Transformers Trading Card Game: A Newbie's View

I have long been a fan of Transformers.  I was in the target audience age of 6-10 when the first comics came out, and my first issue was issue 4, back in November 1984.  I've reviewed Dark of the Moon, and Revenge of the Fallen.  I was delighted (but mostly interested and curious) when I learned of the Transformers Trading Card Game a few months ago, and after watching quite a few YouTube videos, decided to take the plunge and buy some of the cards on eBay.  It's all relative, but £4 for a pack of cards seems expensive, while buying one or two on eBay seemed less so. 

I was impressed with the size, colouring and designs (very reminiscent of G1), so I bought a starter pack (Wave 1 Autobots), and tried my first player-versus-player match with the starter pack cards (I played both players), working through the game mechanics, keeping track of damage with a notepad and pencil, and observing while playing.  I'm no expert at card games (this is my first, and will probably be my only), but I started to notice a few issues with the way I was playing.

A brief summary of my first game: 

Decepticons:  Flamewar, Starscream (Scheming Second in Command), Megatron (Decepticon Leader)

Autobots:
Autobot Hound; Optimus Prime (Autobot Leader); Bumblebee (Courageous Scout)

The Autobots took a pounding due to Megatron's pierce ability; Optimus and Bumblebee were KO'd with just two turns.  Autobot Hound lasted a little longer due to his better health and I was able to repair damage from him a couple of times.  It was a narrow Autobot victory.

In between games 1 and 2, I purchased an additional 58 battle cards - a mix so that I can understand what style suits me, and what I need to play.  I also purchased the Stunticons, so I make sure I have the relevant Stunticon cards to form Menasor.

Game two
Changes from previous game: 

Decepticons 
Exchange Starscream (SSIC) for Ramjet;

Autobots change to Dinobot Swoop (Fearsome Flyer), Optimus Prime (Freedom Fighter)and Optimus Prime (Autobot Leader). 

I modify the decks to make the Decepticon deck more aggressive, while the Autobot deck includes cards like Fling, Field Repair and Repair Bay so that I can last longer in battles (in theory).  At this point I'm still not overly worried about the colours of the icons, I'm just selecting battle cards based on their abilities.

There were a number of issues I had while playing the game here:
- I was getting handfuls of action cards and almost no upgrades.  The action cards enabling me to "Play an upgrade" were useless, and the ability to play an upgrade each turn was being wasted
 - The other hands I were playing ran out of cards.  I wasn't drawing enough  - and this makes sense:  if I can only draw a card, but play an action and an upgrade, I was going to be decreasing my hand by one card per turn until I ran out.  I needed more draw capability.

I did some analysis of the overall cards in Waves 1 and Wave 2, just as a brief diversion:  There are 172 battle cards in total, of which some are duplicates.  I'll produce a deduplicated list another time:
90 (over half) are Action cards
31 are Utilities (and I was not putting enough of these in my decks)
30 are Weapons
21 are Armour

Just based on random sampling, it was no wonder that I was running out of upgrade cards (with so many action cards to choose), and then running out of cards altogether.  I had to re-balance my decks to include more upgrades and fewer actions.

And I needed more draw capability.

Game three
Decepticon PowerHouse versus Mixed Drawers

Decepticons
Megatron (Decepticon Leader)
Ramjet (Sky Smasher) - who needs abilities when you have 7 attack and 14 health?
Flamewar  - a trusty sidekick who brings the star count up to 25

Mixed Drawers
Autobot Hound (Long Range Scout) - when you flit to alt mode, possibility to scrap one and draw two
Optimus Prime (Autobot Leader) - when you flit to alt mode, draw a card
Dead End - when you flip to bot mode, draw a card
Decepticon Drag Strip - brings the total to 25 stars; and when attacking in alt mode and you get a blue and orange icon, draw 2 cards.

