High Priestess and the Celestial Packs

[False]

Is it better to open a Celestial Pack first before opening the High Priestess to more likely get a planet of my choice or it's the other way around? I've tried to do math on this one but I think I've done it wrong so I'm interested in what others have to say about this.

[malogoss]

Priestess first.

If you find your planet there, use it, keep the other card, open the pack.

Else, keep the 2 planet cards and open the pack. You won't find the 2 planets you're holding in the pack, making it more likely to find what you want.

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Telescope breaks that though, you can find a planet of the hand you played the most in a pack even if you have it in inventory, but usually that is a good thing.

[Goblin]

If you open a celestial pack while holding no planet cards, the odds of getting the card you want are 1/12 for the first card drawn, 1/11 for the second one, etc. for as many cards as the pack has. That means chances of NOT getting the card you want is (1-(1/12))*(1-(1/11))*(1-(1/10))... leading to 75% chance of not getting it for 3 card packs, and 58.333% chance for 5 card packs.

If you use the high priestess and get two cards you don't want, you start at 1/10 chance of drawing the card you want, instead of 1/12. That changes the odds of not getting what you want at 70% for 3 card packs, and 50% for 5 card packs. That means you improved your odds that you DO get what you want by either 5% or 8.333%.

If HP does give you what you want, obviously you need to use that planet card first, and the improvement to your odds will be smaller, but it's still always better to use HP first.