US entry and 1941 Barbarossa

[hakon]

I have two major issues with the board game version of wif, these are:

1. US entry is much, much too random. Chit rolls + draws can easily mean several 100s of build points more or less for the US throughout the game. If the US can take option 34 in may/june of 1941 they should almost always win, unless one side is making huge strategical or tactical errors, while if they dont get it until may/june 1942, they are in deep trouble. The luck involved in US entry is probably larger than the accumulated luck of all land, air and naval battles combined.

2. Depending on rules being played. (Most importantly oil and city based volunteers), russia can hold the garrison vs Germany in 1941 in almosst all games. More importantly, if Russia appears to follow such a strategy, Germany is severely restricted in what he can build, if they are to have any chance whatsoever in beating the garrison. In particular, building ships, aircraft and synth oil plants in place of militia, mountain and mech, will almost guarantee that the USSR can hold the garrison.

My main issue here is, that in competitive play, Russia should ALWAYS start the game acting like they plan to hold the garrison. Their first few chits should be placed offensively, so that Germany is in the dark about their garrison level, and also for forcing the Germans into holding a sizable eastern garrison while fighting france (assuming a conventional France-40 strategy.). If Russia draws good chits, and/or if germany build anything that doesnt maximize their garrison, Russia should always avoid a 41 barbarossa, which makes the historical path quite rare.

Counter-arguments usually revolve around the risks of this strategy. In my opionion, these risks are too small, when Russia can hold the garrison almost 100% of the times they try (If they draw too many 0's as garrison chits, they just pull back in 1940.) Also, pulling back during the winter is quite doable. If the US is able take option 34 in nov/dec 41 or jan/feb 42, the USSR can even DOW italy or japan to become active, giving them a lot extra land moves they can use for pulling back quicker.

In our local games, we tend to houserule both these issues in one way or another, I wonder if there is any plan for house optional rules in MWIF that will limit these problems?

One solution for the first problem, is to keep the chit values of the US entry chits much closer to the average. For instance, if the average for a given year is 2.7, most chits drawn should be 2's or 3's, and only a few should be 1 or 4.

The simplest solution for the second problem, would be to just say that germany can DOW russia at will, regardless of garrison. Another way to solve this, for instance, is giving Germany 5 extra chits for conquering france.

Both would be optional rules.

[Shannon V. OKeets]

ORIGINAL: hakon

I have two major issues with the board game version of wif, these are:

1. US entry is much, much too random. Chit rolls + draws can easily mean several 100s of build points more or less for the US throughout the game. If the US can take option 34 in may/june of 1941 they should almost always win, unless one side is making huge strategical or tactical errors, while if they dont get it until may/june 1942, they are in deep trouble. The luck involved in US entry is probably larger than the accumulated luck of all land, air and naval battles combined.

2. Depending on rules being played. (Most importantly oil and city based volunteers), russia can hold the garrison vs Germany in 1941 in almosst all games. More importantly, if Russia appears to follow such a strategy, Germany is severely restricted in what he can build, if they are to have any chance whatsoever in beating the garrison. In particular, building ships, aircraft and synth oil plants in place of militia, mountain and mech, will almost guarantee that the USSR can hold the garrison.

My main issue here is, that in competitive play, Russia should ALWAYS start the game acting like they plan to hold the garrison. Their first few chits should be placed offensively, so that Germany is in the dark about their garrison level, and also for forcing the Germans into holding a sizable eastern garrison while fighting france (assuming a conventional France-40 strategy.). If Russia draws good chits, and/or if germany build anything that doesnt maximize their garrison, Russia should always avoid a 41 barbarossa, which makes the historical path quite rare.

Counter-arguments usually revolve around the risks of this strategy. In my opionion, these risks are too small, when Russia can hold the garrison almost 100% of the times they try (If they draw too many 0's as garrison chits, they just pull back in 1940.) Also, pulling back during the winter is quite doable. If the US is able take option 34 in nov/dec 41 or jan/feb 42, the USSR can even DOW italy or japan to become active, giving them a lot extra land moves they can use for pulling back quicker.

In our local games, we tend to houserule both these issues in one way or another, I wonder if there is any plan for house optional rules in MWIF that will limit these problems?

One solution for the first problem, is to keep the chit values of the US entry chits much closer to the average. For instance, if the average for a given year is 2.7, most chits drawn should be 2's or 3's, and only a few should be 1 or 4.

