Technology is a bad strategic investment

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…  :-(

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.

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.

@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?

@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…)

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).

I use research tokens so tech is a good investment.

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

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?

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).

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?

@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.  :-)

@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).

@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:

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:

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:

@allweneedislove:

Super subs – your researchers have found that putting a snorkel on your diesel  U-boats allows you to submerge with the engines running so you can be extra sneaky and you get 1 more attack pip. for 30ipc you could just buy 5 more subs that would get you 10 more attack pips, 5 more defence pips and 5 more units that can soak up hits.

1 more attack pip is a 50% increase in attacking power.  Over the course of our game, I may buy between 5 and 25 subs with Japan.  I will have a much easier time keeping the USA at bay. I also have only 5 remaining chart 2 techs left, so on my next breakthrough I will get jets, improved shipyards, radar, long range air, or heavy bombers, all of which are extremely useful for Japan.  Plus, you never know how much I’m going to spend on research and when and what I’m going to obtain.

I think you have underestimated the power of tech.  :-)

i do realize this is a ‘Global topic’… but still, i just don’t see how in E40 there is room for investing in this, except for the US and maybe Germany… but again, both of those depend heavily on how Sealion-Barbarossa turns out, and whether Italy is spread thin in the Med-Africa - meaning that if they don’t perform well, they need the extra 5xn cash.

in Global, i would add USSR and Japan to the ‘likely’ list…

ps. if i roll multiple dice and get 2+ 6es, do i still only get the one tech? me with no rulebook, haven t seen it referenced, hence the question. thanks!

@Gabike:

i do realize this is a ‘Global topic’… but still, i just don’t see how in E40 there is room for investing in this, except for the US and maybe Germany… but again, both of those depend heavily on how Sealion-Barbarossa turns out, and whether Italy is spread thin in the Med-Africa - meaning that if they don’t perform well, they need the extra 5xn cash.

in Global, i would add USSR and Japan to the ‘likely’ list…

ps. if i roll multiple dice and get 2+ 6es, do i still only get the one tech? me with no rulebook, haven t seen it referenced, hence the question. thanks!

1 power per turn, extra 6’s ignored. No powers in Europe, only Global.