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Subject: Avoiding researching technologies rss

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J. Alan Henning
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I was surprised to read the many strategy articles here that advocate researching technologies. With a 1 in 6 chance, it costs an average of 30 IPCs to acquire a technology.

As I result, I never spend money on techs but prefer to purchase units.

Am I crazy?
 
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Paulo Soledade
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I really don't think you are crazy but the few times I've played the game, advanced tec did result quiet well. It can give you an important boost specially at the beggining.
Then again you gone have to make yourself a question: "do I feel lucky?"
'cause if you don't, don't try it. It can be very frustrating. Once I've tried twelve dice and did'nt get a four.
 
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Robert Bradford
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I think it's right to not research technologies most of the time, although heavy bombers might be the exception.

My thinking goes like this:

Axis & Allies, at least as we play it, seldom lasts in an interesting form past about the fifth turn. Usually, by that point, the game seems over. There are many close battles over the early turns until one power or another has established what usually amounts to unquestioned regional supremacy on the land or at sea. Newer players usually play much longer games, in which it's correct to develop weapons; but experienced players, not so much.

Taking units off the board in the early going - which is essentially what you choose to do when you try to develop a weapon - is a good way to ensure that you will be supreme in fewer areas. There are - I overgeneralize wildly here, of course - basically six theatres of conflict - the Atlantic (England, Germany, and America), Western Europe (Germany, England, America), Africa and the Middle East (England, Germany, America), Eastern Europe (Russia, Germany), Asia East (Japan, England, Russia, America), and the Pacific (Japan, America).

If one side achieves dominance in four of these theatres, my experience is that that side will win. If you are dominant in three areas, and your opponent(s) are only dominant in one, you will also win. By dominance, I mean a force so great that your opponent(s) would need at least two turns of production dedicated to the theatre in order to have a chance of surviving your onslaught.

So, if you accept my wild overgeneralization:

The Russians can strive for dominance in two theatres; this means that they have about 15 a turn for each in a typical game.

The Germans can strive for dominance in four theatres: I feel that in games where they win two and tie the third, the Axis will win. Typically, they give up on either Africa or the Atlantic, giving them about 15 a turn for each of the three theatres they choose to contest.

The English can strive for dominance in four theatres: if they can manage two wins and a tie, they're doing very well with their 8 a turn to each.

The Japanese struggle in two theatres, and, really, have to win in one and at least fight to a stalemate in the other for the Axis to have a chance to win - this gives them about 15 a turn for each theatre

The Americans can fight in up to five (they're not at their best in Eastern Europe/Russia), and typically chose to fight in three or four, giving them 11 to 14 a turn in each.

Often, dominance can be achieved simply by throwing IPCs at a problem. If the Americans decide that they REALLY want the Pacific, and spent all of their money every turn on a Pacific fleet, they will inevitably blow away a Japanese player of equal skill, even if that player does exactly the same.

Since a small advantage in force in being usually translates into a vast post-battle advantage, several of these theatres - Western Europe, Eastern Europe, the Atlantic, and the Pacific - usually come down to one or two battles, fought at a time when one side is fairly sure of victory.

When that battle is fought, it's best to be the one who is fairly sure of victory.

If you have researched a technology in six dice in the early going, you will be hopelessly behind in one theatre that you could otherwise have contested. There are only six theatres.

The other problem, of course, is that most of the technologies are simply too expensive for their expected cost.

The math is right - on average, I can expect a technology to cost 30 IPCs, although of course it may cost only five.

In order for a technology to be worth 30 IPCs, it would have to have a very large effect on the game.

Super subs make submarines about 1/3 better (since they still only take one hit) - so you would have to have 90 IPCs of submarines on the board for this to be a good choice - and that's 11 subs. This might be worth trying to get before a close attack, if you play with the printed rules that give you the technology immediately, but is pretty obviously a non-starter in general play.

Rockets might seem worthwhile - and I'm not sure that they are not. If you can launch one rocket at an industrial centre, you can expect to break even with the 30 IPC cost in 30/3.5 = 7.6 turns. If it's an industrial centre in a 4 cost territory, then in 10 turns; if in a cheaper one, more. Since the Germans start in rocket range of 3 centres, they can expect to cost their opponents 30 IPCs in 3 turns of successful rocketry, and to then pull 10 IPCs ahead every turn thereafter.

The trouble there, of course, is 30 IPCs of stuff is a lot of stuff to not have on the board, and you won't be in as good a position in 3 turns, even if you've broken even financially.

