Rounding up?

[Cheesehead]

My apologies if this has been addressed, but this question has been bantied about on the WiF list and I was wondering how Steve plans to handle it. How will an odd numbered reorg value be interpreted when rounding up for defensive HQ support? The math wizards out there have made the case that correctly rounding up means that Mao (for example) only gives you a -1 modifier unless there is a +.5 offensive mod that he can reduce. For example: Japan makes a simple 5-1 attack with no flips, no offensive HQ support or any aother modifiers at +10 on the 2D10 system. According to the mathematicians, Mao throwing in defensive HQ support would only reduce the attack to +9 since rounding "up" in this case goes from -1.5 "up" to -1. This is counter-intuitive to many of us, although I acknowledge that it is mathematically correct. I've also seen this rounding issue brought up in air combat. How will MWiF handle this?

Thanks

John

[Shannon V. OKeets]

ORIGINAL: Cheesehead

My apologies if this has been addressed, but this question has been bantied about on the WiF list and I was wondering how Steve plans to handle it. How will an odd numbered reorg value be interpreted when rounding up for defensive HQ support? The math wizards out there have made the case that correctly rounding up means that Mao (for example) only gives you a -1 modifier unless there is a +.5 offensive mod that he can reduce. For example: Japan makes a simple 5-1 attack with no flips, no offensive HQ support or any aother modifiers at +10 on the 2D10 system. According to the mathematicians, Mao throwing in defensive HQ support would only reduce the attack to +9 since rounding "up" in this case goes from -1.5 "up" to -1. This is counter-intuitive to many of us, although I acknowledge that it is mathematically correct. I've also seen this rounding issue brought up in air combat. How will MWiF handle this?

Thanks

John

The pertinent lines of code follow. DRM is a cumulative Extended (real) value for all die roll modifiers, including HQ bonuses. The first two lines of code convert it into an integer value by calling the Round function given below.
========================

if OptRules.TwoD10LandCRT then DieRollMod := Range(Util.Round(DRM), -21, 21)
else DieRollMod := Util.Round(DRM);

========================

function Round(const E: Extended): Longint;
begin
if Frac(E) = 0.5 then
Result := Trunc(E) + 1
else if Frac(E) = -0.5 then
Result := Trunc(E) - 1
else
Result := System.Round(E);
end;

========================

Just in case you can't read code, this says that when the fractional part is -1/2, convert the value to -1. If it is +1/2, convert it to +1. At all other times convert the real value to the closest integer number.

[Ullern]

ORIGINAL: Shannon V. OKeets

ORIGINAL: Cheesehead

My apologies if this has been addressed, but this question has been bantied about on the WiF list and I was wondering how Steve plans to handle it. How will an odd numbered reorg value be interpreted when rounding up for defensive HQ support? The math wizards out there have made the case that correctly rounding up means that Mao (for example) only gives you a -1 modifier unless there is a +.5 offensive mod that he can reduce. For example: Japan makes a simple 5-1 attack with no flips, no offensive HQ support or any aother modifiers at +10 on the 2D10 system. According to the mathematicians, Mao throwing in defensive HQ support would only reduce the attack to +9 since rounding "up" in this case goes from -1.5 "up" to -1. This is counter-intuitive to many of us, although I acknowledge that it is mathematically correct. I've also seen this rounding issue brought up in air combat. How will MWiF handle this?

Thanks

John

The pertinent lines of code follow. DRM is a cumulative Extended (real) value for all die roll modifiers, including HQ bonuses. The first two lines of code convert it into an integer value by calling the Round function given below.
========================

if OptRules.TwoD10LandCRT then DieRollMod := Range(Util.Round(DRM), -21, 21)
else DieRollMod := Util.Round(DRM);

========================

function Round(const E: Extended): Longint;
begin
if Frac(E) = 0.5 then
Result := Trunc(E) + 1
else if Frac(E) = -0.5 then
Result := Trunc(E) - 1
else
Result := System.Round(E);
end;

========================

Just in case you can't read code, this says that when the fractional part is -1/2, convert the value to -1. If it is +1/2, convert it to +1. At all other times convert the real value to the closest integer number.

