USE chits

[Mike Parker]

ORIGINAL: petracelli

ORIGINAL: Mike Parker

Just to make the comment, not that I would do this.

But you can FORCE whatever chit you want in MWIF. So the purists that want the limited chits could put all those chits in a coffee can or what have you and draw them manually then force MWIF to whatever you drew. Sure its not secret but most folks are playing solitaire now anyway, and if you want it to be secret you could set that up with a third party if you really wanted to do so.

Sounds like some sort of solution.

Well I hate to call it a solution as that presupposes there is a problem [:)] and I honestly MUCH prefer the MWIF system. But rather can we say it is an alternate way to play that might appeal to some of the strict WIF purists

[petracelli]

ORIGINAL: Centuur

ORIGINAL: Orm

So far I am very happy with the new chit system in MWIF. [:)]

+1, since this system avoids all kind of "gamey" tactics using the same counters for neutrality pacts....

[Extraneous]

Aren't you all beta testers? Centuur, Mike Parker, Orm, and Zorachus99.

As beta testers can you explain to everyone why the percentages are different?

[Orm]

I am a beta tester but I am not comfortable with making any comment on this except that I like the new chit system. I am convinced that others are more suited to do that than I am. [:)]

[paulderynck]

ORIGINAL: petracelli

Ps also think the values should be the same as in Wif

That would have been a problem. An infinite distribution combined with the original set of values would have skewed US Entry from what normally happens. Please take a look at this thread for an explanation of the way the chit values for an infinite distribution were developed. Taking the odds for the chits from the infinite distribution values which were arrived at (and put in MWiF) should also answer the question about the annual averages.

tm.asp?m=2157223&mpage=1&key=Entry&#2157602

[petracelli]

ORIGINAL: paulderynck

ORIGINAL: petracelli

Ps also think the values should be the same as in Wif

That would have been a problem. An infinite distribution combined with the original set of values would have skewed US Entry from what normally happens. Please take a look at this thread for an explanation of the way the chit values for an infinite distribution were developed. Taking the odds for the chits from the infinite distribution values which were arrived at (and put in MWiF) should also answer the question about the annual averages.

tm.asp?m=2157223&mpage=1&key=Entry�

Thanks for that Paul, and my maths is not what it used to be so forgive me if you answered these questions in your report.

1 have your calculations allowed for the fact that by being aggressive in 1940 the allies will on.y ever be drawing 1940 chits and that the axis run no risk of the 41 chits being added in early. If you have then fair enough and I will have to decide on buying the game or not, if you haven't and USe is remaining as it is brings me to my second question that no one has yet answered.

2 Why has the USE system that works so well in the boardgame been changed. If it is remaining as is dispute my representations tthen will trouble you no longer.

[Centuur]

ORIGINAL: Zorachus99

ORIGINAL: Centuur

ORIGINAL: Orm

So far I am very happy with the new chit system in MWIF. [:)]

+1, since this system avoids all kind of "gamey" tactics using the same counters for neutrality pacts....

Indeed, number crunchers even would get reliable estimates of US entry, and offensive border garrison values.

To me, that is very gamey.

This is the answer to your second question, mr. Petracelli.

On the first question, I won't answer, because it has to do with the statistic system used to get at the US entry which is now in MWIF. That one has to be answered by the ones who made it (I'm not a mathematical expert...).

[AxelNL]

ORIGINAL: Extraneous

Aren't you all beta testers? Centuur, Mike Parker, Orm, and Zorachus99.

As beta testers can you explain to everyone why the percentages are different?

I started in august last year, long after this discussion was finalised. I trust Paul fully, given what he has shown in the Beta site, to have come up with a more than acceptable system. I do think that the explanation given in the manual is a bit minimal for the purists among us, And I fully admit that I had the same question about when drawing a '1' out of a limited bucket of chits, increases the chance of drawing an higher number the next time, and how that was simulated.
After reading the thread Paul provided I understand the decisions much more. I think this whole discussion boils down to below opposite statements:
1. Using a finite set of counters is a design decision to balance unlucky draws because every low number moving out of the limited set decreases the chance it will be drawn again
2. A finite set of counters is an artificial limitation of simulating US behaviour. The decision was made for the paper game because providing more counters would cost more and will fill up the box too much. Besides as the same chits are used for garrison chits above argument is not strong enough. The computer version does not have that limitation.

