Technology is a bad strategic investment

[allweneedislove]

@knp7765:

I kind of agree that Technology Development can be a bad investment.  Especially early on in the game.  It’s hard to risk IPCs on a maybe chance of getting the tech you want when they could be better spent on units for an attack or defense.  Then you leave yourself open to an opponent’s attack, even if you did get the tech you wanted.

i agree.

@knp7765:

I also don’t like the randomness of it.  It really sucks if you need Heavy Bombers for a big air attack and end up getting Super Subs or Radar.  I like the Revised version better where you direct your research.  It’s still pretty much the same chance but at least you are trying for the research you want and don’t end up with one that is useless to you.

i agree that revised had a better method of acquiring tech.

@knp7765:

I also use the research tokens from the Anniversary game.  That was a fantastic idea I think.

i think the tech tokens was the best method for acquiring tech. but using the directed tech from revised and the tech tokens from anniversary can make some techs too cheap to acquire.

@knp7765:

One thing I DON’T like is the way they have changed Heavy Bombers.  You use 2 dice but only get to pick one of them?  To me, that totally negates the concept of “Heavy” Bombers.

yeah heavy bombers were neutered. but if you compare them to the 2 most similar techs they get even more of a boost. super subs give subs one more attack pip, jet fighters give fighters 1 more attack pip. heavy bombers add about 1.3 attack pips.

now think about improved mech and improved art they add one attack pip but you must also have other units to make it work.

@knp7765:

A Heavy bomber carries a bigger bomb load and therefore can get more hits in combat or cause more damage to facilities.  You still have the chance of rolling a 5 or 6 with one or even both dice, (which could represent faulty bombsights, dud bombs, bad directing, etc.) but you still should be able to count BOTH dice.  Heck, on my most recent game, I had an attack with 2 heavy bombers and 1 fighter supported TAC bomber (5 dice) and ended up rolling just 1 hit out of all of that.  So, even heavy bombers aren’t a sure thing.  Plus, they are still vulnerable to AA fire and interceptors and still only take 1 hit to down.  In my games, we will always count BOTH dice for heavy bombers.

you can not think too realistically with anything in axis and allies. remember that the game uses broad brush strokes to represent history. one bomber piece on the board represents an entire bomber division and supporting personnel and equipment.

[Holden]

@allweneedislove:

the most cost effective way to acquire tech is by rolling only one die a turn as not to waste two or more rolls of a 6 in the same turn.

if you roll for one tech a turn the average cost to acquire a tech is 30ipc which is 6 rolls at 5ipc each. if you roll more dice per turn the average goes up.

Got any numbers or fomula to back this up at all? What exactly do you mean “most cost effective way?” Do you mean that this leaves you with some IPC’s left over for purchasing? If so I tend to agree. If you are only interested in aquiring a single tech then spending 5 IPC’s per turn is a good way to ensure that you don’t spend more than you have to, but it doesn’t change the odds at all if you spend all 30 IPC’s at once (it just means you might get some additional techs).

@allweneedislove:

you can figure out the average cost to acquire tech if you always roll 6 dice per turn. i am not that good at math so i can not give you the formula, however i estimate it to cost an average of 43ipc. maybe math teacher gamerman can help me by posting the formula.

I’m not really sure of what you’re talking about here. If you always roll 6 dice per turn (unlikely) then you will spend 30 IPC’s each turn and you will have a 67% chance to develop a tech each turn. I’m not sure where 43 IPC’s came from.

@allweneedislove:

assuming you only roll 1 die at a cost of 5ipc per die roll then the average number of rolls to acquire a tech is 6. 5ipc * 6rolls = 30ipc = average cost to acquire tech.

This is not how averages are calculated. The question is largely meaningless. If you really wanted to calculate the average cost then you’d have to record every game of Axis and Allied played and find out how many IPC’s were spent to aquire tech by the multitude of players. Then you’d have to add those numbers all together and divide by the total number of players.

You’re just making up some arbitrary fomula that sort of seems that it should fit and calling it the average cost. Then your claiming that your average cost cannot be disputed and building an entire thread around it.

[gamerman01]

@Holden:

If you are only interested in aquiring a single tech then spending 5 IPC’s per turn is a good way to ensure that you don’t spend more than you have to, but it doesn’t change the odds at all if you spend all 30 IPC’s at once (it just means you might get some additional techs).