This is no case of math wizard. It's plain rules. There is no such thing as a common math rules in WIF. WIF defines it's own rounding laws:

ORIGINAL: WIF RAW 7 AUG 2004
2.6 Fractions
These rules frequently require a calculation that produces a fraction. When you have to do this, round to the nearest whole number, rounding halves up.
Example: Germany has 21 production points. Her production multiple is 1.25, so she has 26.25 build points. This rounds to 26 points. Next year her production multiple increases to 1.5, so she has 31.5 build points. This rounds to 32.
Rounding a negative number up moves you closer to zero. For example, if the fraction is -1.5, it rounds to -1.
Round off a number immediately before:

• calculating an odds ratio; or
• looking the number up in a table; or
• comparing it to a dice roll or to a fixed value; or
• spending oil (see 13.5.1) or build points.

Example: In an attack, you have 3 units attacking across a river. Their total strength is 17, which halves to 8.5. In addition, you add in 8.5 factors of shore bombardment. You also commit a CV with an air component of 5 as ground support. Its tactical factors are 2.5. Your total attack strength is 19.5. As you are about to calculate an odds ratio, you round it to the nearest whole number ~ 20.

I belive this means Steve have to change his round of method.

[Shannon V. OKeets]

ORIGINAL: ullern

ORIGINAL: Shannon V. OKeets

ORIGINAL: Cheesehead

My apologies if this has been addressed, but this question has been bantied about on the WiF list and I was wondering how Steve plans to handle it. How will an odd numbered reorg value be interpreted when rounding up for defensive HQ support? The math wizards out there have made the case that correctly rounding up means that Mao (for example) only gives you a -1 modifier unless there is a +.5 offensive mod that he can reduce. For example: Japan makes a simple 5-1 attack with no flips, no offensive HQ support or any aother modifiers at +10 on the 2D10 system. According to the mathematicians, Mao throwing in defensive HQ support would only reduce the attack to +9 since rounding "up" in this case goes from -1.5 "up" to -1. This is counter-intuitive to many of us, although I acknowledge that it is mathematically correct. I've also seen this rounding issue brought up in air combat. How will MWiF handle this?

Thanks

John

The pertinent lines of code follow. DRM is a cumulative Extended (real) value for all die roll modifiers, including HQ bonuses. The first two lines of code convert it into an integer value by calling the Round function given below.
========================

if OptRules.TwoD10LandCRT then DieRollMod := Range(Util.Round(DRM), -21, 21)
else DieRollMod := Util.Round(DRM);

========================

function Round(const E: Extended): Longint;
begin
if Frac(E) = 0.5 then
Result := Trunc(E) + 1
else if Frac(E) = -0.5 then
Result := Trunc(E) - 1
else
Result := System.Round(E);
end;

========================

Just in case you can't read code, this says that when the fractional part is -1/2, convert the value to -1. If it is +1/2, convert it to +1. At all other times convert the real value to the closest integer number.

This is no case of math wizard. It's plain rules. There is no such thing as a common math rules in WIF. WIF defines it's own rounding laws:

ORIGINAL: WIF RAW 7 AUG 2004
2.6 Fractions
These rules frequently require a calculation that produces a fraction. When you have to do this, round to the nearest whole number, rounding halves up.
Example: Germany has 21 production points. Her production multiple is 1.25, so she has 26.25 build points. This rounds to 26 points. Next year her production multiple increases to 1.5, so she has 31.5 build points. This rounds to 32.
Rounding a negative number up moves you closer to zero. For example, if the fraction is -1.5, it rounds to -1.
Round off a number immediately before:

• calculating an odds ratio; or
• looking the number up in a table; or
• comparing it to a dice roll or to a fixed value; or
• spending oil (see 13.5.1) or build points.

Example: In an attack, you have 3 units attacking across a river. Their total strength is 17, which halves to 8.5. In addition, you add in 8.5 factors of shore bombardment. You also commit a CV with an air component of 5 as ground support. Its tactical factors are 2.5. Your total attack strength is 19.5. As you are about to calculate an odds ratio, you round it to the nearest whole number ~ 20.

I belive this means Steve have to change his round of method.

This is trivial to change (less than a minute), so that is not an issue.