As MWIF is sanctioned by Harry I trust we have been given a fine baseline here. The statistical work looks solid, although my (discrete event) simulation modelling years are 10+ years behind me. The feedback loops Steve mentioned in the thread are of most interest to me, because in case argument 1 is found to be more important, it will be not difficult to use that to solve things.

[petracelli]

ORIGINAL: Centuur

ORIGINAL: Zorachus99

ORIGINAL: Centuur



+1, since this system avoids all kind of "gamey" tactics using the same counters for neutrality pacts....

Indeed, number crunchers even would get reliable estimates of US entry, and offensive border garrison values.

To me, that is very gamey.

This is the answer to your second question, mr. Petracelli.

On the first question, I won't answer, because it has to do with the statistic system used to get at the US entry which is now in MWIF. That one has to be answered by the ones who made it (I'm not a mathematical expert...).

I give up, enjoy.

[Mike Parker]

Okay here is a nice (at least I think nice) article explaining the situation in a basic way. The MWIF way is with replacement, and the WIF is without replacement.

https://www.ma.utexas.edu/users/parker/ ... g/repl.htm

[Extraneous]

The percentages are different between WiF and MWif. Because for each year MWif loads a new set of percentages for available chits each year.

1939
MWiF Zeros x50 (1.7%) ~ WIF Zeros x1 (3.2%)
MWiF Ones x910 (30.2%) ~ WIF Ones x9 (29%)
MWiF Twos x751(24.9%) ~ WIF Twos x8 (25.8%)
MWiF Threes x636 (21.1%) ~ WIF Threes x6 (19.4%)
MWiF Fours x630 (20.9%) ~ WIF Fours x6 (19.4%)
MWiF Fives x40 (1.3%) ~ WIF Fives x1 (3.2%)
MWiF Sixes x0 (0%) ~ WIF never had Sixes
Average MWiF 2.333443818 ~ WIF 2.322580645

1940
MWiF Zeros x10 (2.7%) ~ WIF Zeros x5 (9%)
MWiF Ones x191 (52.3%) ~ WIF Ones x19 (35%)
MWiF Twos x67 (18.4%) ~ WIF Twos x14 (26%)
MWiF Threes x62 (17%) ~ WIF Threes x9 (17%)
MWiF Fours x33 (9%) ~ WIF Fours x6 (11%)
MWiF Fives x2 (0.5%) ~ WIF Fives x1 (2%)
MWiF Sixes x0 (0%) ~ WIF never had Sixes
Average MWiF 1.789041096 ~ WIF 1.907407407

1941
MWiF Zeros x3 (0.2%) ~ WIF Zeros x5 (7.2%)
MWiF Ones x205 (22.3%) ~ WIF Ones x20 (29%)
MWiF Twos x246 (26.7%) ~ WIF Twos x17 (17%)
MWiF Threes x226 (24.6%) ~ WIF Threes x20 (29%)
MWiF Fours x190 (20.7%) ~ WIF Fours x6 (8.7%)
MWiF Fives x45 (4.9%) ~ WIF Fives x1 (1.4%)
MWiF Sixes x5 (0.5%) ~ WIF never had Sixes
Average MWiF 2.597826087 ~ WIF 2.072463768

1942
MWiF Zeros x10 (0.2%) ~ WIF Zeros x5 (6.4%)
MWiF Ones x200 (3.9%) ~ WIF Ones x20 (25.6%)
MWiF Twos x1050 (20.6%) ~ WIF Twos x17 (21.8%)
MWiF Threes x1823 (35.8%) ~ WIF Threes x34 (43.6%)
MWiF Fours x1050 (20.6%) ~ WIF Fours x6 (7.2%)
MWiF Fives x764 (15%) ~ WIF Fives x1 (1.2%)
MWiF Sixes x200 (3.9%) ~ WIF never had Sixes
Average MWiF 3.333137139 ~ WIF 2.228915663

