The IPC value of being the attacker

[Fillmore]

After making a post in the AA42 German strategy thread where I mentioned the value of using subs as a cheap way to see the first round of a battle where the odds are against you I used an AA42 dice calc to see what the value of the SZ10 attack was, then I thought to use it to see what the value of being the attacker was in that battle and found that it was over 10% and thus significant.

In case you had not thought about it, using those dice calcs to evaluate the net IPC expectation of an attack does not yield the correct results in cases where the attacker can intelligently withdraw from battle; the ability to do that is significant.

The standard calculation is that attacking SZ2 with bomb+fighter has an expected value of +7.4IPC; the flaw with this calcualtion is that it assumes the attacker is always fighting to the end no matter what. It turns out that the ability to withdraw after a bad first round (note that if everyone misses in the first round then statistically you can just count the second round as the firwst round i.e. when I say the first round I mean the first round in which any side makes any hits) significantly improves the expected value of the bet (being well versed in poker I tend to think of attacks as bets and IPCs as money, so in my mind I am calculating the expected value of the bets).

By my calculations the play in question actually has an IPC value of +8.19. How I get this is by noting that 1 time in 9 neither plane will hit, but the BB will hit the fighter; the standard calculation assumes the attacker will continue the fight in this case, but in fact he should not. Having a single bomber attacking a BB + transport has a net expected value of -7.06 and so it is a bet that should not be made; the attacker should just retreat at this point. Since this occurs slightly more than 1/9 I calculate that retreating in this case saves .79IPC in value overall. Why slightly more than 1/9 you ask? 1/18 noone hits first round, and then 1/9 of those are also situations where you gain IPC by retreating so I added those in (its not much but it makes it 8.19 rather than 8.184 which I would round down to 8.18).

It is a rare situation, but it seems to me it is one which can come into play in this game, where a battle that has a net -IPC expectation can have a net +ICP expectation if you account for the ability of the attacker to withdraw from an undesireable first round. I think people are sort of familiar with the result of this calculation when also accounting for the value of territory because most people seem to understand that attacking a single infantry with 2 infantry is a slightly good play. If you account for the future value of a territory which cannot or will not be recaptured anytime soon it can be a fairly large expected value (like the UK1 attack on New Guinea).

Finally, talking about recapture, don't forget to include the expected value of casualties inflicted when the opponent retakes the territory you just took. As an example many Russian players will evacuate Karelia and Archangel allowing the German tank to blitz through and take them both. You might think that is a negative play since Germany is gaining 4IPC for only 1 turn while surely losing the tank which costs 5IPC; the thing is that in retaking Archangel the Russians will lose a 3IPC infantry 1/2 the time, so by my calculation the play has at least a net +.5IPC expectation (and if you are not playing LL and Russia attackes the lone tank with less that overwhelming force it could be worth more).

[bb82]

Nice post. Yeah, there are a lot of factors to consider when making your in-game choices. And rarely does IPC account for many other important factors such as position of units on the board and your overall game plan. Kind of like with looking at raw stats. It can get real complicated quickly and doesn't tell the whole story. It may even be an entirely different story for each person.

(being well versed in poker I tend to think of attacks as bets and IPCs as money, so in my mind I am calculating the expected value of the bets).

I like this analogy. But ICPs are only part of the story in regular dice games.

[ace15]

The problem with your German tank running through to Archangel scenario is that Karelia will have to be staffed by a German unit to prevent Russia from taking doing damage to Norway or just regaining the territory for free. This reduces your value to 0 points if the German tank kills an infantry during the R2 counter. It also takes a front line tank out of play at a time when it might be sorely needed. The Russian counter in Archangel will probably use new purchases from R1 that will not be needed to defend the front lines on R2 (dead zones), and use an unexposed armor or two to support the attack. When I am the Russians, I like to see the Archangel blitz on G1 as I am sure most experienced players do.

However, the rest of your essay is well written and I enjoyed the read. Thanks for posting it.

[Fillmore]

I generally stack Norway so no worries about Russians attacking it (I''ll trade my inf for their tanks any time). I don't care if Russia takes Karelia for free, I took it AND Archangel for the cost of 1 tank and Russia had to pay to kill the tank. I have never been a situation where I thought "oh man, if only I still had that tank I sent to Archangel".

Back on my opriginal subject I have also thought about the notion of IPC gain per IPC bet, rather than net IPC advantage, as a potenital measure of plays in certain circumstances. Russia for example is not in a position where they can afford to make a lot of big bets even if they have positive expextation; using a poker analogy it is as though they are playing with a short stack (i.e. a small bankroll for the size of game they are in).

[Sarten]

I like the rest of your post Fillmore, but you are overvaluing the value of that tank move. You really need to think of it this way - you are going to be getting Karelia and it's 2 ipc no matter what. Either you blitz through and back with a tank, drop an infanty on there or stack it - all three scenarios net you the 2 ipc free - your additional tank to archangel does not add to that in any way. So the actual scenario is 2 ipcs from archangel + 50% chance of killing an infantry (in most cases Russia can retake Karelia and therefore any armor assets sent to Archangel will not be exposed to a counter and even if that is not the case it gets into normal trading of territory ipc expected values).

