Mudkip said:
Mozartrules, 40% chance of starting with Dunsparce?!?! Please take a Maths lesson before you post :lol: it's 47% actually
I should also stay away from this thread, but it is hard not to respond.
Mudkip, I have no doubt that that you are a better Pokemon player
than I am, your results are certainly better (*). Feel free to critisize my memory (I specifically quoted from that) and my opinions about decks. But you are not going to do well questioning my math ability
, at least not until you finish your PhD.
I don't know how you get the 47%, but I believe that number is wrong. Did you by any chance do 7 * (4/60) which is 46.67%? The easiest way to see why that calculation is wrong is that you would get more than 100% chance of getting a Dunsparce in your first 16 cards.
The correct way to calculate this is to find the chance of not having one of the 4 cards when you draw 7. First card is 56/60, second is then 55/59 and continue multiplying the probabilities (because they all have to be true) until you get 50/54.
Non-Duns. Total Probability Combined prob.
56 60 0.933333333 0.933333333
55 59 0.93220339 0.870056497
54 58 0.931034483 0.810052601
53 57 0.929824561 0.753206804
52 56 0.928571429 0.699406318
51 55 0.927272727 0.648540404
50 54 0.925925926 0.600500374
So the 60.05% is the chance of not having a Dunsparce in your opening hand which gives the appr. 40% chance for having (at least) one. This kind of calculation involving a single card type is trivial to make in Excel and I would advise all deck designers to have the most commonly used numbers available.
I used the same approach to find the chance of some cards all being in your prizes, you have to draw 54 cards without getting one of them. That kind of calculation is important for evaluating how many of a particular card (i.e. Rayquaza) you need to put in your deck to avoid that calamity.
Calculations with multiple cards are more difficult (i.e. what are my chances of having a Wynaut (of 4) in my opening hand and having a psychic energy to attack in my opening had or first draw), but well within the capabilities of a simple spreadsheet even if you continue this a little further and allow the use of a supporter during your first turn.
You could - correctly - argue that the real chance is higher because you have to add the extra cards that you may get from the opponent's mulligan, but that complicates things a lot because you have to make assumptions about the number of basics that the opponent plays (certainly doable if we make an assmption on something like 13) and that won't even include the Fossil choices that the opponent may make. I find it hard to imagine that it would make a 7% difference since that isn't achieved until you average opening hand size reaches 9.
The final argument you could make for the number not being 40% is that decks - this is a known fact - are not shuffled perfectly, but I am not sure which direction the change might go. I have in storage a great book by two French mathematicians who studied these issues for Contract Bridge (also a fantastic source for discussions on shuffling quality and methods), but I think it would be hard to apply their findings to Pokemon.
(*)
I work long hours (pricing interest rate derivatives!) so I don't have much time for playing Pokemon. I go to the league less than once a month and attend the standard CCs and Prerelease tournament.
