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The new card Yusri, Fortune's Flame has the clause, that if you win 5 flips off it's attack trigger ability, you can cast any card in your hand, for free!.

Whenever Yusri, Fortune’s Flame attacks, choose a number between 1 and 5. Flip that many coins. For each flip you win, draw a card. For each flip you lose, Yursi deals 2 damage to you. If you won five flips this way, you may cast spells from your hand this turn without paying their mana costs.

emphasis mine

Normally this gives you a 1/32 chance (1 in 2 to the power of 5), but what happens if you have Krark's Thumb out?

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The probability to win all 5 coin flips with Krark's Thumb is 0.75^5, or 23.7%, up from 3.1% without Krark's Thumb.

Normally, you would have a 50% chance to win a single coin flip. Since multiple coin flips are independent of each other, you can just multiply their probabilities, so you get a (0.5)^5 = 0.031 (3.1%) probability to have 5 coin flips go your way.

Each Krark's Thumb essentially halves the probability of losing a coin flip. For one Thumb, It goes from 50% to 25%, so the chance to win goes to 1 - 0.25 = 0.75. The probability to win 5 such coin flips is (0.75)^5 = 0.237, or 23.7%

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  • This is a clever way to do it. I didn't twig the extra thumb halves the failure rate. Much simpler.
    – AncientSwordRage
    Jun 5, 2021 at 9:55
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For each of the two coins that you flip with Krak's Thumb you have an extra chance to win.

This is not the same as flipping double, and keeping the best 5.

Here is the anydice code I used to calculate this

output 5 d [highest 1 of 2d2] -5 named "Flips won"
Dice rolled Probability to get at least that many
0 100.00%
1 99.90%
2 98.44%
3 89.65%
4 63.28%
5 23.73%

So 23.73% of the time you get to cast your cards for free!

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