So your net from the tank to Archangel is 3.5 ipcs versus an expect loss of 5 ipcs. That's not to say this should never be done. For instance if you are stacking karelia and also trading ukraine, bel, and archangel, and russia only has two fighters, then it may well be worth it to make Russia expose either armor or artillery to retaliation, but that becomes a different value proposition than the one you were discussing earlier.

Just my two cents - but hey I'm just newly returned to A&A revised and absolute beginner at A&A 42 so take anything I say with a grain of salt.

[Fillmore]

Ahh, I see your point; I had neglected the blitz through and back of Karlelia without occupying. I would still nitpick with your evaluation; the move all the way to Arch still has a net value of +.5 (4 + 1.5 - 5), not -1.5 as your math would imply. What I had missed was that the blitz in and out has a net value of +2.0, which makes it a net +1.5 better than the move to Arch. It is not that I overvalue the move to Arch, it is that I failed to see an alternative move with the same tank that had a better value.

[rockismyreligion]

The problem with your German tank running through to Archangel scenario is that Karelia will have to be staffed by a German unit to prevent Russia from taking doing damage to Norway or just regaining the territory for free. This reduces your value to 0 points if the German tank kills an infantry during the R2 counter. It also takes a front line tank out of play at a time when it might be sorely needed. The Russian counter in Archangel will probably use new purchases from R1 that will not be needed to defend the front lines on R2 (dead zones), and use an unexposed armor or two to support the attack. When I am the Russians, I like to see the Archangel blitz on G1 as I am sure most experienced players do.

However, the rest of your essay is well written and I enjoyed the read. Thanks for posting it.

I agree.

[Sarten]

Ahh, I see your point; I had neglected the blitz through and back of Karlelia without occupying. I would still nitpick with your evaluation; the move all the way to Arch still has a net value of +.5 (4 + 1.5 - 5), not -1.5 as your math would imply. What I had missed was that the blitz in and out has a net value of +2.0, which makes it a net +1.5 better than the move to Arch. It is not that I overvalue the move to Arch, it is that I failed to see an alternative move with the same tank that had a better value.

I should have clarified - the move to Archangel has a net of -1.5 compared to a your baseline move to Karelia. Absolute value wise it is a positive net of .5 yes. But I should also add that it is very disingenuous to think in terms of absolute value gain it will lead to bad plays.

As an extreme example. Suppose that Germany is empty (no aa gun either) with 40 ipcs in the bank and there are 30 tanks in western europe. Russia can either send in one tank to germany with a net expected value of 50 (40 ipcs +10 for the capital) or it can send in that tank to blitz germany and then western europe with a net expected value of 50.0000001 (approximately the chance of taking it with that 1 tank). If you only look at absolute expected values you would always attack the western europe and that makes no sense.

[Fillmore]

EDIT - ha, I misscalculated the value of going into WE, it is actually 52.5 since half the time you kill one of the enemy tanks. While in that contrived scenario the values are really equal, there is also no real reason to stay in Germany; but in a realistic scenario there are quantifiable reasons to stay in German, e.g. the ability of an ally to stack there before Germany can counter, and the value of removing the units allocated to retaking Germany from some other attack.

Well, your number is not even remotely close to the chance of a sinle tank taking a zone from 30, odds of that are literally astonomical. Also, that is not even how you calculate the value because if you stay in Germany then you get half the value of an enemy unit from the counter; so going through to WR is 50.0 + 1.0 x 10^-(HUGENUMBERHERE) while staying in Germany is 52.5 (50+ half the value of a tank that you kill when Germany retakes).

Thinking in terms of absolute value will only lead to bad play if you fail to properly assign value to the options. Things like position do have quantifiable value even if quantifying it is tremedously complex and involves a lot of unceartainty.

I view the baseline as no move. You might say that a blitz in and out is a non move with value, but I still consider it a move since it precludes the opportunity to retreat during the non combat move phase.

[bb82]

Things like position do have quantifiable value even if quantifying it is tremedously complex and involves a lot of unceartainty.

Honestly believing that to be true has more validity in LL than regular dice.

For something that is actually tremendously complex and that involves a lot of uncertainty more likely just implies subjective rather than objective analysis. Too may get hung up on trying to quantify everything and miss the big picture entirely. Regular dice is much more about risk management and adapting than quantifying. Quantify away though. It just has more meaning to you than another.

I've slowly learned the following as a fundamental truth in revised. Since revised has such a nice balance with a small axis bid that opens up short term and long term options for both sides, good players will make for good games regardless of the strategies they use.

In this case that just means blitz arch or not depending on what works for you.

Quantifying LL is more attainable. But what fun is that .

[UtzChips]

As an extreme example. Suppose that Germany is empty (no aa gun either) with 40 ipcs in the bank and there are 30 tanks in western europe. Russia can either send in one tank to germany with a net expected value of 50 (40 ipcs +10 for the capital) or it can send in that tank to blitz germany and then western europe with a net expected value of 50.0000001 (approximately the chance of taking it with that 1 tank). If you only look at absolute expected values you would always attack the western europe and that makes no sense.