1943
MWiF Zeros x0 (0%) ~ WIF Zeros x5 (5.3%)
MWiF Ones x900 (14.7%) ~ WIF Ones x20 (21.1%)
MWiF Twos x2023 (33.1%) ~ WIF Twos x17 (17.9%)
MWiF Threes x1390 (22.7%) ~ WIF Threes x46 (48.4%)
MWiF Fours x900 (14.7%) ~ WIF Fours x6 (6.3%)
MWiF Fives x600 (9.8%) ~ WIF Fives x1 (1.1%)
MWiF Sixes x300 (4.9%) ~ WIF never had Sixes
Average MWiF 2.865368886 ~ WIF 2.326315789

Summary: The Axis should take advantage of the fact that the chit draw will be low in 1940. The chance of drawing above a One in MWiF in 1940 is only 45% vs.WiF where the chance is 66%.

[paulderynck]

ORIGINAL: petracelli

ORIGINAL: paulderynck

ORIGINAL: petracelli

Ps also think the values should be the same as in Wif

That would have been a problem. An infinite distribution combined with the original set of values would have skewed US Entry from what normally happens. Please take a look at this thread for an explanation of the way the chit values for an infinite distribution were developed. Taking the odds for the chits from the infinite distribution values which were arrived at (and put in MWiF) should also answer the question about the annual averages.

tm.asp?m=2157223&mpage=1&key=Entry�

Thanks for that Paul, and my maths is not what it used to be so forgive me if you answered these questions in your report.

1 have your calculations allowed for the fact that by being aggressive in 1940 the allies will on.y ever be drawing 1940 chits and that the axis run no risk of the 41 chits being added in early. If you have then fair enough and I will have to decide on buying the game or not, if you haven't and USe is remaining as it is brings me to my second question that no one has yet answered.

2 Why has the USE system that works so well in the boardgame been changed. If it is remaining as is dispute my representations tthen will trouble you no longer.

1. Over 25 potential axis strategies were simulated (some VERY agressive, some passive) and each run 100,000 times. This was an iterative process, but finally after blending all those strategies, a distribuion was arrived at that was much closer to the same runs (which did include running out of chits) as those same scenarios using the finite WiF chits.

Besides, the axis would still be stupid to do actions "just because" when they still could be unlucky and put 3s & 4s into US entry. I agree with the previous poster who stated axis strategy does not hinge on US entry chit variance.

Bottom line is the ability to analyze what's in any of the chit pools vs. known chits is vastly reduced, but the overall distribution profiles will remain close to what happens in WiF.

2. Designer's decision, and Steve provided the rationale for it in a previous post in this thread.

[Shannon V. OKeets]

ORIGINAL: paulderynck

ORIGINAL: petracelli

ORIGINAL: paulderynck



That would have been a problem. An infinite distribution combined with the original set of values would have skewed US Entry from what normally happens. Please take a look at this thread for an explanation of the way the chit values for an infinite distribution were developed. Taking the odds for the chits from the infinite distribution values which were arrived at (and put in MWiF) should also answer the question about the annual averages.

tm.asp?m=2157223&mpage=1&key=Entry�

Thanks for that Paul, and my maths is not what it used to be so forgive me if you answered these questions in your report.

1 have your calculations allowed for the fact that by being aggressive in 1940 the allies will on.y ever be drawing 1940 chits and that the axis run no risk of the 41 chits being added in early. If you have then fair enough and I will have to decide on buying the game or not, if you haven't and USe is remaining as it is brings me to my second question that no one has yet answered.

2 Why has the USE system that works so well in the boardgame been changed. If it is remaining as is dispute my representations tthen will trouble you no longer.

1. Over 25 potential axis strategies were simulated (some VERY agressive, some passive) and each run 100,000 times. This was an iterative process, but finally after blending all those strategies, a distribuion was arrived at that was much closer to the same runs (which did include running out of chits) as those same scenarios using the finite WiF chits.

Besides, the axis would still be stupid to do actions "just because" when they still could be unlucky and put 3s & 4s into US entry. I agree with the previous poster who stated axis strategy does not hinge on US entry chit variance.