The simplest solution for the second problem, would be to just say that germany can DOW russia at will, regardless of garrison. Another way to solve this, for instance, is giving Germany 5 extra chits for conquering france.

Both would be optional rules.

More optional rules. My favorite![;)]

Your points are well made.

One change in the chits (which was requested by Harry Rowland) is that there is not a fixed number of chits, but instead a probability distribution. This means that the chit you draw does not depend on other chits that have been drawn. And, the USSR drawing chits doesn't affect the chits the USA gets when it draws. Each chit is drawn against a probability distribution for the current year - that's it.

It isn't difficult to write/read those probability distributions (1 for each year) from a CSV (comma separated values) file. That would let the players decide what the "counter mix" should be. I also would like to separate the neutrality pact probability distributions from the USA entry ones entirely. It always bothered me that they were the same.

This proposed solution has the advantage that all of this could be set up by the player using the CSV file without me having to write code to support additional options and continually process them during the game.

[hakon]

In friendly games, the players can always agree not to stuff the border with Russia. Having the opportunity to modify the CSV files for chit draws would also make it possible to make US entry somewhat less random in such games, provided both parties agree.

What I was looking for, was a standardized pair of options, that could be used in more competitive games, hoping that such these options could be accepted as some kind of standar play, which can only be achieved if these options are included in the options form during game startup.

[JanSorensen]

Going from a finite pool to an infinite pool only makes the problem larger as getting one large chit no longer lowers the average in the remaining pool. In my opinion it is a clear mistake to use an unlimited pool for that exact reason. The system does not need the added variance from this change.

The decision is obviously Harry Rowland's to make but I believe you should ask him again if he really wants this change despite the added variance. It would be interesting to hear his reasoning if so.

[Shannon V. OKeets]

ORIGINAL: hakon

In friendly games, the players can always agree not to stuff the border with Russia. Having the opportunity to modify the CSV files for chit draws would also make it possible to make US entry somewhat less random in such games, provided both parties agree.

What I was looking for, was a standardized pair of options, that could be used in more competitive games, hoping that such these options could be accepted as some kind of standar play, which can only be achieved if these options are included in the options form during game startup.

In a sort of strange way, I think this is beyond my authority. Or at least the authority I am willing to assume.

You are asking me to give some sort of official recognition to a house rule by including it within the "official" options. Can you make a quick estimate of how many more of those requests I am likely to recieve if I say yes to any one house rule? And how many people will be offended if I do not "bless" their house rule(s)?

My going in position, when I signed my contract with Matrix, was to implement WIF FE (RAW 7). That is still my position. Your request for flexibility on the chit distribution was something I could make available rather painlessly through the CSV files. Many other players have asked for stuff, which involves writing a lot of additional code. For instance, adding additional options to the options list. I deny all those requests on the basis of not increasing my task list.

I am also very uncomfortable with the role of adjudicator of what is "right" in regard to WIF rules. In my experience they are quite slippery and hard to get ahold of. I therefore fall back on RAW 7 (often suplemented by clarifications from forum members). Besides which, I really don't have the time to thrash out all the different pluses and minuses for the numerous viewpoints on controversial topics. I had to do that for play balance in China and it wasn't a fun event.

As I see it, I am providing you with the capability to play the game the way you wanted. Then you ask for more.[:-]

[Mziln]

This assumes no USA entry chits are generated or they are canceled out due to actions taken by the other players. And that you can find 10 USA entry options that you just must have before May/June 1941.

Using your example lets assume you choose an entry option every turn and 50% of all entry options move an entry chit to the tension pool. There would be 9 chits in the entry pools and 5 in the tension pools. We divide the USA pools as equally as possible

(a) 5 (entry chits) x 2.7 = 13.5 rounded to 14 the USA entry pool total would be (14 x 1.5) + 6 = 27
(b) 4 (entry chits) x 2.7 = 10.8 rounded to 11 the USA entry pool total would be (11 x 1.5) + 7 = 23.5

(a) 3 (tension chits) x 2.7 = 8.1 rounded to 8
(b) 2 (tension chits) x 2.7 = 5.4 rounded to 5

This gives no chance of a DoW. Unless option 34 has been selected.

On the other hand if all the entry and tension pools are directed at a single major power.

The USA entry pool total would be (9 (entry chits) x 2.7) x 1.5 = 36
The USA tension pool total would be (5 (tension chits) x 2.7) x 1.5 = 21

This gives a chance for a DoW of 40% against Japan or of 30% against Germany/Italy. Since option 34 could have been selected.

