Pokémon TCG: Sword and Shield—Brilliant Stars

New rules that impact the number of basics per deck

S

SteveP

Active Member
With the new Mulligan rule (opponent draws only 1 card instead of 2) and the new Fossil trainer rule (Fossils may be played as starting Pokemon), I'm guessing that the average number of "real" basics included in E-on decks will drop. Furthermore, cards like Lanette and Fan Club make it possible to further reduce the number of basics. In the past, my minimum basic count was 11-12. When Fan Club came out (and Traders were still available in Modified), I dropped down to 9-10. Now, I'm thinking I can drop to 6-7 "real" basics, thereby making it possible to run a two Stage-2 combo line.

Anyway, my point is that I'm expecting to see "real" basics replaced by Fossils in many decks and more multiple Stage+ decks. JMO.
 
A note on the mulligan rule: It's still card advantage for your opponent, even if it is less. So, don't lower the number of Basics just because of this reduction. For other reasons, go ahead, have fun. Just as a quick aside.
 
Ever since "eon" was introduced, i have SIGNIFICANTLY dropped the amount of basics in my deck. Not so much is it the lack of needing more basics, but the fact that there arent very many good basics to begin with. The new marril is solid in almost ANY deck simply because it is the only basic with free retreat. So yeah, i would like to increase the amount of basics in my deck, but there arent many good ones out there(which needs to be remedied).
 
You are correct that the mulligan rule reduces the advantage that you
give your opponent. However, don't forget that with a lower number
of pokes in your deck you greatly increase the odds that you'll start
with only "one" pokemon. This in turn will increase the number of times
that you lose on the second or third turn when you don't get any drawing
cards. Without elm or cleffa this may happen with a greater frequency.
Also if you go first you don't get to draw further increasing the
early risk factor.
 
If you are interested in the math behind the probabilities of drawing any given number of basics from your deck in your opening hand then look up the hypergeometric distribution. Don't be put off by all those factorials or Combinations...many spread sheets have the Hypergeometric function built in.
 
NoPoke said:
If you are interested in the math behind the probabilities of drawing any given number of basics from your deck in your opening hand then look up the hypergeometric distribution. Don't be put off by all those factorials or Combinations...many spread sheets have the Hypergeometric function built in.
Click to expand...


aahh...now we have to think.....it's been awhile since i've looked at statistical
tables.......but just eye balling it .....if you started with 6 pokes in a deck
of 60 the odds of starting with just one would be 6/60 + 6/59 + 6/58 + 6/57
+ 6/56 + 6/55 + 6/54 = approximately 42/60 or a little over 70 %. Am
I doing this correctly?????? So about 70% of the time you would start
with only 1 pokemon. Which means in reverse that about 30% of the time
you would start with 0 or more than 1. Help me out. Am I even close.

It would be interesting if someone did a statistical chart showing the probabilites
for different number of pokemon and a second chart showing odds of starting with a drawing card.....hint...hint....
perhaps we have way too much free time on our hands......
 
Eh... eh... aaaaAAAAH!!! No, not the thinking! Well, once I get to a point where I can use that Deck Builder more often, I could probably construct a chart, since it has a feature where it tells you the probability of drawing a Basic depending on how many are in your deck.
 
pity that the deckbuilder gets the answer wrong :(..

It looks like it is using a 63 card deck for its calculation of having a basic to start with.

BTW I found that I did have a MyNintendo account even though I'm a foreigner. It seems that there was a loophole in the signup procedure some months ago whereby you didn't HAVE to provide an address. So as long as I don't edit MyNintendo details I should be able to log in for a while.


The probability of not muliganing is = (1-probability_of_starting_with_none)

so for 6 basics it is 1- 54/60*53/59*52/58*....*48/54 which is 0.5414
(this is 1-hypgeomdist(0,7,6,60) in Excel
ie 1-hypgeomdist(in_hand,hand_size,number_in_deck,deck_size) )

very roughly you muligan half the time with 6 basics.

=================================

Be careful how you calculate the probability of starting with just a single basic. Since you are STARTING you have to remove all those cases where you did get zero basics .