This has been an excellent thread with 9 out 10 posts that were very informative. The above, however, has me confused, as I am not following you here

Where does the 50.000000001 come from? Is the 50 the gain from taking Berlin & the .000000001, your calc for how often 1 tank kills 30?

If so, I was unaware that you can blitz a tank thru a capitol?!

My tanks always stick like glue to the territory with the IC, but then, I only play Revised. I was unaware that was possible in 42.

[Sarten]

This has been an excellent thread with 9 out 10 posts that were very informative. The above, however, has me confused, as I am not following you here

Where does the 50.000000001 come from? Is the 50 the gain from taking Berlin & the .000000001, your calc for how often 1 tank kills 30?

If so, I was unaware that you can blitz a tank thru a capitol?!

My tanks always stick like glue to the territory with the IC, but then, I only play Revised. I was unaware that was possible in 42.

The contrive scenario is taking away from the point I was trying to make which is that you can not calculate absolute value of a move and make that move if it nets a positive result. You need to always calculate the relative value of a move versus an equally valid move and see if it is worthwhile. Going back to the case of blitzing Karelia and then taking Archangel, you can't do the calculation of the move into taking Archangel based on the value of Karelia. Otherwise, if Karelia happened to be worth 100 then you would be saying that taking Archangel is a 103.5 expected gain, if Karelia happened to be worth 1 then blitzing the tank to Archangel would be -0.5 In both cases the move should be calculated versus the fact that you will be taking Karelia anyway.

[UtzChips]

This has been an excellent thread with 9 out 10 posts that were very informative. The above, however, has me confused, as I am not following you here

Where does the 50.000000001 come from? Is the 50 the gain from taking Berlin & the .000000001, your calc for how often 1 tank kills 30?

If so, I was unaware that you can blitz a tank thru a capitol?!

My tanks always stick like glue to the territory with the IC, but then, I only play Revised. I was unaware that was possible in 42.

The contrive scenario is taking away from the point I was trying to make which is that you can not calculate absolute value of a move and make that move if it nets a positive result. You need to always calculate the relative value of a move versus an equally valid move and see if it is worthwhile. Going back to the case of blitzing Karelia and then taking Archangel, you can't do the calculation of the move into taking Archangel based on the value of Karelia. Otherwise, if Karelia happened to be worth 100 then you would be saying that taking Archangel is a 103.5 expected gain, if Karelia happened to be worth 1 then blitzing the tank to Archangel would be -0.5 In both cases the move should be calculated versus the fact that you will be taking Karelia anyway.

Way too much head snappin' math for me! No wonder I'm gettin' pounded in the pbem games!

I could do all this math in a pbem game & it's probably something along the lines of what bb82 does, [or at least something just as time consuming because he only does a max of 2 pbe games at a time in the ladder league] and I like just stickin' the units in the battle calc, pressin' run & lookin' for that magic number of 70+% success.

If I get it, it's YAHTZEE, let's roll the bones! [Result: 37.86% win rate ]

I'm going to live play only in the ladder league for me from now on.

[Sarten]

Way too much head snappin' math for me! No wonder I'm gettin' pounded in the pbem games!

I could do all this math in a pbem game & it's probably something along the lines of what bb82 does, [or at least something just as time consuming because he only does a max of 2 pbe games at a time in the ladder league] and I like just stickin' the units in the battle calc, pressin' run & lookin' for that magic number of 70+% success.

If I get it, it's YAHTZEE, let's roll the bones! [Result: 37.86% win rate ]

I'm going to live play only in the ladder league for me from now on.

BTW I forgot to answer the original question - it's the aa gun that stops you from blitzing Capitols, not the Capitol itself. Of course it was a dumb scenario since most of the time if that is the situation Germany has 3 AA guns in it's Capitol not zero I also think that over reliance on the battle calculator is something that you should wean yourself off of in order to become a better player. Think about the 30% of the time that you are not winning that battle. Do you have a safe line of retreat? Will you lose a major asset if the first round goes badly and then you have to pull out of the battle? Can you reinforce your retreat zone so that it is unhittable even if you lose the battle?

I am not a conservative player in that I will take 70% battles if they come my way and I know that even if I get a bad round I can always pull back (most 3 inf versus 1 inf type fights). On the other hand, I would not take a 90% battle if I had a clear positioning advantage and time was on my side (i.e. a 90% attack on Moscow with Japan when Germany is doing well... I'd rather just wait for it to get to 100%).

Anyway, anyone on this thread who wants to put their money where their mouth is feel free to toss me a PBEM challenge - revised or '42 and you can determine a fair bid (I tend to think 6-7 g for revised and 2-3 r for '42). At the end of the day you can do all the odds calcs you want, strategy trumps situational awareness, and dice.

[rem400]

It's actually the AA gun and/or the IC that prevent a tank blitz in both Revised and 42. No blitzing through an enemy controlled captial since they all have IC's stuck in them.