Patrice correct me if I am wrong [8|]

[hakon]

Jan:

The variance introduced from using fixed distributions really depends on those distributions. Particularily important is how/whether the distribution takes into account chits remaining in the pool from the year before. 1939 chits are way higher than 1940 chits, so creating a distribution for 1940 based solely on the 1940 chits will actually _reduce_ the variance by quite a bit during that critical year, and will also bias the total chit numbers, so that option 22 is likely to come late. The same goes in 1941 - the variance will be lower than when using mixed pools. Note that the BIAS in 1941 will point upwards a bit, so the total bias at the end of 1941 should be quite small.

The variance of the tension chits will remain as high as ever, though this is less important, IMO, as the US can adjust the number of entry actions according to draws.

Mziln:
Remeber that option 34 requires that both your entry/tension values are at least 34/17 IN BOTH POOLS. Since option 34 is the key to the US production gearing for the rest of the game, this is the number of critical importance. Most US players will aim at reaching this option as early as at all possible, and all other actions are taken primarlily to have JUST THE RIGHT tension level to take option 34 as early as possible. The exact turn that the US can declare war, matters much, much less.

Assuming an average value on the chits of 2.3, taking option 34 is optimized by having 8/8 chits int the entry pools and 4/4 in the tension pools, for a total of 24 chits.

My experience is that the average time for this to happen is during the 41/42 winter, but it depends a lot on lucky draws (getting a 5 instead of a 0 means you just won 2 turns), as well as the agression level of both sides.

As an illustration: Getting option 34 in mar/apr of 41 (which I have seen a few times) means that 5/6 turns EVERY YEAR, the US will get about 11 BP more than if option 34 comes in jan/feb of jan/feb of 1942 (which is average). This is 55bp a year for almost 5 years (for a total of about 230bp), and it usually also means that option 22 was taken early (an extra 50bp). In addition to this, total war tends to happen about 5 turns earlier in this scenario (another 50). In total, this means that the US all game income will be more than 300bp ABOVE AVERAGE.

In fact, each turn to or from means another 60 build points, so the difference between drawing a 5 and a 0 is about 120bp.....

Steve:
I understand your reluctance to making non RAW optional rules. My suggestions were just meant as proposals, based on my personal experience (as well as calculations). If they are not backed by your own experience or that of a large majority of the existing player community, I agree that you are probably better off ignoring them. As you point out, I can always modify the CSV files.

[c92nichj]

Mziln I am not following what you are trying to say in your post.

For me it looks very unlikely that option 34 have been choosen by M/J '41.

With somewhat normal play you would have:
6 '39 chits(AVG 2.3) (1 chit from axis agression)
9 '40 chits (AVG1.3) (3 chits from axis agression)
5 '41 chits (AVG 3.5) (2 chits from axis agression)

A Total chit value of ~ 43.
You would need to have 51 in chit value optimally distributed to be able to take option 34, that would happen closer to ND '41 which is what it usually end up in the games I havbe been playing as well.

[c92nichj]

Getting option 34 in mar/apr of 41 (which I have seen a few times)

This must have been coupled with a fair level of axis agression.
Someone did a calculation on the yahoo wiflist a while ago and the chance of wierd USE result was way below 5%

[JanSorensen]

ORIGINAL: hakon
Jan:

The variance introduced from using fixed distributions really depends on those distributions. Particularily important is how/whether the distribution takes into account chits remaining in the pool from the year before. 1939 chits are way higher than 1940 chits, so creating a distribution for 1940 based solely on the 1940 chits will actually _reduce_ the variance by quite a bit during that critical year, and will also bias the total chit numbers, so that option 22 is likely to come late. The same goes in 1941 - the variance will be lower than when using mixed pools. Note that the BIAS in 1941 will point upwards a bit, so the total bias at the end of 1941 should be quite small.

You bring up a good point - namely which fixed distribution to use in years after 1939. Knowing how much Steve already posted I have a feeling he may have revealed that already but I do not recall seeing it. Maybe someone can point to the post is one exists - or deny that it has been posted yet in which case Steve might be pursuaded to do so.

Once the exact details are known I would like to run some simulations (millions atleast) to determine what the difference between the finite pool given by the chits and the infinite pool will be for various important thresholds both for mean and variance. I have a gut feeling that the variance will still be somewhat larger with the infinite pools nomatter which way earlier years are included (or not included). Its definitely not given that the variance will be lower - but only simulations (or closed form calculation) of the statistics will tell.