Results
Better.  Ramjet and Megatron are still lethal, especially when given upgrades (Ramjet especially, as he has no abilities of his own).  I drew a "Disarm" for the Mixed Drawers, which ended Ramjet's resistance, and they eventually won.  I like that card!

I know I'm probably playing a biased game, but it's not completely deliberate.  I'm just subconsciously rooting for Optimus and Hound (my favourite G1 characters).

Questions

However, all this single-handed playing has led me to ask some questions:

1. How do you (as a player) select your characters and battle cards?  Do you pick characters with cool abilities, and then build a deck around them?  Or do you look at the battle cards and think "That would be fun, if I could find the right mêlée/ranged/leader character to play it with"?

2.  How do you balance the proportion of actions/armour/utilities/weapons?  What split do you use?

3.  How do you increase your draw capacity?  Cards, or flip abilities?

My ongoing battle card deck

This is still a work in progress, but here's what I'm going to try in my next game

Actions
Inspiring Leadership x3
Repair Bay x3  (actually, I only own 2 at the moment... need to fix this!)
Rest and Relaxation x3 (I know it's a green icon, but that much repair is very useful)
Fling x2
Field Repair x2
Treasure Hunt x2 (still upping my upgrade count)
Disarm x2 (this was a killer against Ramjet and I liked playing it)

Armour
Evasive Maneuvers x2
Body Armor x2
Scrapper Gauntlets x3
Reinforced Plating x2
Cooling Vents x2

Weapons
Grenade Launcher x2
Handheld Blaster x2
Enforcement Batons x2

Utilities
Debilitating Crystal x2
Security Console x2
Data Pad x2

17 Actions
11 Armour
6 Weapons
6 Utilities
40 total.

Any thoughts?  Next time - a data analysis view of the Transformers Card Game, looking at the different coloured pips on the cards.

Three-Factor Multi-Variate Testing

TESTING ALL POSSIBILITIES WITHOUT TESTING EVERYTHING

My favourite part of my job is determining what to test, and planning how to run a test.  I enjoy the analysis afterwards, but the most enjoyable part of the testing process is deciding what the test recipes will actually be.  I've covered - at length - test design and planning, and also multi-variate testing.  I particularly enjoy multi-variate testing, since it simply allows you test all possibilities without having to test everything.

In my previous posts, where I introduced MVT, I've only covered two-factor MVT: should this variable be black or red?  Should it a picture of a man or a woman?  Should it say 'Special offer' or 'Limited time'?  Is it x or is it y?  How do you analyse MVT results? In this post, I'm going to take the discussion of testing one step further, and look at three-factor multi-variate testing:  should it be x, y or z?

Just as there are limited opportunities for MVT, the range of opportunities for three-factor MVT is potentially even more limited.  However, I'd like to explain that this doesn't have to be the case, and that it just takes careful planning to determine when and how to set up a test where there are three possible 'best answers'.

SCENARIO

You run a domestic travel agency, which specialises in arranging domestic travel for customers across the country (this works better if you imagine it in the US, but it works for smaller countries too).  You provide a full door-to-door service, handling everything from fuel, insurance, tickets, transfers  - whatever it takes, you can do it.  Consequently, you are in high demand around Christmas and Thanksgiving (see, I told you this worked better in the US), and potentially other holiday periods.  Yes, you're a travel agency firm based on Planes, Tranes and Automobiles.

It's the run-up to the largest sales time of the year, as you prepare to reunite distant family members across the country for those big family celebrations and parties and whatever else.  What do you lead with on your website's homepage?

Planes?
Trains?
Or automobiles?

If you want to include buses, look out for a not-yet-planned post on four-factor MVT.  I'll have it ready by Christmas.

So far, this would be a straightforward A/B/C test, with a plane, a car and a train.  Your company colours are yellow, so let's go with that:

Your marketing team are also unsure how to lead with their messaging - should they emphasise price, reliability, or an emotional connection?

They can't choose between
"Cross the country without costing the world" (price)
"Guaranteed door-to-door on time, every time" (reliability)
"Bring your smile to their doorstep this holiday" (emotional)

So now we have nine recipes, A-I.

