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Comparison of tech rolls: Classic vs. Anniversary



  • It’s clear that the new tech rules revise the way that rolls are handled compared to the MB version, but the effects didn’t seem immediately obvious.  So I wrote a little program to see how tech developments emerged over time in the two games.  The graphs below (showing the turn when two tech results are achieved) show that tech success is now more predictable since it’s clustered into a smaller number of possible turns and occurs earlier, costing less:

    Buying 1 Tech Roll/Researcher per Turn:

    2nd Edition
    1
    2 ***
    3 *****
    4 ******
    5 ******
    6 *******
    7 *******
    8 ******
    9 ******
    10 ******
    11 *****
    12 *****
    13 *****
    14 ****
    15 ****
    16 ***
    17 ***
    18 ***
    19 **
    20 **
    Avg turn = 11.2
    Avg cost = 56.1

    Anniversary Edition
    1
    2 ***
    3 ********
    4 ***************
    5 ******************
    6 ******************
    7 ***************
    8 **********
    9 ******
    10 ***
    11 **
    12 *
    13
    14
    15
    16
    17
    18
    19
    20
    Avg turn =  6.0
    Avg cost = 30.0

    Buying 2 Tech Rolls/Researchers per Turn:

    2nd Edition
    1 ***
    2 **********
    3 *************
    4 *************
    5 ************
    6 **********
    7 *********
    8 *******
    9 *****
    10 ****
    11 ***
    12 ***
    13 **
    14 *
    15 *
    16 *
    17 *
    18
    19
    20
    Avg turn =  6.3
    Avg cost = 62.5

    Anniversary Edition
    1
    2 *********
    3 **********************
    4 **************************
    5 *********************
    6 ************
    7 ******
    8 **
    9 *
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    Avg turn =  4.3
    Avg cost = 43.4



  • Wow this is pretty cool. Why not show it for 1 tech breakthrough though, as opposed to 2?


  • 2018 2017 2016 '11 Moderator

    I agree, since you cannot get two break throughs in a turn in Anniversary.



  • Here it is for 1 tech breakthrough, stopping when that’s been achieved:

    1 Tech Roll/Researcher per Turn:

    2nd Edition
    1 ****************
    2 **************
    3 ************
    4 **********
    5 ********
    6 *******
    7 ******
    8 *****
    9 ****
    10 ***
    11 ***
    12 **
    13 **
    14 **
    15 *
    16 *
    17 *
    18 *
    19 *
    20 *
    Avg turn =  5.9
    Avg cost = 29.5

    Anniversary Edition
    1 *****************
    2 *************************
    3 ************************
    4 *****************
    5 **********
    6 ****
    7 **
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    Avg turn =  3.0
    Avg cost = 15.0

    2 Tech Rolls/Researchers per Turn:

    2nd Edition
    1 ******************************
    2 *********************
    3 ***************
    4 **********
    5 *******
    6 *****
    7 ***
    8 **
    9 **
    10 *
    11 *
    12 *
    13
    14
    15
    16
    17
    18
    19
    20
    Avg turn =  3.3
    Avg cost = 32.7

    Anniversary Edition
    1 ******************************
    2 ************************************
    3 ***********************
    4 *********
    5 **
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    Avg turn =  2.2
    Avg cost = 21.8

    Because it cuts off at 20 turns, a little bit of the “long tail” (i.e. horrible luck) is missing for the 1 Roll per Turn/2nd Edition (this is also true for two-tech version posted above).  Mathematically, the Avg turn should be 6.0 and the Avg cost should be 30.0 here.



  • Great analysis Lema099!

    It really puts into perspective the average cost of unlocking a tech vs. the average turn of unlocking.

    Interestingly, you can compare unlocking a tech to purchasing and IC or aircraft carrier.



  • Here it is for 1 tech breakthrough

    Yes, now we’re talkin!

    It might also be interesting to see how things change if you buy 1 additional token per turn until you get a breakthrough. So, for instance, you get 1 roll on the first turn, 2 rolls on the second, 3 rolls on the third, etc. until you get something.



