There is definitely something wrong with the shuffling and drawing mechanic...
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It's a little anecdotal, at best, but I want to chime in here.
I just played 5 games in a row where my one-and-only basic pokémon in my starting hand was Crobat V. After 3, I got frustrated. After 5 I closed the game completely.
Let me explain, I have 10 basic Pokémon. It isn't much but it is there. Of those 10, only 2 are Crobat V. To pull Crobat V, and only Crobat V, in the first 7 cards five times in a row has astronomically low odds (obv not impossible).
Being an engineer with a background in software, I decided to do my own analysis.
I built a deck of 60 cards. 2 were "c" to indicate Crobat, 8 were "b" (basic) and 50 were "t" (trainer).
I then shuffled the deck using a pseudorandom number shuffle algorithm.
I then ran that shuffle algorithm 20000 times. Of those 20000 times, only 1600 times did "c" show up in the first 7 cards. That is ~8% chance of pulling Crobat V as the only basic pokémon. To hit the 8% chance five times in a row is a 0.004% chance.
To put that in perspective, you have a 0.006% chance of being struck by lightning.
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@rgilbert90 how many of those 20000 hands were only T cards? because mulligans are a thing, and that increases your chance of opening specific basics if you run a low count of basics that are not the pokemon you don't want to open.
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@rgilbert90 i added mulligans to your algoritm. The chances of opening crobat in an individual game with 2 crobats and 8 other basics is ~10.8%
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@rgilbert90 update, i did the equation again, this time from 0 instead of using your approximation as a base, and the chances of crobat V being your only basic with the conditions you mentioned before went up to 12.14%
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Depending on your shuffling algorithm, Crobat V can appear between 8-12% of the time as your only basic Pokémon. This is true.
But I am specifically mentioning that it happened 5 games in a row, albeit with a mulligan or two in between.
After accounting for mulligans, I also did notice an increase to about 10-11% so your 12 isn't too far off.
But out of 20,000 runs, not once did it ever hit 5 in a row where an individual Crobat V was my only basic pokémon--admittedly, the counter reset on a mulligan.
I did hit 4 in a row so if there was a mulligan and then a Crobat V again, that would have technically been 5 in a row one time in 20,000 runs which would have been a 1/20000 chance of happening. Which is that 0.005% so it would have checked out.
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@rgilbert90 oh, i found my mistake, you are correct is about 10-11%
the equation is simple:
(chance of having crobat in your opening hand) * (chance of the other 6 cards not being basics)/(chance of opening a basic)
chances being in decimals, not in percentages, and it only works with basics, any other type of card requires a more complex equation.
0.22146*0.3997/0.74138 = 0.1014729 or 10.14729%
for that to happen 5 times is 0.001075% or 1/93023.2558
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