A: Plane plus Price B:  Plane plus reliability C: Plane plus emotions	D: Car plus Price E:  Car plus reliability F: Car plus emotions	G: Train plus price H: Train plus reliability I: Train plus emotions

Now, somebody in the exec suite has decided that now might be the time to try out a new set of corporate colours.  Yellow is bright and cheery, but according to the exec, it can be seen as immature, and not very sophisticated.  The alternatives are red and blue (plus the original yellow).

Here goes:  there are now 3x3x3 possible variations - that's 27 altogether.  And you can't run a test with 27 recipes - for a start, there aren't enough letters in the alphabet.  There's also traffic and timing to consider - it will take months to run a test like that to get any level of significance.  Nevertheless, this is an executive request, so we'll have to make it happen.

Firstly, the visuals:  if this was just a two-variable test, then we'd have nine recipes, as you can see below.


However, each of these vehicle/colour combinations has three more options (based on the marketing message that we select) - here is a small sample of the 27 total combinations, to give you an idea.


   
This is not a suitable testing set, but it gives you an idea of the total variations that we're looking at.  The next step, as we did with the more straightforward two-factor MVT, is to identify our orthogonal set - the minimum recipes that we could test that would give us sufficient information to infer the performance of the recipes that we don't test.  It's time to charge up your spreadsheet.

THE RECIPES - AN ORTHOGONAL SET

There are 3*3*3 = 27 different combinations of colour, text and vehicle... here's the list, since you're wondering ;-)

Recipe	Colour	Vehicle	Message
A	Red	Plane	Price
B	Red	Plane	Reliability
C	Red	Plane	Emotions
D	Red	Train	Price
E	Red	Train	Reliability
F	Red	Train	Emotions
G	Red	Car	Price
H	Red	Car	Reliability
I	Red	Car	Emotions
J	Blue	Plane	Price
K	Blue	Plane	Reliability
L	Blue	Plane	Emotions
M	Blue	Train	Price
N	Blue	Train	Reliability
O	Blue	Train	Emotions
P	Blue	Car	Price
Q	Blue	Car	Reliability
R	Blue	Car	Emotions
S	Yellow	Plane	Price
T	Yellow	Plane	Reliability
U	Yellow	Plane	Emotions
V	Yellow	Train	Price
W	Yellow	Train	Reliability
X	Yellow	Train	Emotions
Y	Yellow	Car	Price
Z	Yellow	Car	Reliability
AA	Yellow	Car	Emotions

The recipes with the faint green shading would form a simple orthogonal set; here they are for clarity:

Recipe	Colour	Vehicle	Message
A	Red	Plane	Price
E	Red	Train	Reliability
I	Red	Car	Emotions
K	Blue	Plane	Reliability
O	Blue	Train	Emotions
P	Blue	Car	Price
U	Yellow	Plane	Emotions
V	Yellow	Train	Price
Z	Yellow	Car	Reliability

Note that each colour, vehicle and message appear three times each; there are therefore nine recipes that we need.  This is still a considerable number, but it's a significant saving from 27 in total.

THE ANALYSIS

Which colour?  How to find the best variation for each element

Select the recipes which will give us a reading on the best colour by choosing recipes where the other variants cancel to noise:

This is simple (and simpler than the two-factor version):  we simply add the results for all the "red" recipes, and compare with the sum of all the "blue" recipes and, compare with the data for all the "yellow" recipes.