I seem to recall there is something about rounding in the favor of the defender, though where I read in the rules than eludes me at the moment.

[paulderynck]

ORIGINAL: Shannon V. OKeets
This is trivial to change (less than a minute), so that is not an issue.

I seem to recall there is something about rounding in the favor of the defender, though where I read in the rules than eludes me at the moment.

You always round "up". Fine for positive numbers, but in at least one place in the RAW it is explained that FREX -1.5 rounds "up" to -1 (somewhere in air combat I think).

[paulderynck]

ORIGINAL: Cheesehead

My apologies if this has been addressed, but this question has been bantied about on the WiF list and I was wondering how Steve plans to handle it. How will an odd numbered reorg value be interpreted when rounding up for defensive HQ support? The math wizards out there have made the case that correctly rounding up means that Mao (for example) only gives you a -1 modifier unless there is a +.5 offensive mod that he can reduce. For example: Japan makes a simple 5-1 attack with no flips, no offensive HQ support or any aother modifiers at +10 on the 2D10 system. According to the mathematicians, Mao throwing in defensive HQ support would only reduce the attack to +9 since rounding "up" in this case goes from -1.5 "up" to -1. This is counter-intuitive to many of us, although I acknowledge that it is mathematically correct. I've also seen this rounding issue brought up in air combat. How will MWiF handle this?

Thanks

John

In the latest FAQ published, Question 11.16-5 illustrates the answer. You determine the number from the combat odds, then add or subtract (or both) for HQ support (along with any other modifiers) then, unless playing with fractional odds, you round the result. In this case the round up of a dot five will favor the attacker.

[bredsjomagnus]

I seem to recall there is something about rounding in the favor of the defender, though where I read in the rules than eludes me at the moment.

 
I think that that is the case when you have to flip half of youre units; if you have one suvivor it stays up, but if you have two survivors one is turned over etc.

[Shannon V. OKeets]

ORIGINAL: paulderynck

ORIGINAL: Cheesehead

My apologies if this has been addressed, but this question has been bantied about on the WiF list and I was wondering how Steve plans to handle it. How will an odd numbered reorg value be interpreted when rounding up for defensive HQ support? The math wizards out there have made the case that correctly rounding up means that Mao (for example) only gives you a -1 modifier unless there is a +.5 offensive mod that he can reduce. For example: Japan makes a simple 5-1 attack with no flips, no offensive HQ support or any aother modifiers at +10 on the 2D10 system. According to the mathematicians, Mao throwing in defensive HQ support would only reduce the attack to +9 since rounding "up" in this case goes from -1.5 "up" to -1. This is counter-intuitive to many of us, although I acknowledge that it is mathematically correct. I've also seen this rounding issue brought up in air combat. How will MWiF handle this?

Thanks

John

In the latest FAQ published, Question 11.16-5 illustrates the answer. You determine the number from the combat odds, then add or subtract (or both) for HQ support (along with any other modifiers) then, unless playing with fractional odds, you round the result. In this case the round up of a dot five will favor the attacker.

Ok. I'll correct the code so -2.5 goes to -2 when rounded; and likewise for other negative numbers.

[Shannon V. OKeets]

ORIGINAL: bredsjomagnus

I seem to recall there is something about rounding in the favor of the defender, though where I read in the rules than eludes me at the moment.

I think that that is the case when you have to flip half of youre units; if you have one suvivor it stays up, but if you have two survivors one is turned over etc.

I am pretty sure that is how it is already written, but I'll double check tomorrow.

The other case that is somewhat unusual is keeping sufficient units ('half') in the home country of minor countries. I've looked at that code and it appears correct.

[brian brian]

(1/2 of total units) + 1 can leave the country. the total units number will always be positive, with odd numbers rounded up.

1/2 of surviving attacking units do not have to flip face down on some attack results. we play that if an HQ is already flipped after using HQ support, that can be one of the units you have to flip, because of the negative clause, which implies how many units you get to leave face-up, not how many you have to flip. others may vary on that point I think.


I'm not sure I like the idea that HQ-I Chiang can't use HQ support, if -0.5 rounds "up" to 0. We play that he can add a -1 to an attack on the 2d10. I have never liked that method of working with negative numbers.