Bottom line is the ability to analyze what's in any of the chit pools vs. known chits is vastly reduced, but the overall distribution profiles will remain close to what happens in WiF.

2. Designer's decision, and Steve provided the rationale for it in a previous post in this thread.

I'll just add one thought here.

Yes, the probabilities of drawing low values for the markers in 1940 are better if the Axis takes a lot of aggressive actions in 1940. But obviously that means the Axis will have taken a lot of aggressive actions in 1940 and the US will have accumulated more markers than they would have otherwise. More markers for the US means they can choose more US Entry Options. Or the Allies could also take more aggressive actions in 1940, with a lower risk of losing high valued markers.

Think of the markers as cards. Giving your opponent a lot of cards is usually bad (in most card games), even if they are poor cards you're giving him.

I see the effect of the modified US Entry marker design on Axis strategy to primarily concern making decisions in late 1940 versus early 1941. And that trade-off was always present in the board game version too - every year, starting in 1939.

[Extraneous]

I'm just curious what kind of Monte Carlo simulation (Normal (“bell curve”), Lognormal, Uniform, Triangular, Pert, or Discrete)?

(Chits = Markers)

What happens when the available chit values have been reduced?

Axis actions cause much less impact on possible US entry even though more chits can be generated.
Allied actions which cause the removal of chits from the US entry pools have far more impact on possible US entry.

Higher total chits values allow you to choose more USE options not just more chits.

[paulderynck]

Here is the theory: http://en.wikipedia.org/wiki/Monte_Carlo_method

The answer is none of the above. The idea was to define the distribution that would perform like the board game chits. The available chit values haven't been reduced. The odds of their occurances have been changed. In the boardgame, because it is a finite distribution, as soon as you draw a chit, you change the odds of drawing any other value. FREX if you draw the only zero chit in Sept/Oct 1939, the odds of drawing all other values increases and the odds of drawing another zero before Jan/Feb 1940 are, well, zero.

But Steve wanted to use an infinite distribution, so if the odds of getting the zero are 1 in 30 (until it is drawn in WiF), then in MWiF it would be one in 30 every time a chit was drawn throughout 1939. In cases of extremely bad luck, you could draw all zeros! So in fact, the odds for a zero in 1939 bcame less than 1 in 30 for MWiF, but those odds remain the same until 1940, no matter how many zeros are drawn (as unlikely as that may be).

Similarly the odds for all the other chit values were adjusted annually so that over hundreds of thousands of trial runs, the MWiF chits were yielding close to the same totals for the US Entry Pools as would the WiF chits, given the same number of draws.

Your last two observations require a lot more explanation as to what you are talking about.

[Extraneous]

Just for the record: I am not judging the efforts of the beta testers. I'm just crunching the numbers.

If the odds in 1939 of drawing a Zero is approximately 1 in 30 (actually 100 / 3.2 = 31.25).

1939 (Approximately)
Zeros MWiF 1 in 60 ~ WIF 1 in 31
Ones MWiF 1 in 3 ~ WIF 1 in 3
Twos MWiF 1 in 4 ~ WIF 1 in 4
Threes MWiF 1 in 5 ~ WIF 1 in 5
Fours MWiF 1 in 5 ~ WIF 1 in 5
Fives MWiF 1 in 75 ~ WIF 1 in 31

1940 (Approximately)
Zeros MWiF 1 in 37 ~ WIF 1 in 11
Ones MWiF 1 in 2 ~ WIF 1 in 3
Twos MWiF 1 in 5 ~ WIF 1 in 4
Threes MWiF 1 in 6 ~ WIF 1 in 6
Fours MWiF 1 in 11 ~ WIF 1 in 9
Fives MWiF 1 in 183 ~ WIF 1 in 54


(Limited chits) In WiF when a Zero is drawn then you can't draw another unless a Zero is in or is returned to the available chits pool.

(Unlimited chits) In MWiF those are the odds every time a chit is drawn throughout that year.


In cases of extremely bad luck you could draw all Zeros. Yes that would be bad but It is a possibility.

So for MWiF the odds for drawing a Zero was changed from 1 in 31 to 1 in 60 (100 / 1.7 = 60.34).