[hakon]

ORIGINAL: c92nichj

Mziln I am not following what you are trying to say in your post.

For me it looks very unlikely that option 34 have been choosen by M/J '41.

With somewhat normal play you would have:
6 '39 chits(AVG 2.3) (1 chit from axis agression)
9 '40 chits (AVG1.3) (3 chits from axis agression)
5 '41 chits (AVG 3.5) (2 chits from axis agression)

A Total chit value of ~ 43.
You would need to have 51 in chit value optimally distributed to be able to take option 34, that would happen closer to ND '41 which is what it usually end up in the games I havbe been playing as well.

Patrice has a game report on his site where option 34 was taken in jan/feb 41 (if I am not mistaken). The earliest I have seen, is mar/apr, which I have seen twice in my 5 FE games. The other results I have seen, are may/june 41, jul/aug 41 and may/june 42. (I was the US in that last one).

Two out of those 5 games were decided almost solely by US entry, while two of the early-entry games were decided by USSR knock-out before the US really could bring his economy to bear. The last game (the late entry one) was decided by poor axis play (a combination of a failed eastern front as well as an under-garrisoned italy, which was conquered in early 1943).

[hakon]

ORIGINAL: JanSorensen

ORIGINAL: hakon
Jan:

The variance introduced from using fixed distributions really depends on those distributions. Particularily important is how/whether the distribution takes into account chits remaining in the pool from the year before. 1939 chits are way higher than 1940 chits, so creating a distribution for 1940 based solely on the 1940 chits will actually _reduce_ the variance by quite a bit during that critical year, and will also bias the total chit numbers, so that option 22 is likely to come late. The same goes in 1941 - the variance will be lower than when using mixed pools. Note that the BIAS in 1941 will point upwards a bit, so the total bias at the end of 1941 should be quite small.

You bring up a good point - namely which fixed distribution to use in years after 1939. Knowing how much Steve already posted I have a feeling he may have revealed that already but I do not recall seeing it. Maybe someone can point to the post is one exists - or deny that it has been posted yet in which case Steve might be pursuaded to do so.

Once the exact details are known I would like to run some simulations (millions atleast) to determine what the difference between the finite pool given by the chits and the infinite pool will be for various important thresholds both for mean and variance. I have a gut feeling that the variance will still be somewhat larger with the infinite pools nomatter which way earlier years are included (or not included). Its definitely not given that the variance will be lower - but only simulations (or closed form calculation) of the statistics will tell.

It is hard to say which effect is bigger, and it also depends a bit on whether you use the AfA counters or not.

[Shannon V. OKeets]

ORIGINAL: JanSorensen

ORIGINAL: hakon
Jan:

The variance introduced from using fixed distributions really depends on those distributions. Particularily important is how/whether the distribution takes into account chits remaining in the pool from the year before. 1939 chits are way higher than 1940 chits, so creating a distribution for 1940 based solely on the 1940 chits will actually _reduce_ the variance by quite a bit during that critical year, and will also bias the total chit numbers, so that option 22 is likely to come late. The same goes in 1941 - the variance will be lower than when using mixed pools. Note that the BIAS in 1941 will point upwards a bit, so the total bias at the end of 1941 should be quite small.

You bring up a good point - namely which fixed distribution to use in years after 1939. Knowing how much Steve already posted I have a feeling he may have revealed that already but I do not recall seeing it. Maybe someone can point to the post is one exists - or deny that it has been posted yet in which case Steve might be pursuaded to do so.

Once the exact details are known I would like to run some simulations (millions atleast) to determine what the difference between the finite pool given by the chits and the infinite pool will be for various important thresholds both for mean and variance. I have a gut feeling that the variance will still be somewhat larger with the infinite pools nomatter which way earlier years are included (or not included). Its definitely not given that the variance will be lower - but only simulations (or closed form calculation) of the statistics will tell.

Ok.

But I am not explaining this code. If you know what these numbers should be, you will understand them.

In the first comment the 4 is what CWIF used. The 3 is the correction I made based on looking at the uncut countersheets from WIF FE and Africa Aflame. I am virtually certain that this code is correct - I have checked it 5 times.