For the Americans, Japanese and English, this is a complete non-starter; for the Russians, it might be worthwhile in games where the German player doesn't try for Russia, but...in practice...that's almost never. Even if they weren't planning to, Russia taking a turn off from buying units might change their mind, even if they spread it over a couple of turns.

Jet fighters...hm...I'd say fighters defend about 1/3 as often as they attack...a 25% increase 25% of the time means that I'd have to have, hm, 16*30 = 480 IPCs of fighters on the board, or 48 fighters, to consider this a good buy. I'm not saying I wouldn't try it with, say, seven English fighters sitting in Russia staring down a German horde, but, really, at that point it might be worth considering flying home. A nearly useless technology.

Long range aircraft are pretty good - I would say that they double the range of fighters, on average, in terms of the number of areas that can be reached, and they help bombers, too. This is hard to really quantify, but at times it's like just adding two or three fighters a turn to the map. If you find that you're in that sort of position, or you anticipate being in it, and it's not obvious to you that just having a few more fighters on the board RIGHT NOW will be the same, by all means take a crack at these. Especially good if you can get the benefit the turn you try it - England, after all, is not well defended on turn one.

Combined bombardment is, um, amazingly weak. Destroyers are not a worthwhile purchase in numbers greater than one; combined bombardment adds an expected value of, probably, 1.5 per turn to each destroyer that can participate in an amphibious assault - so it would take 20 destroyer turns for these to pay off. The Americans are the only country that typically starts their first turn with two destroyers...

Heavy bombers really are very good, especially in the printed rules. Essentially, they double the value of a bomber. Bombers are not an especially overcosted unit, and everyone starts with one except for the Russians. I'm not sure that any countries best strategy requires that they develop them, but they are reasonable for everyone (except, probably, Russia).

After all, if I have one bomber, and I consider that it's really worth 15 IPCs, and I anticipate that I'll want 4 bombers, I can either spend an average of 30 IPCs and buy one bomber to have two heavy bombers, or I can spend 45 IPCs and buy three bombers to have 4 normal bombers.

After I've developed them and bought my first bomber, well, everything after that is pure profit. Having one half-cost unit available makes up for a lot of positional faults associated with not having put units on for a turn or so.

Of course, if I have already lost, this isn't going to help enough...all right, enough rambling.

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J. Alan Henning
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Great article! I really appreciate the detail.

I've always felt guilty that I'd always rather take an additional tank than a chance at weapons R&D, but most of our games only last four or five turns...

Have you written anything else anywhere about A&A?
 
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cree dawg
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If you are playing with extremely good players, like me and my two brothers, the game can last forever. I have been playing this game scince the first version came off the shelf, and I will be the first to tell you that the only nation you can buy weapons development for without leaving yourself thin is usa. It is far too risky with any other nation. All the other nations are basically right in battle at the start and you must commit all ipc's to units.
 
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Marcel van der pol
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Math is wrong.
I think your math is quite wrong. Its a 1-in-6 chance when rolling ONE die. It is on average LESS than that when rolling more dice.

For example, you want heavy bomber (a 6), and roll three dice, costing 15 IPC. You then have a chance of P to obtain the tech:

P = 1 - NOT(P)

P = 1 - [(5/6) * (5/6) * (5/6)]

P = 1 - (125/216)

P = 91/216

On average per die rolled, this equals a 0.8426-in-6 chance of acquiring the tech.

The idea behind the math is that it doesn't matter how many 6's you roll, since you are only going to acquire the tech ONCE. Hence, extra 6's rolled are "wasted" in terms of the probability of obtaining the technology. For example, rolling two 6's has no advantage over rolling one 6 in terms of acquiring the technology you need.

So, if you really want to spend money on tech, buy no more than a single die each turn. This will give you the highest chance per IPC spent of obtaining the technology (with Germany, Rockets will almost immediately cause problems for Russia and England). The added advantage is that you can still compete in most theaters of war while spending 5 IPC each turn on Technology. While over the course of the game those IPC will add up, if you are lucky enough to get the tech early, the tech DOES give you enough advantages and allows you to capitalise on your excellent research. I find that for Germany, Rocket technoloy almost always causes heaps of problems for the Allies as Germany starts with 3 Anti-aircraft and only needs to position them well in order to strike at the allied production advantage.
 
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Philip Thomas
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The old game had a tech which reduced the costs of all units by 1 IPC. I guess this has been cut, cos with the new rules allowing tech targeting it would be too good.