Let's take a look at some hypothetical data, based on the orthogonal recipe set shown above:

Recipe	a	e	i	k	o	p	u	v	z
Visits	1919	1922	1932	1939	1931	1934	1915	1955	1944
Bookings	193	194	189	194	205	192	200	209	206
Revenue (k)	£14.2	£14.6	£14.4	£14.3	£15.6	£13.94	£14.8	£15.7	£15.4
Conversion	10.1%	10.1%	9.8%	10.0%	10.6%	9.9%	10.4%	10.7%	10.6%
Lift	-	0.4%	-2.7%	-0.5%	5.6%	-1.3%	3.8%	6.3%	5.4%
Avg Booking Value	£73.58	£75.26	£76.19	£73.71	£76.10	£72.60	£74.00	£75.12	£74.76
Lift	-	2.3%	3.6%	0.2%	3.4%	-1.3%	0.6%	2.1%	1.6%
RPV	£7.40	£7.60	£7.45	£7.37	£8.08	£7.21	£7.73	£8.03	£7.92
Lift	-	2.7%	0.7%	-0.3%	9.2%	-2.6%	4.4%	8.5%	7.1%

I've shown the raw metrics and the calculated metrics for the recipes, but it's important to remember at this point:  the recipes shown here probably won't include the best recipe.  After all, we're testing nine recipes out of a total of 27, so we have only a one in three chance of selecting the optimum combination.
What we need to do next, as I mentioned above, is to combine the data for all the yellow recipes, and compare with the red and the blue.

Recipes	aei	kop		uvz
Colour	Red	Blue	Lift vs Red	Yellow	Lift vs Red
Visits	5773	5804		5814
Bookings	576	591		615
Revenue (k)	£43.2	£43.84		£45.9
Conversion	9.98%	10.18%	2.1%	10.58%	6.0%
ABV	75.00	74.18	-1.1%	74.63	-0.5%
RPV	7.48	7.55	0.9%	7.89	5.5%

So we can see from our simple colour analysis (adding all the results for the recipes which contain Red, vs Blue, vs Yellow) that Yellow is the best.  The Conversion has a 6% lift, and while Average Booking Value is slightly lower, the Revenue Per Visit is still 5.5% higher for the yellow recipes than it is for the Red.

Now we do the same for the vehicles: plane, train or car?

Recipes	aku	eov		ipz
Vehicle	Plane	Train	Lift vs Plane	Car	Lift vs Plane
Visits	5773	5808		5810
Bookings	587	608		587
Revenue (k)	£43.3	£45.9		£43.74
Conversion	10.17%	10.47%	3.0%	10.10%	-0.6%
ABV	73.76	75.49	2.3%	74.51	1.0%
RPV	7.50	7.90	5.4%	7.53	0.4%

Clear winner in this case:  it's Train, which is the best for conversion, average booking value and revenue per visit.

And finally, the messaging:  emotional, price or reliability?

Recipes	apv	iou		ekz
Message	Price	Emotion	Lift vs Price	Reliability	Lift vs Price
Visits	5808	5778		5805
Bookings	594	594		594
Revenue	43.84	44.8		44.3
Conversion	10.23%	10.28%	0.5%	10.23%	0.1%
ABV	73.80	75.42	2.2%	74.58	1.0%
RPV	7.55	7.75	2.7%	7.63	1.1%

And in this case, it's Emotion which is the best, with clearly better average booking value and revenue.  It would appear that price is not the best way to lead your messaging.

CONCLUSION AND THOUGHTS

The best combination is:

Yellow Train, with Emotion messaging.

Notice that the performance of the recipes that we actually tested is in agreement with the winning combination (based on the calculations)

Recipes that contain none of the winning elements performed the worst:

A  - Red Plane, Price :  RPV £7.40
K - Blue Plane, Reliability:  RPV £7.37
P - Blue Car, Price  :  RPV £7.21
Recipes that contain just one of the winning elements produced slightly  better results:

E - Red Train, Reliability:  £7.60
I - Red Car, Emotions:  £7.45
Z - Yellow Car, Reliability: £7.92*

Recipes that contained two of the three winning elements were the best performers:

O - Blue Train, Emotions:  £8.08
U - Yellow Plane, Emotions:  £7.73
V - Yellow Train, Price: £8.03

I would strongly recommend running a follow-up test, with the two winners from the first selection (O and V) along with the proposed winner based on the analysis, Yellow Train with Emotions.  It's possible that this proposed winner will be the best; there's also the possibility that it may be close to but not as good as O or V. 