================
function PickEntryChit(Year: Integer = 0): Byte;
begin
if Year = 0 then Year := TimeDate.Date.Year; // Default: use the current year

ChitYear := Year;

case Year of
1939:
begin
case RollX(rsEntryChit, 0, TEntryChitRoll.HighRoll, nil, nil,
TEntryChitRoll.RollRange) of
0..2: Result := 0; // 4 3

3..9: Result := 1; // 6 7

10..16: Result := 2; // 6 7

17..22: Result := 3; // 7 6

23..28: Result := 4; // 5 6

else Result := 5; // 2 1 (29)
end;
end;

1940:
begin
case RollX(rsEntryChit, 0, TEntryChitRoll.HighRoll, nil, nil,
TEntryChitRoll.RollRange) of
0..8: Result := 0; // 12 6

9..23: Result := 1; // 12 8

24..35: Result := 2; // 11 5

36..44: Result := 3; // 10 3

45..51: Result := 4; // 6 1

else Result := 5; // 2 1 (52)
end;
end;

1941:
begin
case RollX(rsEntryChit, 0, TEntryChitRoll.HighRoll, nil, nil,
TEntryChitRoll.RollRange) of
0..8: Result := 0; // 12 0

9..24: Result := 1; // 13 1

25..39: Result := 2; // 14 3

40..52: Result := 3; // 14 4

53..62: Result := 4; // 9 3

63..66: Result := 5; // 5 3

else Result := 6; // 1 1 (67)
end;
end;

1942:
begin
case RollX(rsEntryChit, 0, TEntryChitRoll.HighRoll, nil, nil,
TEntryChitRoll.RollRange) of
0..8: Result := 0; // 12 0

9..24: Result := 1; // 13 0

25..40: Result := 2; // 15 1

41..56: Result := 3; // 17 3

57..70: Result := 4; // 13 4

71..78: Result := 5; // 9 4

else Result := 6; // (79..81) 3 2
end;
end;

else
begin // 1943 +
case RollX(rsEntryChit, 0, TEntryChitRoll.HighRoll, nil, nil,
TEntryChitRoll.RollRange) of
0..8: Result := 0; // 12 0

9..24: Result := 1; // 13 0

25..40: Result := 2; // 15 0

41..57: Result := 3; // 18 1

58..73: Result := 4; // 15 2

74..85: Result := 5; // 13 4

else Result := 6; // (86..93) 8 5
end;
end;
end;
end;

class function TEntryChitRoll.HighRoll: Byte;
// # of chits to randomly select from
begin
case ChitYear of
1939: Result := 29;

1940: Result := 52;

1941: Result := 67;

1942: Result := 81;

else Result := 93; // 1943 +
end;
end;

[hakon]

The way I interpret the code, is as follows:

All draws are made as if no draws had been made before, using all chit that would have been available up until that time.

The consequence of this, is that average chit value per year, is as follows (using my excel sheet of chits, there could be some minor mistake there):

1939: 2.26
1940: 1.87
1941: 2.22
1942: 2.56

There is a net bias to this, coming from the fact that old chits can be re-picked any number of times, while with limited chits, you would be more likely to draw 1941-chits in 1942. This is not in itself a bad thing.

The most important issue with this way of drawing, is that it maximizes variance, as in 1941 you can draw anything from 0 to 6. (The difference being almost 3 turns for when option 34 can be taken, meaning a difference of up to about 180build points for a single chit).

It would be fun to create a simmulation using the described algorithm, paired with a given set of actions, to see how big variance one can expect on option 34. (A rough guess would be a std dev of about 2 turns.)

[JanSorensen]

@Steve,

Thank you, that was most helpful.

@Hakon,

I havent played WiF in quite a number of years but if you can specify a number of actions with their effect on chits and in detail whats needed in terms of drawn chits to pick option 34 I will see about doing the simulations.

[JanSorensen]

Steve,

Should the '1' not be a '0' in this line? Otherwise the rest does not make sense.

Code: Select all

else Result := 5; // 2 1 (52)

I would probably have used an array rather than the case structure as I find that easier to adjust as well as verify but thats obviously a matter of personal taste. Something like:

Code: Select all

	{6,				// 1941 chits
 	 5,5,5,			
 	 4,4,4,
 	 3,3,3,3,
 	 2,2,2,1,
 	 5,				// 1940 chits, the 5 is suspect
 	 4,
 	 3,3,3,
 	 2,2,2,2,2,
 	 1,1,1,1,1,1,1,1,
 	 0,0,0,0,0,0,
 	 5,				// 1939 chits
 	 4,4,4,4,4,4,
 	 3,3,3,3,3,3,
 	 2,2,2,2,2,2,2,
 	 1,1,1,1,1,1,1,
 	 0,0,0};

Maybe someone with the counters can confirm or deny the '5' in 1940.