We never bought tech in the old game, odds being even if you got the tech you would not get the right one.
 
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Robert Bradford
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Quote:
I think your math is quite wrong. Its a 1-in-6 chance when rolling ONE die. It is on average LESS than that when rolling more dice.

For example, you want heavy bomber (a 6), and roll three dice, costing 15 IPC. You then have a chance of P to obtain the tech:

P = 1 - NOT(P)

P = 1 - [(5/6) * (5/6) * (5/6)]

P = 1 - (125/216)

P = 91/216

On average per die rolled, this equals a 0.8426-in-6 chance of acquiring the tech
.


An excellent point.

I do - and did - realize that, however, re-reading my post, I notice that I never did address it. My own practice, which I inexplicably did not mention, is to spend 5 IPCs on the first turn to try to develop rockets with Germany, and to spend 5 IPCs on the first turn to try to develop heavy bombers with the US. If the Germans buy significant fleet on the first turn, which is quite common, and usually the beginning of a longer (six or seven) turn game, I sometimes try for rockets on turn two with Russia and get a tank instead of my fourth fighter.

And that's it. If those don't work out, I don't try again. I don't always try for rockets with Germany, either.

Since I roll exactly once all game, it's true that, for me, the expected cost of a technology is 30 IPCs.

Unless you are buying a technology for use in the same turn, it's clearly inefficient (in a minor way) to buy more than one dice for it.

That said, I would argue that spending 15 IPCs over 3 turns on technology is still enough for the Germans to have lost an entire theatre of operations - and, worse, if you develop rockets on the third turn, you won't have broken even (on average) until turn five, when the game, according to me, is usually over. If, like us, you play by Harris' tournament rules, and you don't get the technology until the end of the turn, not until turn six will this have been worthwhile.

Generally, I feel that five infantry, or two subs, or a tank and three infantry, or...really, whatever...would be better on the board than developing rocketry on turn three.
 
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LC
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Those who think they are good players should check out the TripleA site. They have a Java software package to allow players to play by email. Some really good competition there.

Unless there is a mismatch in player abilities, then your average game will probably last 15 - 20 turns before it is decided and sometimes 30 turns.

I look at the game in phases of 6 - 8 turns per phase. In the opening phase, both players are attempting to gain a slight advantage over the other. Taking risks here is not a good idea. Not saying you can't try different strategies but here is NOT where you want to develop technology unless you are a gambler. Probably the player who attempts to develop technology here vs one who doesn't will lose at least 50% of the time - probably more.

The middle phase (the next 6 - 8 turns) is where the players attempt to turn their advantage gained in the opening phase into a decisive lead. This is where you NEED to take risks if you are behind. Developing technology should be attempted if you are losing but not so far behind that doing so will sink the game for you.

Finally the end phase is where the player with the decisive advantage needs only time to finish it off barring some incredible reversal of fortune. Usually players will surrender prior to or during this phase. Most people do not play it out to the bitter end.

It goes without saying that if you have an advantage but it is not decisive, then you should NOT develop technology. I've seen players do this and spend a bunch of IPC on technology that they did not get and subsequently lose their advantage and the game.
 
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Robert Bradford
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Actually, some quick math convinces me of another thing:

If you roll one dice a turn, the expected cost of a technology by the time you develop it isn't more than 30. It's less than 30.

I don't have the skills to be absolutely sure - I've been out of school for a while - but:

On the first turn, I spend 5, and have a 1 in 6 chance of getting the tech for exactly 5. On the second turn, I spend another five if I need to (5 in 6), and have a 1 in 6 chance of getting the tech for ten...summing the expected payouts with the chance of having the technology, and going down to turn 14, rolling one dice a time for a technology, my sums say that the expected cost of a technology that you try to develop slowly is 21 IPCs.

To be sure, the technology won't always be developed by turn 14, but it usually will be.

Maybe this is wrong and stupid. But I think it is right. Interesting stuff, math. I should really learn more.
 
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Bill the Pill
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"There are - I overgeneralize wildly here, of course - basically six theatres of conflict - the Atlantic (England, Germany, and America), Western Europe (Germany, England, America), Africa and the Middle East (England, Germany, America), Eastern Europe (Russia, Germany), Asia East (Japan, England, Russia, America), and the Pacific (Japan, America)."

I love bcmeatpuppet's description of the world above. If you drop Africa/Mid East and assume Pacific means USA, it is the same as George Kennan explaining the five areas contested during the cold war and thus important to containment. I enjoyed reading the rest of his post, as well.
 
