't do it without about 35 adjusted meld, *including* at least 4 aces.) Estimate what you've got, between the play and your meld. Then you know what support you need:

--The cumulative probability he'll have 20 support or less, is about 54%. So it's close to a tossup. If you're heavily offensively oriented...therefore, you don't have high hopes of saving...then...bidding may work.

--The cumulative probability he'll have 25 or less is about 70%...more than 2 to 1 against you. BAD odds. And a little worse in the second scenario when partner's already passed...probably enough worse to make it about 3 to 1 against you. It'd be worth taking a shot only in some pretty specific situations...double bidder out, or if you have reason to believe you can push the opponent to bid again when he shouldn't.
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