#6 Poker Run - Royal Flush! (2021) Mystery Cache

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bootecacher: Archiving since some stages are no longer in play. Thanks to those who visited.

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Hidden : 6/9/2021
Difficulty:
2 out of 5
Terrain:
2 out of 5

Size: Size: small (small)

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Geocache Description:


This cache is Not at the posted coordinates. To find the cache you must solve the following puzzle.

Girl in a jacket


A Royal Flush is a poker hand that has a very specific composition: the ten, Jack, Queen, King and Ace, all of the same suit.

To calculate the probability of being dealt a Royal Flush, we need to know two numbers:

(1) The total number of possible poker hands.

(2) The total number of ways that a Royal Flush can be dealt.

The order in which the cards are dealt does not matter. Since the order does not matter, this means that each hand is a combination of five cards from a total of 52. We use the formula for combinations and see that there are a total number of C( 52, 5 ) = 2,598,960 possible distinct hands.

In a Royal Flush, the value of all five cards are completely specified (10, J, Q, K, Ace all of the same suit).

Since there are four suits of hearts, diamonds, clubs, and spades, there are only four possible royal flushes that can be dealt.

The probability of being dealt a Royal Flush is the number of Royal Flushes divided by the total number of poker hands. There is only a probability of 4/2,598,960 = 1/649,740 = 0.00015% of being dealt this hand.

How long would it take to go through 649,740 poker hands? If you were dealt 20 hands of poker every night of the year (this would only amount to 7300 hands/year),  it would take 89 years to see one Royal Flush.

Girl in a jacketGirl in a jacketGirl in a jacketGirl in a jacket

Use the code numbers gathered from the other 5 caches in this Poker Run (2021) series in the following equation to obtain the final cache coordinates:

N 46 AB.CDE W 063 FG.HIJ
 Checksum: N=30, W=27

Additional Hints (No hints available.)



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