[Shannon V. OKeets]

ORIGINAL: JanSorensen
Steve,

Should the '1' not be a '0' in this line? Otherwise the rest does not make sense.

Code: Select all

else Result := 5; // 2 1 (52)

I would probably have used an array rather than the case structure as I find that easier to adjust as well as verify but thats obviously a matter of personal taste. Something like:

Code: Select all

	{6,				// 1941 chits
 	 5,5,5,			
 	 4,4,4,
 	 3,3,3,3,
 	 2,2,2,1,
 	 5,				// 1940 chits, the 5 is suspect
 	 4,
 	 3,3,3,
 	 2,2,2,2,2,
 	 1,1,1,1,1,1,1,1,
 	 0,0,0,0,0,0,
 	 5,				// 1939 chits
 	 4,4,4,4,4,4,
 	 3,3,3,3,3,3,
 	 2,2,2,2,2,2,2,
 	 1,1,1,1,1,1,1,
 	 0,0,0};

Maybe someone with the counters can confirm or deny the '5' in 1940.

The comment is wrong, but not the code.

This is a much cleaned up version of what I inherited. The original had no comments and no spacing. I avoid rewriting whole sections of functioning code unless there is a pressing need. Just in case you missed it, I inherited 100,000 lines of code without comments. This routine is truly trivial by comparison to almost any of the other sections of code I am modifying.

[JanSorensen]

Gotcha, thanks for the reply. The only reason I bothered mentioning the alternative approach was that you said you had checked this section 5 times

[JanSorensen]

I just ran a simulation of finite vs infinite pools. I used the case mentioned by c92nichj picking 6x39 chits, 9x40 chits and 5x41 chits noting the sum of the chits drawn but not the composition. I used 10 million iterations for each case.

The raw data are shown below. I prefer to provide the raw data so people can do their own analysis.

As can be seen the variance in the infinite case is far greater than the variance in the finite case. Getting a sum of 55+ is roughly 3 times as likely in the infinite case for example (1.8% vs 0.5%). The means are about the same though - so at this particular point there is little bias.

I stand by my earlier comment though that I find it puzzling that Harry Rowland wants to increase the variance compared to the board game - and by this much.

Code: Select all

Sum	Infinite	Finite
 11	1	0
 12	0	0
 13	6	0
 14	7	0
 15	34	0
 16	42	0
 17	97	0
 18	223	2
 19	515	16
 20	1042	39
 21	1946	136
 22	3591	338
 23	6262	823
 24	10688	1802
 25	17186	3901
 26	27476	7615
 27	41598	14529
 28	61456	25951
 29	87400	43921
 30	120128	69969
 31	162099	107449
 32	210665	157835
 33	265637	220362
 34	325944	296546
 35	389533	382864
 36	451042	472133
 37	509378	561550
 38	560771	641518
 39	600623	707812
 40	627526	749960
 41	636507	767915
 42	632374	756646
 43	613818	720676
 44	578649	660081
 45	532386	583324
 46	477171	498752
 47	418864	411131
 48	358794	325421
 49	298407	250690
 50	243863	185473
 51	193415	131654
 52	150468	89809
 53	114225	59640
 54	83884	38273
 55	60448	23283
 56	42359	13857
 57	29108	7845
 58	19388	4294
 59	12845	2208
 60	7981	1061
 61	5035	500
 62	3067	248
 63	1814	91
 64	1028	36
 65	580	11
 66	287	3
 67	152	2
 68	92	3
 69	41	0
 70	25	2
 71	4	0
 72	3	0
 73	0	0
 74	1	0
 75	1	0

[Shannon V. OKeets]

ORIGINAL: JanSorensen

Gotcha, thanks for the reply. The only reason I bothered mentioning the alternative approach was that you said you had checked this section 5 times

I double checked the counter mix for the chits mostly. That was because when I checked what CWIF was using, I found major differences.

The victory hexes were perfect.

There were only a handful of counter errors (out of 3000+ counters with 4 or more numbers per counter).

Map mistakes are still being unearthed as I write this.

I tend to check everything, including code I have written ("What was I thinking when I wrote that?").