Really I'd prefer to play with "straight fractionals" and 3 dice. Simply add all combat factors and modifiers, and never round any of them. It is hard to get in to that habit after so many years of rounding things. So if a a Japanese 7-3 INF is attacking a 2-4 Chinese CAV across a river, the factors are 3.5:2, for a +3.5 attack. Then if Chiang intervenes with HQ support, it would be a +3 attack. Aside from the difficulty of remembering not to round things, the other reason this never gets off the ground for me or my regular opponent is that HQ support and combat dice luck are so critical for the Japanese, that whoever is playing the Axis is never that enthused about finally moving to that system. And once the game starts with the regular 2d10 and a fractional dice and rounding the HQ support and the factors halved for rivers, etc. from the first few combats, we just keep playing that way.

[composer99]

The rounding in the defender's favour happens when you calculate combat odds (when not using fractional odds) - e.g. a combat ratio of 4.999:1 in the attacker's favour rounds to 4:1 rather than to 5:1.
 
Though I may be wrong.

[Ullern]

ORIGINAL: composer99

The rounding in the defender's favour happens when you calculate combat odds (when not using fractional odds) - e.g. a combat ratio of 4.999:1 in the attacker's favour rounds to 4:1 rather than to 5:1.

Though I may be wrong.

No this is correct, and probably the fact that Steve was referring to. It's rule 11.16.5 under the headline Odds ratio. This is typical WIF _ that there are some exceptions hidden deep inside the rules. I believe it would have been better if this exception was written with the general rounding off rule in 2.6, but that's not how it is. It get's even more complex if you play with fractional odds optional.

[Shannon V. OKeets]

ORIGINAL: ullern

ORIGINAL: composer99

The rounding in the defender's favour happens when you calculate combat odds (when not using fractional odds) - e.g. a combat ratio of 4.999:1 in the attacker's favour rounds to 4:1 rather than to 5:1.

Though I may be wrong.

No this is correct, and probably the fact that Steve was referring to. It's rule 11.16.5 under the headline Odds ratio. This is typical WIF _ that there are some exceptions hidden deep inside the rules. I believe it would have been better if this exception was written with the general rounding off rule in 2.6, but that's not how it is. It get's even more complex if you play with fractional odds optional.

Thanks. This isn't really rounding; it is truncation. Any fractional portion is simply ignored/eliminated. I'll check the code again, but I believe this is already coded to use truncation.

Working from memory (I read through this code yesterday), the process when fractional odds are not being used starts by rounding the combat factors for the attacker and defender. Then the ratio of A:D is calculated as an Extended value (real number). The A:D ratio is compared against the odds for each column in the CRT, starting with the highest/last column. When a column is found where the A:D ratio is greater than the column odds, then that is the CRT column based on the combat factors. Die roll modifications are applied after this.

Note that there are many optional rules involved in these calculations. The primary ones are whether fractional odds are being used and whether it is 1D10 versus 2D10. But there are several others: snow bonuses, HQ support, and combat engineers. Then there is also terrain, supply, and weather. Really, the code for this is straight forward, though the bits and pieces need to be done in the right order, and there are a lot of bits and pieces.

[Froonp]

ORIGINAL: Cheesehead

My apologies if this has been addressed, but this question has been bantied about on the WiF list and I was wondering how Steve plans to handle it. How will an odd numbered reorg value be interpreted when rounding up for defensive HQ support? The math wizards out there have made the case that correctly rounding up means that Mao (for example) only gives you a -1 modifier unless there is a +.5 offensive mod that he can reduce. For example: Japan makes a simple 5-1 attack with no flips, no offensive HQ support or any aother modifiers at +10 on the 2D10 system. According to the mathematicians, Mao throwing in defensive HQ support would only reduce the attack to +9 since rounding "up" in this case goes from -1.5 "up" to -1. This is counter-intuitive to many of us, although I acknowledge that it is mathematically correct. I've also seen this rounding issue brought up in air combat. How will MWiF handle this?

This question, that was asked to Harry for the FAQ, can shed light to this issue :

*************************************************
Q11.16-5> Playing 2d10, how is HQ Support supposed to work, especially with roundings and Fractional Odds.

