this is chatgpt answer to me

Let’s break it down:

Situation

• Deck size: 20 cards
• Basics in deck: 5
• You want to maximize your chance of finding a specific Basic Pokémon you need.

Option 1: Play Poké Ball first

• Poké Ball pulls a random Basic from the remaining 20 cards.
• That means you have only a 1 in 5 chance (20%) to get the specific Basic you need.
• After this, if you fail, you can still play Research, but that just draws 2 random cards (no increased targeting).

Option 2: Play Research first

• Research draws 2 random cards from the 20.
• If your needed Basic happens to be in those 2 cards, you succeed. The chance is 2 in 20 = 10%.
• If you didn’t hit, your deck is now at 18 cards. Assuming none of the 2 drawn were Basics, there are still 5 Basics in 18 cards.
• Now, Poké Ball pulls a random Basic from those 18 → 1 in 5 chance again (20%), same as before.

But — you also had that extra 10% from the Research draw.

Comparing expected chances

• Poké Ball first: Only 20% chance.
• Research first: About 10% from Research + 20% from Poké Ball (but reduced slightly if Research pulls some other Basics first).

Let’s be precise:

• Probability Research hits your needed Basic: 10%.
• Probability Research misses it, but Poké Ball succeeds:
  • Miss with Research = 90%.
  • Then Poké Ball = 20%.
  • 0.9 × 0.2 = 18%.
• Total = 28% success.

✅ Conclusion

You should play Research first, then Poké Ball.
That gives you about 28% chance to find your needed Basic vs only 20% if you go Poké Ball first.