Odds in Pokemon
Part 2 – The Surprises of Prizes
Welcome to my second of my articles about odds in Pokemon. As I promised in my previous article, I will tackle the probabilities of getting cards in your Prizes in this article.
Before starting this article, there is a thing that you need to have in mind. Suppose you’re starting a game of Pokemon. You shuffle your deck and draw 7 cards, then (assuming you don’t mulligan), you set aside the next 6 cards of your deck as your Prizes. That means that the probability of getting the actual 6 prize cards depends on what you had drawn in your 7-card hand… or does it?
The answer is… no it doesn’t. Remember that your 7-card hand consists of 7 random cards. You didn’t select the 7 cards from the deck; you just drew them from the top of your deck. Unless you cheat (and I strongly advise against cheating, in any game), you cannot predict beforehand the exact cards you’ll draw in your opening hand. That means that, if, instead of first drawing your 7 card hand, and then place your 6 prizes, you do it vice-versa, i.e. you first set aside your 6 prizes and then draw your 7 card hand, you don’t alter any probabilities whatsoever.
I remember there was a time where I was not convinced of the last sentence I’ve just typed myself. So I started to find the odds of the Prize cards such that they depended on the first 7 cards drawn (which was much more difficult than doing it the easy way)… and, lo and behold, the answers were exactly the same as those obtained as if I placed the first 6 cards of my deck as my prizes! Thus I was finally convinced that there’s no difference, probability-wise, in the order you draw your hand and your prizes. (Of course, there is a difference rule-wise.) This is actually a very important point for everyone to grasp.
After settling that argument, it’s time for the table containing the odds of getting your cards in your prize cards:
|
Number of the same card in your deck |
Probability of that card not being in your prizes |
Probability of that card appearing once in your prizes |
Probability of that card appearing twice in your prizes |
Probability of that card appearing three times in your prizes |
Probability of that card appearing four times in your prizes |
|
1 |
9 out of 10 games (90.00%) |
1 out of 10 games (10.00%) |
|
|
|
|
2 |
8 out of 10 games (80.85%) |
2 out of 11 games (18.31%) |
1 out of 118 games (0.85%) |
|
|
|
3 |
18 out of 25 games (72.48%) |
1 out of 4 games (25.09%) |
1 out of 42 games (2.37%) |
1 out of 1711 games (0.06%) |
|
|
4 |
16 out of 25 games (64.85%) |
3 out of 10 games (30.52%) |
1 out of 23 games (4.40%) |
1 out of 452 games (0.22%) |
1 out of 32509 games (0.003%) |
Suppose you have 4 Steven’s Advice in your deck and you want to know the probability that none of them ends up in your prizes. Then you go in the first column and go to the row marked ‘4’. Then move horizontally to the second column, which gives the probabilities of cards not appearing in your prizes and read out “16 out of 25 games (64.85%)”. That means that, in roughly 16 out of 25 games, none of your 4 Steven’s Advice will be in your prizes.
Or suppose you have 1 tech Strength Charm in your deck and you wish to know the probability that it will end up as one of your six prizes. So you go in the first column where ‘1’ is displayed, then move to the right to the column where the probability of the card appearing once in your prizes is displayed. It turns out that your tech card will be in your prizes 10% of the time, or in 1 game out of 10. (This is actually very easy to calculate.)
Comments on the table above
As you can see from the above table, the probability of getting the same card more than once in your prize cards is very small, even if you play 4 of the same card. That means that if you find yourself with 2 or more of the same card in your Prizes, consider yourself extremely unlucky (unless they are Basic Energy cards).
Another thing concerns playing the maximum 4 allowed of any card. I remember once asking the question: “If you play 4 of a card, doesn’t that make it easier for one of them to end up as your prizes? What if these odds are so high that it’s actually better to play 3 of the card, saving one deck space for another card you could insert in the deck?” While the answer to the first question above is obviously yes, the answer to the second question is that the odds are not high enough. Indeed, looking at the table above, the odds of getting cards in your prizes when playing 4 of the same card are not very different from the odds of getting cards in your prizes when playing 3 of the same card. That means that you can safely play 4 of the card you want to play without fearing too much that one of them will end up in your prizes.
Conclusion
I hope you again found this article of some use.
The next article will tackle the odds of getting a particular card depending on how many cards you have left in your deck. When should I expect to draw one of my maxed-out card (a card you play 4 of)? And what about getting it in my opening hand? Stay tuned.
Remember that if you have any questions (like from where I got those values, etc.), or you want to know the odds of anything in particular, feel free to email me at xactcreations@yahoo.com. You can also AIM me (my nickname is xactxx). I’ve got a few emails asking me about how I got the numbers of the table of last week’s article… sorry if I answered you a bit late. Hopefully I made up for it with my thorough answer.
I repeat, if you would like to know the odds of something in particular, like particular combos (probability of getting a Lass and a Cleffa in your opening hand, for example), just email me or AIM me. I’ll answer your questions on this website if it is interesting, sort of like the Deck Doctors do. So start sending!