Staying with six basics for now these are the results from the hypergeometric distribution

H(0,7,6,60)=0.458563922
H(1,7,6,60)=0.401243432
H(2,7,6,60)=0.122829622
H(3,7,6,60)=0.016377283
H(4,7,6,60)=0.00096337
H(5,7,6,60)=2.22316E-05
H(6,7,6,60)=1.39821E-07

and the sanity check is that that lot does add up to 1 ie there are no other posibilities.

Now given that you are starting then the muligan is no longer an option: so you divide all the other answers by (1-H(0,7,6,60)) and set the probability of not starting to zero.

thus with six basics your starting hand will have the following basic counts when you start.

0 basics: probability is ZERO (by definition)
1 basic : probability is 0.741072581
2 basics: probability is 0.226858954
3 basics: probability is 0.03024786
4 basics: probability is 0.001779286

and its miniscule for the 5 and 6 card cases much as before.

So with 6 basics you will muligan half the time giving your opponents a single card advantage on average. And when you do start 3/4 or the time you will just have a lone basic and 1/5 of the time you will be blessed with two basics. Once in every thirty games you will have three basics when you start.

=========================

HTH :-D


[edit: SteveP's original assertion that we will see some viable decks with very few REAL basics may well be true. It does hinge on the number of draw cards in your opening hand. I might take EZ1's hint, provided that I can adequately explain the reasoning behind the numbers! :( ]
 
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Thank NoPoke for the Math. TheCrossFormatKid, I've never considered that "good" basics are necessary if you're going to evolve them anyway.

Anyway, my reasoning here anticipates that lots of decks will use Fossil trainers in order to stall and build up the bench. Without Double Gust, the bench is a safe-haven for bench-sitting Powers and battle-prepping. JMO.
 
These are the results of the Hypergeometric distribution with 12 basics...

H(0,7,12,60)=0.191
H(1,7,12,60)=0.381
H(2,7,12,60)=0.293
H(3,7,12,60)=0.111
H(4,7,12,60)=0.022
H(5,7,12,60)=0.002

So now for the specific case of a mix of fossils. To make things simpler we will have 6 REAL basics and 6 Fossils.

So 1 in 5 games you will mulligan. Acceptable.

Renormalising the results for those 81% of the games when you do start...
(ie divide the above results by {1-H(0,7,12,60)}

We get..

Start with 0 basics = 0.000
Start with 1 basic = 0.471
Start with 2 basics = 0.362
Start with 3 basics = 0.137
Start with 4 basics = 0.027
Start with 5 basics = 0.003

So its still not great: Half the time you are still stuck with a single pokemon either a real one or a fossil. (incidentally this is one of the reasons why the FTKO was so common!)

So lets break out the fossils from the real basics in the above. Since there are 6 of each in the deck the pattern is a simple Binomial distribution weighted as above.


Start with a single Fossil = 0.24
Start with a single Pokemon = 0.24
Start with a single Fossil and a single Pokemon = 0.16
Start with two Fossils = 0.08
Start with two Pokemon = 0.08

Its not looking too good for actually having a benched pokemon :(

1/4 of the time you have a lone fossil, 1/4 of the time you have a lone poke, 1/3 of the time you will have a benched poke, and 1/5 of the time some other confiiguration.

Now you could choose to muligan the lone fossil. But that is just giving your opponent yet more chance of card advantage.

--------------------

So what do all these numbers actually tell us? I'll leave you to make your own conclusions. But be warned that there are lots of aspects of the Pokemon tcg that aren't factored in here. The biggest one is how reliable the new draw and search engine is without Elm and Cleffa.

Here's a clue though:If you get to play me then don't be surprised if under the new tournament rules I elect to go second if I win the toss. Does depend upon which deck I'm playing though ;)
 
Great job on the math NoPoke. A couple of thoughts.

1. Good news or bad news but not no news. If
no news is worse than bad news then wouldn't no news
by definition be a form of bad news thereby making no news
an impossibility??????way too much free time....

2. Regarding going first versus second(off on a tangent) wouldn't
you have to closely weigh the advantages of the draw card versus
the opportunity to be the first to play an energy, utilize a draw
card, inflict damage or make a defensive move like playing shaman etc., or
inflicting a status effect. I may be wrong but I suspect that
going first is still the better play in most situations.
Only time will tell......
 
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