  • However, in AA50, Researchers stay from turn to turn, choosing to buy 2 Researchers on the 1st turn will generate the same rough odds for obtaining a tech within the first 3 turns as buying 1 Researcher on 1st, 1 on 2nd, and 1 on 3rd.  However, the cost of obtaining it in the given period is cheaper, and is more likely to happen earlier:

    2 Researchers, then stop (net Cost: 10 IPCs)
    Turn 1. 2 Rolls (30% chance of obtaining tech by now)
    Turn 2. 2 Rolls (51% chance of obtaining tech by now)
    Turn 3. 2 Rolls (66% chance of obtaining tech by now)

    1 Researcher per turn (net Cost: 15 IPCs)
    Turn 1: 1 Roll (17% chance of obtaining tech by now)
    Turn 2: 2 Roll (42% chance of obtaining tech by now)
    Turn 3: 3 Roll (66% chance of obtaining tech by now)

    How about you give the figures for buying 1, 2, or 3 Researchers on turn 1, then not buying any more until you get the tech.



  • @TG:

    It really puts into perspective the average cost of unlocking a tech vs. the average turn of unlocking. 
    Interestingly, you can compare unlocking a tech to purchasing and IC or aircraft carrier.

    Good way to put it.  You could also choose to go cheaper if you don’t mind waiting, or more expensive if you need a breakthrough ASAP.  As mentioned by wodan46, buying researchers up front and letting them work from turn to turn is quite effective.  But if you don’t have the IPCs to spare up front, you can increase the researcher pool over time.  I like how this system is more flexible and more interesting than the old “buy the dice and roll them” approach.

    @Unknown:

    It might also be interesting to see how things change if you buy 1 additional token per turn until you get a breakthrough. So, for instance, you get 1 roll on the first turn, 2 rolls on the second, 3 rolls on the third, etc. until you get something.

    That’s what’s happening with the Anniv. Ed. charts above, which is why their payoffs are so much faster than the 2nd Edition ones.  The 1 or 2 “Rolls” per turn are actual rolls for 2nd Ed., but are Researcher tokens for Anniv. Ed. which accumulate.  Sorry for the confusion; I’ve edited the headings to make that clear.

    @wodan46:

    How about you give the figures for buying 1, 2, or 3 Researchers on turn 1, then not buying any more until you get the tech.

    Here that is, stopping after getting the one tech breakthrough:

    One Researcher bought on turn 1 (and no others)
    1 *****************
    2 **************
    3 ************
    4 **********
    5 ********
    6 *******
    7 ******
    8 *****
    9 ****
    10 ***
    11 ***
    12 **
    13 **
    14 **
    15 *
    16 *
    17 *
    18 *
    19 *
    20 *
    Avg turn = 6.0
    Avg cost = 5.0

    Two Researchers bought on turn 1 (and no others)
    1 *******************************
    2 *********************
    3 ***************
    4 **********
    5 *******
    6 *****
    7 ***
    8 **
    9 **
    10 *
    11 *
    12 *
    13
    14
    15
    16
    17
    18
    19
    20
    Avg turn = 3.3
    Avg cost = 10.0

    Three Researchers bought on turn 1 (and no others)
    1 ******************************************
    2 ************************
    3 **************
    4 ********
    5 *****
    6 ***
    7 **
    8 *
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    Avg turn = 2.4
    Avg cost = 15.0



  • What kind of “program” are you writing?  What equation/algorithm are you using?



  • @shifty:

    What kind of “program” are you writing?  What equation/algorithm are you using?

    It’s written in BlitzMax. The source below should (hopefully :)) not be too hard to understand - if you have questions, feel free to ask:

    
    ' Compares 2nd ed. A&A tech dev cost/rate with Anniv. ed. A&A
    ' 20 turns to test; record turn number that a total of 2 breakthroughs were achieved.  Test 1 & 2 rolls/turn.
    ' If two breakthroughs aren't achieved, "turn 0" is recorded (ignored for graphing & turn average)
    ' (When going for two breakthroughs, two aren't achieved in about 2% for both 2nd and Anniv.)
    