Er, this isn’t Classic.  Limit one breakthrough per turn.  That’s why buy a single die is the most “cost effective”.  It avoids waste.

[San Chillos]

Ok… I have more to do than read every post on these forums but as far as I’ve been, allweneed is totally correct. The average cost to get a technology if you buy a number x of die every turn is given by the relation (cost by turn)/(probability to get a tech) where the probability is expressed by a number between 0 and 1. In mathematical terms, we have costaverage = 5*x/(1-(5/6)x).

-Buying 1 die a turn gives an average of 5*1/(1-(5/6)1) = 30 IPCs.

-Buying 2 dice a turn gives an average of 5*2/(1-(5/6)2) = 32.7 IPCs.

-Buying 6 dice a turn gives an average of 5*6/(1-(5/6)6) = 45.1 IPCs.

@Holden:

@allweneedislove:

assuming you only roll 1 die at a cost of 5ipc per die roll then the average number of rolls to acquire a tech is 6. 5ipc * 6rolls = 30ipc = average cost to acquire tech.

This is not how averages are calculated. The question is largely meaningless. If you really wanted to calculate the average cost then you’d have to record every game of Axis and Allied played and find out how many IPC’s were spent to aquire tech by the multitude of players. Then you’d have to add those numbers all together and divide by the total number of players.

You’re just making up some arbitrary fomula that sort of seems that it should fit and calling it the average cost. Then your claiming that your average cost cannot be disputed and building an entire thread around it.

No, allweneed is right. Holden, your method doesn’t work in theory unless you try it an infinite number of times. Good luck… :wink:

In conclusion, yes, techs really suck in this game…  :-(

[gamerman01]

Fine, San Chillos, but work on this:

Obviously if you took a million rolls (1 per turn), you would be paying right around 30 IPC’s per tech.

But if I roll 1 die a turn, on average how many turns until I hit my first breakthrough?  Is it (1+6)/2 = 3.5?  Or is the 6th round average?  I could figure this out, but too tired and lazy right now, and it looks like you could handle it.

[San Chillos]

The number of turns you need on average with x die each turn is given by 1/(probability to get a tech each turn). So, it is n_turnsaverage = 1/(1-(5/6)x).

So, with 1 die every turn, on average, you will get a tech every 6 turns.

[gamerman01]

@San:

The number of turns you need on average with x die each turn is given by 1/(probability to get a tech each turn). So, it is n_turnsaverage = 1/(1-(5/6)x).

So, with 1 die every turn, on average, you will get a tech every 6 turns.

I know that 6 is the average number of turns that you would get a given result (in this case, a “6”).

But if you take a set of 6 rolls and assume that one is a hit (a “6”) wouldn’t that hit, on average, be in the middle of the 6 rolls?  Wouldn’t the average (expected, if you will) first hit of a 6 (a breakthrough) come between attempt #3 and attempt #4?

I worked about 12 hours today and it’s time for bed.  When I’m not fatigued, I could probably figure this out, but do you understand my question?

If I roll a die per turn, on average when would I hit my first 6?  Are you saying on the 6th attempt?  Because I’m not sure that’s right (but without crunching the numbers or using formulas).  I’m thinking I could expect on average to hit it sooner.

Put another way - after rolling a die 3 times, would I not have a 50/50 chance of hitting a tech by that point?  Isn’t that when I would hit my first tech, on average, after 3 rolls?  Above average luck - hitting on roll 1, 2, and or 3, and below average luck, hitting on turn 4 or later?

[allweneedislove]

@gamerman01:

@San:

The number of turns you need on average with x die each turn is given by 1/(probability to get a tech each turn). So, it is n_turnsaverage = 1/(1-(5/6)x).

So, with 1 die every turn, on average, you will get a tech every 6 turns.

I know that 6 is the average number of turns that you would get a given result (in this case, a “6”).

But if you take a set of 6 rolls and assume that one is a hit (a “6”) wouldn’t that hit, on average, be in the middle of the 6 rolls?  Wouldn’t the average (expected, if you will) first hit of a 6 (a breakthrough) come between attempt #3 and attempt #4?