*There's also an argument for including Z (Yellow Car, Reliability) as an outlier, given its performance.  

There are some clear losers that do not need to be pursued:  notice how two of the bottom three performing recipes contain Blue and Price.  All of the Price recipes that we tested - A, P and V, had lower than typical Average Booking Value, and this includes recipe V, which was one of the best recipes.  With a different message (Emotions, most likely), Recipe V would be a runaway success.

It's not surprising that a follow-up is needed; remember that we've only tested nine out of 27 combinations, and it's unlikely that we'll have hit the optimum design first time around.  However, by careful selection of our original recipes, we need only test four more (at the most) to identify the best from all 27.  Finding the best combination from 27, by only testing 13 is a definite winner.  This is the power of multi-variate testing: the ability to test all possibilities without having to test everything.

Here's my series on Multi Variate Testing

Preview of Multi Variate testing
Web Analytics: Multi Variate testing 
Explaining complex interactions between variables in multi-variate testing
Is Multi Variate Testing an Online Panacea - or is it just very good?
Is Multi Variate Testing Really That Good - 
Hands on:  How to set up a multi-variate test
And then: Three Factor Multi Variate Testing - three areas of content, three options for each!

Maths Puzzle: Magic Hexagons

The final puzzle I'll be discussing from the MatheMagic book is 'Magic Hexagons'.  For this one, I'll cover the basic puzzle from the book, and then look at extending it (until I come unstuck).

The puzzle is borderline trivial:
Place the numbers 1-7 in this hexagon so that the three lines through the central hexagon all have the same total.  

The method is straighforward: place the number in the middle of the range (4) in the central position, and then pair the others around it so that the smallest is with the largest (1 and 7), then the next smallest with the next largest (2 and 6), and finally the last pair (3 and 5).

However, extending this (in the same way as I did with the triangles in my previous post) is not trivial at all.  There are many solutions for the regular hexagon with side length = 3, but I took my calculations along a slightly different path and came completely unstuck.

Consider this hexagonal grid, with irregular sides:  is it possible to populate them so that all the straight-line paths with length four have the same sum? 

The five lines shown here with arrows indicate the lines (each containing four hexagons) that I will attempt to balance.

First attempt:  place the smaller numbers (1, 2) in the central hexagons, and those at the middle of the range (6, 7) then try to pair up the numbers around the outside of the shape.

Not a great start, but I was able to make some improvements by changing the numbers in the four central hexagons.  I still have 2 in the central area, but have included 4 instead of 1, and 8 instead of 6.  Still working on keeping the mid-range and low-end numbers in the middle. 

The issue is that the numbers in dark blue (in this example, 4 and 7) are included in three separate lines (the vertical, and two diagonal lines) and swapping numbers in and out of these hexagons affects three different lines (and the ones you're swapping into).  The numbers in the pale blue hexagons are also considered in two different lines (the two diagonal lines that intersect) and again there's too much juggling to do.  In the simple example, and in the regular 3x3 hexagon puzzle, each number only contributes to one line and swapping with other numbers only affects the start and destination lines.  In my puzzle, there are between two and six lines being affected (depending on the location of the two numbers being swapped).

So, is it possible to solve this puzzle?  Short answer: no, I don't think it is.

If you've enjoyed this article, I can suggest a few more that I've written more recently:

Snakes and Ladders (investigating the Collatz Conjecture)
Crafty Calculator Calculations (numerical anagrams with five digits)
More Multiplications (numerical anagrams, four digits)
Over and Out (reduce large numbers to zero as quickly as possible)
Calculator Games: Front to Back
Calculator Games: Up, up and away with Ulam sequences
Calculator Games: The Kaprekar Constant

The Mathemagic Series:

Arrange nine coins in ten straight lines
Solve 1/a + 1/b + 1/c = 1  for unique a, b, c
Magic Triangles