    Strict
    
    Local breakthroughs, totalCost, turn, totalTurns
    Local answer[21], prefix$, graph$
    Local breakthroughLimit = 2
    
    For Local rolls = 1 To 2 ' actual rolls for 2nd Ed, Researchers for Anniv.
    	Print;Print; Print rolls + " Tech Roll(s)/Researcher(s) per Turn:"
    
    	Print; Print "2nd Edition"
    	totalCost = 0
    	totalTurns = 0
    	For Local c = 0 To 20
    		answer[c] = 0
    	Next
    
    	For Local test = 1 To 100000 ' a hundred thousand tests for accuracy
    		breakthroughs = 0
    		turn = 0
    		While breakthroughs < breakthroughLimit And turn <= 20
    			turn :+ 1
    			totalCost :+ rolls * 5 ' each roll costs 5 IPCs
    			For Local c = 1 To rolls
    				If Rand(6) = 6 Then breakthroughs :+ 1
    			Next
    		Wend
    		totalTurns :+ turn
    		If turn > 20 Then
    			answer[0] :+ 1
    		Else
    			answer[turn] :+ 1
    		EndIf
    	Next
    
    	' display results
    	For Local c = 1 To 20
    		graph = ""
    		' divide results by 1000 so each asterisk represents one percent
    		For Local cc = 1 To Int(answer[c]/1000.0 + .5)
    			graph :+"*"
    		Next
    		If c < 10 Then prefix = " " Else prefix ="" ' extra space for single digits
    		Print prefix + c + " " + graph
    	Next
    	Print "Avg turn = " + totalTurns / 100000.0
    	Print "Avg cost = " + totalCost / 100000.0
    
    	Print; Print "Anniversary Edition"
    	totalCost = 0
    	totalTurns = 0
    	For Local c = 0 To 20
    		answer[c] = 0
    	Next
    	Local researchers ' researchers accumulate from turn to turn
    	For Local test = 1 To 100000
    		researchers = 0
    		breakthroughs = 0
    		turn = 0
    		While breakthroughs < breakthroughLimit And turn <= 20
    			turn :+ 1
    			totalCost :+ rolls * 5 ' each researcher costs 5 IPCs
    			researchers :+ 1 * rolls ' accumulate 1 researcher per "roll"
    			Local success
    			For Local c = 1 To researchers
    				If Rand(6) = 6 Then success = True ' only one regardless of # of sixes rolled
    			Next
    			If success Then
    				researchers = 0 ' eliminate accumulated researchers when successful
    				breakthroughs :+ 1
    			EndIf
    		Wend
    		totalTurns :+ turn
    		If turn > 20 Then
    			answer[0] :+ 1
    		Else
    			answer[turn] :+ 1
    		EndIf
    	Next
    
    	' display results
    	For Local c = 1 To 20
    		graph = ""
    		' divide results by 1000 so each asterisk represents one percent
    		For Local cc = 1 To Int(answer[c]/1000.0 + .5)
    			graph :+"*"
    		Next
    		If c < 10 Then prefix = " " Else prefix ="" ' extra space for single digits
    		Print prefix + c + " " + graph
    	Next
    	Print "Avg turn = " + totalTurns / 100000.0
    	Print "Avg cost = " + totalCost / 100000.0
    
    Next
    
    

    I release it into the public domain (modify it as desired/convert it to the language of your choice).  breakthroughLimit is initially set for 2, which generated the first set of graphs in this thread (I hand-rounded the accuracy to a single decimal place when copy/pasting results in the thread). Setting it to 1 (i.e. stopping after getting one breakthrough) produced the second set above. I also made another, slightly tweaked version to generate the “only buy Researchers on turn 1” version for wodan46.


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