I worked about 12 hours today and it’s time for bed.  When I’m not fatigued, I could probably figure this out, but do you understand my question?

If I roll a die per turn, on average when would I hit my first 6?  Are you saying on the 6th attempt?  Because I’m not sure that’s right (but without crunching the numbers or using formulas).  I’m thinking I could expect on average to hit it sooner.

Put another way - after rolling a die 3 times, would I not have a 50/50 chance of hitting a tech by that point?  Isn’t that when I would hit my first tech, on average, after 3 rolls?  Above average luck - hitting on roll 1, 2, and or 3, and below average luck, hitting on turn 4 or later?

the average cost is 30ipc. the average number of rolls is 6. above average luck is hitting on roll 1,2,3,4, or 5. below average luck is hitting on roll 7,8,9,10,11,12 or more.

[San Chillos]

@gamerman01:

I know that 6 is the average number of turns that you would get a given result (in this case, a “6”). But if you take a set of 6 rolls and assume that one is a hit (a “6”) wouldn’t that hit, on average, be in the middle of the 6 rolls?  Wouldn’t the average (expected, if you will) first hit of a 6 (a breakthrough) come between attempt #3 and attempt #4?

Average simply means that you should expect to need 6 turns to get a tech if you buy one die every turn i.e, you will get it on your 6th turn with absolute average luck. If it was to hit in the middle of the 6 rolls, the average would be 3.5. However, it’s interesting to note that the probability to hit with the first die (1/6 = 16.7%) is higher than with any other die simply because the probability to need a specific die decreases with the number of dice rolled before it. You only have a probability of (1/6)*(5/6)5 = 6.7% to hit on your 6th turn in fact. However, you have more chances to need at least 10 rolls (you need to miss (5 chances out of 6) on your 9 first rolls (exponent 9) -> (5/6)9 = 19.4% probability) than to hit on your first roll. So, yes, 6 is the average but you should not rely too much on “average luck” simply because the probability to get a very different result (better or worse) is relatively high. (In probability theory, this is related to the variance if you’re interested…)

[gamerman01]

So you’re saying I’m lucky for hitting 7 techs with a single die in my first couple of 1940 games?  :-D  (See the playboardgames forums - there’s proof)

I’ve hit 7 out of approximately 10-12 attempts.  Apparently my sacrifices to the dice gods are the kind they like.

I still say you can’t win if you don’t play.  The only sure thing is that you definitely will not get a tech if you never put 5 IPC’s down to get one.

Allweneed, I’m hoping to post J1 tonight (if I didn’t already tell you - I think that I did)

And thanks for the responses, allweneed and Chillos.  I think that you are right, but like I said without sitting down and thinking hard about it for a couple minutes, I wasn’t sure (that expected average time to hit a 6 would be right around the 6th roll)

Finally, I will make the point that tech was never intended to be a “good strategic investment”, so arguing that it’s not is kind of misguided effort.  Tech is there to give you a competitive advantage over your opponent (and for fun).  It’s also the ONLY possible way to instantly power up your units all over the board, and that means buying units are not a good comparison against it (in other words, you’re not comparing apples to apples).

[finnman]

I use research tokens so tech is a good investment.

[BJCard]

I’d rather have a guarantee of more units to subsequently roll dice with then hope for tech that really isn’t game breaking.

[JamesAleman]

Just out of curiosity, how many game turns do you anticipate in Global?

Does that have an impact on the investment value of Tech? Meaning, say I bought a tech a round, how many rounds am I prepared to wait for a tech, and how many rounds will remain for me to deploy or take advantage of that tech?

Lets say for arguments purpose, that the game last 12 rounds before a winner is clear or certain. If I buy 1 roll a turn, it is reasonable to think I got it by round 6, and had 6 rounds to use it. How does that compare versus a 10 or 8 round game?

Any thoughts?

[gamerman01]

So far my games have all been blowouts, and have only lasted maybe 6-9 rounds.  I would think a reasonably close game would go 20+, with maybe 5-10% of games going into the 30’s.  Just guessing.  I had AA50 games go past 22 rounds even with tech, so I would think this is reasonable…

You have a 50/50 chance of obtaining a tech by the 3rd roll, btw.  Chillos and Allweneed, you were really no help with my question.  You’re saying you would expect a tech on average after 6 rolls.  I say you should expect a 1/6 chance of rolling a 6 each time you roll, and you can expect a 50% chance of obtaining one after 3 rolls (and there is some chance you will have 2 or 3 by 3 rolls).