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Joe McKinley
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bcmeatpuppet wrote:
Actually, some quick math convinces me of another thing:

If you roll one dice a turn, the expected cost of a technology by the time you develop it isn't more than 30. It's less than 30.

I don't have the skills to be absolutely sure - I've been out of school for a while - but:

On the first turn, I spend 5, and have a 1 in 6 chance of getting the tech for exactly 5. On the second turn, I spend another five if I need to (5 in 6), and have a 1 in 6 chance of getting the tech for ten...summing the expected payouts with the chance of having the technology, and going down to turn 14, rolling one dice a time for a technology, my sums say that the expected cost of a technology that you try to develop slowly is 21 IPCs.

To be sure, the technology won't always be developed by turn 14, but it usually will be.

Maybe this is wrong and stupid. But I think it is right. Interesting stuff, math. I should really learn more.


If you extend this out to an infinite number of turns, the expected cost approaches 30 IPCs.

(Expected cost = 5/6*SUM(N*(5/6)^N) where N = 1..Infinity)

This infinite summation equals exactly 30.
 
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Marcel van der pol
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Another way to look at it is this:

P(t) of obtaining the technology during turn number t (calculation prior to turn 1) rolling a single die each turn

P(1) = 1/6 = 16.7%
P(2) = 5/6 * 1/6 = 13.9%
P(3) = [(5/6)^2] * 1/6 = 11.6%
P(4) = [(5/6)^3] * 1/6 = 9.7%

Etc.
However, this assumes that the player does NOT change strategy midway during the game.

In any case, the average cost of a technology is 30IPC when rolling a single die each turn, while it is more than that when rolling more dice each turn. It also takes on average 6 turns to get the technology, while it takes shorter when rolling more dice.

As a function of the number of dice
1) P = 1/6 = 16.7% Av = 1/P = 6 rolls, 30 IPC
2) P = 1 - (5/6)^2 = 11/36 = 30.6% Av = 36/11 = 3.27 rolls, 32.7 IPC
3) P = 1 - (5/6)^3 = 91/216 = 42.1% Av = 2.37 rolls, 35.6 IPC
4) P = 1 - (5/6)^4 = 671/1296 = 51.8% Av = 1.93 rolls, 38.6 IPC
5) P = 1 - (5/6)^5 = 4651/7776 = 59.8% Av = 1.67 rolls, 41.8 IPC
6) P = 1 - (5/6)^6 = 31031/46656 = 66.5% Av = 1.50 rolls, 45.1 IPC

Etc.
The question is, is it relevant to spend on average more money for a single technology in order to acquire it sooner? Awnser: yes it is, but there is no doubt an optimal point after which the extra IPC spent will not matter greatly to the outcome and only undermine your position.

Yes, statistics are very tricky, depending on what exactly you want to calculate. Averages by themselves mean little, as you need the standard deviation (ie the spread of the probability around the average) to complete the probability function. You could get "lucky" and get the technology you wanted with a single roll of the die on turn 1. You could get "unlucky" and not get it after rolling three times with 6 dice, although the chance of that happening is much smaller than the "lucky" first turn roll.

In the end, since average IPC spent goes up once you start rolling more than one die, if I decide to spend IPC on tech I usually do so only during the first three turns and only a single die each. A German Rocket invention during those first three turns can seriously wreck the allied game plan as both Englands and Russia's industrial production crumble under the weight of the attacks.

On average, Germany rocket technology costs the Allies 3.5 (UK) + 3 (Russia Ukraine) = 6.5 IPC each turn. If Germany spent 15 IPC to acquire the tech, you need about three turns to break even, after which Germany gains the advantage. This advantage can be gained earlier once Russia itself can be targeted, which it is in Germany's best interest to do,
Note that this assumes that there is no significant board position loss due to the 15IPC investment, which is a slightly doubtfull supposition.
 
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Interesting. One thing to keep in mind is that the results of a turn 1 analysis do not apply to future turns. For example, suppose that I calculate with 4d6 my odds of getting tech is 52% and I intend to roll 1 tech dice each turn for 4 turns. Now on turn 1 I miss my tech roll. This 52% now does not apply to turn 2 unless you are going to carry it through turn 5. This does not invalidate your earlier analysis, it just means you have more information on turn 2 than you did on turn 1 (i.e. you missed tech on turn 1 EDIT or you got tech).

The average cost of succussfully developing tech is slightly less than 20 IPC but as previously stated this is meaningless without knowing the standard deviation. There is a 1 in 10 chance of not getting tech after spending 85 IPC (13 dice). A lot of people moan and groan about this saying they are really unlucky but I guarantee that if the odds of winning the lottery were that good (1 in 10) we'd all be buying tickets.

But again I think tech is too expensive in the early game as it can give your opponent a big advantage. Suppose I'm playing the Axis and my strategy as the Axis is always to try and develop one tech for Japan and one tech for Germany. Since I know I'm going to develop tech then it is better to get it earlier rather than later. Based on a cost benefit analysis I decide that each power will spend 20 IPC on turn 1 for tech. Now here are the statistics:

A) In 2 out of 5 games both Germany and Japan will get tech
B) In 3 out of 4 games only one power will get tech
C) In 1 out of 4 games neither power will get tech

But in scenarios B & C you lose. You lose because you've spent 40 IPC to develop 1 or 0 technologies!!! So overall you will lose 60% of your games against an equal skilled player simply because you decided you had to have tech. Yes I think the game is that balanced.

In my opinion there are only 4 times when you should consider rolling for tech.

#1) After your opponent rolled for tech and failed. This is a big judgement call. If your opponent did not spend much than it is better to buy units. If you opponent spent 20 or more IPC than it is a consideration of whether the extra units will help more or rolling for tech is better - you can still miss.

#2) After capturing an enemy capital (flush with cash)

#3) If you are desperate and it is the only thing that might give you a chance to pull off a victory.

#4) You are in a position to overwhelmingly win the game and you opponent refuses to surrender. Buying tech may speed up your ultimate victory.

Just my 2 cents.
 
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Quote:
In any case, the average cost of a technology is 30IPC when rolling a single die each turn, while it is more than that when rolling more dice each turn. It also takes on average 6 turns to get the technology, while it takes shorter when rolling more dice.

As a function of the number of dice
1) P = 1/6 = 16.7% Av = 1/P = 6 rolls, 30 IPC
2) P = 1 - (5/6)^2 = 11/36 = 30.6% Av = 36/11 = 3.27 rolls, 32.7 IPC
3) P = 1 - (5/6)^3 = 91/216 = 42.1% Av = 2.37 rolls, 35.6 IPC
4) P = 1 - (5/6)^4 = 671/1296 = 51.8% Av = 1.93 rolls, 38.6 IPC
5) P = 1 - (5/6)^5 = 4651/7776 = 59.8% Av = 1.67 rolls, 41.8 IPC
6) P = 1 - (5/6)^6 = 31031/46656 = 66.5% Av = 1.50 rolls, 45.1 IPC


This analysis suggests that you are guaranteed to get tech after rolling x dice over y turns.

Here is a breakdown of what you can expect your success probability to be based on the number of dice you roll in any give turn:

1 dice = 16.7%
2 dice = 30.6%
3 dice = 42.1%
4 dice = 51.8%
5 dice = 59.8%
6 dice = 66.5%
7 dice = 72.1%
8 dice = 76.7%
9 dice = 80.6%
10 dice = 83.8%
11 dice = 86.5%
12 dice = 88.8%
13 dice = 90.7%
14 dice = 92.2%
15 dice = 93.5%
20 dice = 97.4%
25 dice = 99.0%
30 dice = 99.6%
42 dice = 100.0%

Now note when rolling 42 dice the odds are NOT 100%. It is just that they are so close to 100 that rounding brings it to 100.

What this table shows is the law of diminishing returns. It is more efficient IPC wise to roll fewer dice over many turns to get tech and not overspend. Personally I think it is unwise when pursuing a tech strategy to roll more than 4 dice per turn.

Remember that when rolling dice over many turns you cannot take into account the failures you had in previous turns. Past rolls do not impact future rolls - one of the hardest concepts to get across to the ("I'm really unlucky") type of player.
 
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Joe McKinley
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Pz V wrote:
The average cost of succussfully developing tech is slightly less than 20 IPC but as previously stated this is meaningless without knowing the standard deviation.


This is wrong.

The expected cost of developing tech is given by this formula:

Expected cost = 5*D*(1-(5/6)^D)*SUM(N*(5/6)^(D*(N-1)))

where D is the number of dice purchased each turn until you are successful in getting the tech. N = the number of turns (Sum from 1..Infinity to get exact expected results.)

D = 1 ===> Expected cost = 30 IPC
D = 2 ===> Expected cost = 360/11 = 32.72... IPC
D = 3 ===> Expected cost = 3240/91 = 35.60... IPC
D = 4 ===> Expected cost = 25920/671 = 38.63... IPC
D = 5 ===> Expected cost = 194400/4651 = 41.80... IPC
D = 6 ===> Expected cost = 1399780/31031 = 45.11... IPC
D = 7 ===> Expected cost = 9797760/201811 = 48.55... IPC
D = 8 ===> Expected cost = 67184640/1288991 = 52.12... IPC
...

This has nothing to do with statistics. It is pure probability. (Probability is not the same thing as statistics.) Standard deviation is irrelevant. (Except as a means to describe the nature of the probability distribution.)

The more dice you purchase each turn, the higher the expected cost to acquire the tech. The minimum expected cost is 30, corresponding to spending a single die each turn until you acquire the tech.

Note that

Expected cost = 5*D*Expected Number of Turns

D = 1 ===> Expected Number of Turns = 30/5 = 6 turns
D = 2 ===> Expected Number of Turns = 360/11/10 = 3.27... turns
D = 3 ===> Expected Number of Turns = 3240/91/15 = 2.37... turns
D = 4 ===> Expected Number of Turns = 25920/671/20 = 1.93... turns
D = 5 ===> Expected Number of Turns = 194400/4651/25 = 1.67... turns
D = 6 ===> Expected Number of Turns = 1399780/31031/30 = 1.50... turns
D = 7 ===> Expected Number of Turns = 9797760/201811/35 = 1.39... turns
D = 8 ===> Expected Number of Turns = 67184640/1288991/40 = 1.30... turns

These are the same results Marcel posted above, just derived in a different order.

What do these numbers mean? They really just indicate that tech is too expensive to consider in most cases. The only reason tech is really ever justified is if you're tired of the same old game and want to mix it up a bit. Take a risk. There's a chance that you'll get an early tech advantage and enjoy a game that plays out a little differently than your typical game. There's also a chance that you won't ever get the tech, and you'll be at a monetary disadvantage, which should be enough to cause the game to play out a little differently in the other direction.

I.e., tech should be attempted for fun, not profit.
 
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Jack Kazumoto
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odds are misleading, which is why vegas always wins folks.

the fact is, your odds are 1/6 per dice. you can roll 42 dice and get 42 misses. you can roll 42 dice and get 42 hits. or 50-50 or 60-40, or whatever. the question to ask yourself is... do you feel lucky punk?

you either open yourself up to the possibilty of getting a tech or you buy a tank. a purchase or a gamble.
 
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J. Alan Henning
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Thanks to everyone who posted for their thoughts. Nice to know that I'm not the only geek who uses math to calculate odds when playing.

Since neither I nor any of my opponents ever roll for tech, I'm thinking at some point that we will have a house rule giving each player one free tech roll per turn (provided that they own their capital). Technology development was certainly an important part of World War II, and it's shame we've all optimized our strategies to exclude it.

Thanks again!
 
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Michael Bradley
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How about house rules to discount the "weaker" technologies. Like it would cost 3 IPCs each die to roll for super subs, but 5 each to roll for heavy bombers. It seems that, as the rules stand, there are some techs that are just plain stupid to roll for. House rules for discounted dice might bring some of these techs back into play.
 
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RIK FONTANA
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Hey Guys, after years from the game, I have several matches coming up soon. Thought I would look through the A&A Strategy section at bgg. This thread in particular has certainly been one of the most interesting and enjoyable. Robert, excellent job on the strategy section. Marcel thanks for the math and probability explanations. All'round very helpful.
 
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cree dawg
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hell
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Rook wrote:


the fact is, your odds are 1/6 per dice. you can roll 42 dice and get 42 misses. you can roll 42 dice and get 42 hits. or 50-50 or 60-40, or whatever. the question to ask yourself is... do you feel lucky punk?


very good point rook, people get caught up with all these numbers and equasions and end up over-anylizing things. I usually buy 2 to 3 dice and I hit it more than not. I look at it as if I really need it, such as long range aircraft for japan or super subs for germany, than it is worth trying 10 to 15 ipc a turn to try and get it. For me, overthinking things takes the fun out of the game. Take a chance, get froggy and leap!
 
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cree dawg
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TedTorgerson wrote:
You should buy your tech units 2 rounds in advance (subs bombers or fighters) knowing you will be positioning them the next turn then rolling for tech the following turn.

You might as well buy them before hand, you could always use them for skirmishes before the big battle.
 
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