Example : an attack with 20 factors against 6, with a 5-reorg HQ using his support:
(a) +6.6 have 60% chance of being +7 and 40% chance of +6 then other modifications are added meaning a +3 (+2.5 rounded) for the HQ to either +9 or +10.
(b) +6.6 + 2.5 for the HQ = +9.1 have 10% chance of being +10 and 90% chance of +9.


Answer> (b), see 2.6.. Date 30/11/2007
*************************************************

[Shannon V. OKeets]

ORIGINAL: Froonp

ORIGINAL: Cheesehead

My apologies if this has been addressed, but this question has been bantied about on the WiF list and I was wondering how Steve plans to handle it. How will an odd numbered reorg value be interpreted when rounding up for defensive HQ support? The math wizards out there have made the case that correctly rounding up means that Mao (for example) only gives you a -1 modifier unless there is a +.5 offensive mod that he can reduce. For example: Japan makes a simple 5-1 attack with no flips, no offensive HQ support or any aother modifiers at +10 on the 2D10 system. According to the mathematicians, Mao throwing in defensive HQ support would only reduce the attack to +9 since rounding "up" in this case goes from -1.5 "up" to -1. This is counter-intuitive to many of us, although I acknowledge that it is mathematically correct. I've also seen this rounding issue brought up in air combat. How will MWiF handle this?

This question, that was asked to Harry for the FAQ, can shed light to this issue :

*************************************************
Q11.16-5> Playing 2d10, how is HQ Support supposed to work, especially with roundings and Fractional Odds.

Example : an attack with 20 factors against 6, with a 5-reorg HQ using his support:
(a) +6.6 have 60% chance of being +7 and 40% chance of +6 then other modifications are added meaning a +3 (+2.5 rounded) for the HQ to either +9 or +10.
(b) +6.6 + 2.5 for the HQ = +9.1 have 10% chance of being +10 and 90% chance of +9.


Answer> (b), see 2.6.. Date 30/11/2007
*************************************************

This is how it is coded in MWIF.

[paulderynck]

ORIGINAL: brian brian


1/2 of surviving attacking units do not have to flip face down on some attack results. we play that if an HQ is already flipped after using HQ support, that can be one of the units you have to flip, because of the negative clause, which implies how many units you get to leave face-up, not how many you have to flip. others may vary on that point I think.

I would not agree to that. Somewhere there's a clarification that if you flip due to advancing into terrain that exceeds your movement factor, then you can't count that towards the number of attackers that flip. By the same token, if you are going to flip anyway due to HQ support, then the half-flip result should be applied to the units remaining face-up.

Since half the remaining units are not turned face-down (per the 2D10 notes), the rounding in this case works in favor of the attacker.

[Froonp]

ORIGINAL: paulderynck

ORIGINAL: brian brian


1/2 of surviving attacking units do not have to flip face down on some attack results. we play that if an HQ is already flipped after using HQ support, that can be one of the units you have to flip, because of the negative clause, which implies how many units you get to leave face-up, not how many you have to flip. others may vary on that point I think.

I would not agree to that. Somewhere there's a clarification that if you flip due to advancing into terrain that exceeds your movement factor, then you can't count that towards the number of attackers that flip. By the same token, if you are going to flip anyway due to HQ support, then the half-flip result should be applied to the units remaining face-up.

Since half the remaining units are not turned face-down (per the 2D10 notes), the rounding in this case works in favor of the attacker.

This is simple.
"Facing" is the very last item of the land combat sequence (11.16.5).
It is placed after "Advancing after combat", so unit that flipped face-down due to "advance after combat" is face-down during the "facing" step. So it does not count in the "remaining face up units".

The steps within 11.16.5 Land Combat are :
- Choosing combat tables
- Odds ratios
- Rolling dice
- Results
- Retreats
- Shatter
- Advancing after combat
- Facing

Example :
6 units attack.
One of them is a HQ that uses its HQ support.
Half flip result occurs.
2 units advance after combat in the vacated enemy hex, 1 of them flips due to having not enought movement points.
There are 4 remaining units, 2 are kept face-up (2 are flipped face-down).

6 units attack.
One of them is a HQ that uses its HQ support.
Half flip result occurs.
2 units advance after combat in the vacated enemy hex, both of them flip due to having not enought movement points.
There are 3 remaining units, 2 are kept face-up (1 are flipped face-down).

[brian brian]

as I said, I have suspected we played it differently. I don't think I've ever looked at explicit combat sequence steps to figure it out.

[Shannon V. OKeets]

ORIGINAL: Froonp

ORIGINAL: paulderynck

ORIGINAL: brian brian


1/2 of surviving attacking units do not have to flip face down on some attack results. we play that if an HQ is already flipped after using HQ support, that can be one of the units you have to flip, because of the negative clause, which implies how many units you get to leave face-up, not how many you have to flip. others may vary on that point I think.

I would not agree to that. Somewhere there's a clarification that if you flip due to advancing into terrain that exceeds your movement factor, then you can't count that towards the number of attackers that flip. By the same token, if you are going to flip anyway due to HQ support, then the half-flip result should be applied to the units remaining face-up.

Since half the remaining units are not turned face-down (per the 2D10 notes), the rounding in this case works in favor of the attacker.

This is simple.
"Facing" is the very last item of the land combat sequence (11.16.5).
It is placed after "Advancing after combat", so unit that flipped face-down due to "advance after combat" is face-down during the "facing" step. So it does not count in the "remaining face up units".

The steps within 11.16.5 Land Combat are :
- Choosing combat tables
- Odds ratios
- Rolling dice
- Results
- Retreats
- Shatter
- Advancing after combat
- Facing

Example :
6 units attack.
One of them is a HQ that uses its HQ support.
Half flip result occurs.
2 units advance after combat in the vacated enemy hex, 1 of them flips due to having not enought movement points.
There are 4 remaining units, 2 are kept face-up (2 are flipped face-down).

6 units attack.
One of them is a HQ that uses its HQ support.
Half flip result occurs.
2 units advance after combat in the vacated enemy hex, both of them flip due to having not enought movement points.
There are 3 remaining units, 2 are kept face-up (1 are flipped face-down).

I am sure you took this from RAC (or RAW) but there are a few items missing from your list:

Defections (i.e., Vichy French units), converting shattered results to retreats, destroying units due to overstacking after retreats, and destroying units due to violation of foreign troop commitments after retreats.

Instead of 'facing' I prefer 'disorganize units'. No units become organized as a result of combat; the only possible change is for them to become disorganized.

[Froonp]

ORIGINAL: Shannon V. OKeets
I am sure you took this from RAC (or RAW) but there are a few items missing from your list:

Defections (i.e., Vichy French units), converting shattered results to retreats, destroying units due to overstacking after retreats, and destroying units due to violation of foreign troop commitments after retreats.

Right, I took that from 11.16.5.

Also, I wanted to add that if in case there was AA units that fired at enemy Ground Supporting missions and then attacked, that these were turned face-down after Advancing after combat (see 22.4.2) (like Supporting HQ -- see 11.16.3).

So, if I take my previous example and add a AA unit that becomes :

Example :
6 units attack.
One of them is a HQ that uses its HQ support to support the attack.
Another one is a AA unit that fires at enemy Ground Support Missions.
Half flip result occurs.
2 units advance after combat in the vacated enemy hex and stay face-up because they have enough movement points to advance.
There are 4 remaining face-up units, 2 are kept face-up (2 are flipped face-down).

6 units attack.
One of them is a HQ that uses its HQ support to support the attack.
Another one is a AA unit that fires at enemy Ground Support Missions.
Half flip result occurs.
2 units advance after combat in the vacated enemy hex, 1 of them flips due to having not enought movement points.
There are 3 remaining face-up units, 2 are kept face-up (1 is flipped face-down).

6 units attack.
One of them is a HQ that uses its HQ support to support the attack.
Another one is a AA unit that fires at enemy Ground Support Missions.
Half flip result occurs.
2 units advance after combat in the vacated enemy hex, both of them flip due to having not enought movement points.
There are 2 remaining face-up units, 1 is kept face-up (1 is flipped face-down).