[San Chillos]

You have 42.1% chances of getting at least one technology by the 3rd roll. (The probability of missing on your 3 first rolls is (5/6)3 = 0.579 or 57.9% so you will have at least one tech 42.1% of the time.)

By the way Gamerman, what was exactly your question?

[gamerman01]

@San:

You have 42.1% chances of getting at least one technology by the 3rd roll. (The probability of missing on your 3 first rolls is (5/6)3 = 0.579 or 57.9% so you will have at least one tech 42.1% of the time.)

By the way Gamerman, what was exactly your question?

My question was when should one expect to hit their first tech, on average, when rolling 1 die per round.  In other words, at one point does one get to a 50/50 chance of getting a tech?

So as you pointed out, after 3 attempts, on average you would have between 1 and 3 techs 42.1% of the time.  After 6 attempts, you would have between 1 and 6 techs about 2/3 of the time.  (So I don’t know why you and Allweneed are saying you could expect to have a tech on your 6th roll, on average)  After 4 rolls, you have over 50% chance of hitting between 1 and 4 techs.  These stats are all assuming you buy one die at a time.

In fact, I hit 4 straight techs with the Axis in a game I’m playing from round 2 into round 3.  So my point is, you have a 100% of getting zero tech if you never buy a research die and if you never buy a research die you are not projecting the threat of hitting an instant tech to your opponent, who can play less defensively in accordance with the lack of threat.  :-)

[San Chillos]

@gamerman01:

My question was when should one expect to hit their first tech, on average, when rolling 1 die per round.  In other words, at one point does one get to a 50/50 chance of getting a tech?

In more technical terms, the “average” is the “population mean”. In our case, each “individual” of the population is a single rolling sequence until you get a tech and its value is the number of rolls needed to get it. If you try until you get a tech an infinite or at least an extremely high number of times (let’s say a million times or even more), you will find that the average number of rolls done to get a tech is 6. It’s that simple. Yes, you can get it on your first roll; however, you could need 20 rolls to get it. On average however, you will need 6 rolls i.e. you will get it with your 6th roll.

You have about a 50/50 chance (48.2%) to miss your first 4 rolls so the fifth roll may be the “point” you’re looking for…

@gamerman01:

In fact, I hit 4 straight techs with the Axis in a game I’m playing from round 2 into round 3.  So my point is, you have a 100% of getting zero tech if you never buy a research die and if you never buy a research die you are not projecting the threat of hitting an instant tech to your opponent, who can play less defensively in accordance with the lack of threat.  :-)

I agree with you. However, the effective (average) cost for acquiring techs could be much lower and it would not hurt the game at all. I know Larry doesn’t like techs and it shows more than ever. IMO, the AA50 system is much more interesting (and fun).

[gamerman01]

@San:

However, the effective (average) cost for acquiring techs could be much lower and it would not hurt the game at all. I know Larry doesn’t like techs and it shows more than ever. IMO, the AA50 system is much more interesting (and fun).

Agreed.  :-) For a more exciting game, play with tokens or reduce the cost of a researcher to 4 or even 3.  Or, keep it at 5 and don’t use tokens, but allow multiple breakthroughs per turn (ala Classic).

Thanks for the intelligent discussion, San Chillos.

[San Chillos]

@San:

Agreed.  :-) For a more exciting game, play with tokens or reduce the cost of a researcher to 4 or even 3.  Or, keep it at 5 and don’t use tokens, but allow multiple breakthroughs per turn (ala Classic).

Thanks for the intelligent discussion, San Chillos.

Yes, we do play with tokens costing 6 IPC each. Always fun to have to throw a die or two every turn. :-D By the way, you’re welcome.  :wink:

[gamerman01]

http://www.axisandallies.org/forums/index.php?topic=20405.new

This is a link to the debate game.

I just hit super subs with Japan on J1 for 5 IPC’s, after rolling a 5 (miss) for Germany.  It’s gonna be a loooong game in the Pacific for Allweneed…  :wink: