# Euchre: What are the Odds?

In this article, we will explore explore the chances of rare card combinations, offering insights for the most curious players.

## 1. Getting All Four Jacks

First, let’s determine the total number of possible 5-card hands that a player can receive from a 24-card deck. We’ll use the notation “C(n, k)” to represent the combination of selecting k items from a set of n items. The formula for combinations is:

C(n, k) = n! / (k! * (n – k)!)

In this case, n = 24 (total number of cards in the deck) and k = 5 (number of cards in each hand).

Total possible hands = C(24, 5) = 24! / (5! * (24 – 5)!) = 42,504

Now, let’s calculate the number of favorable outcomes, which is the number of hands that contain all four Jacks.

Number of favorable outcomes = C(4, 4) * C(20, 1) = 1 * 20 = 20

The combination C(4, 4) accounts for the selection of all four Jacks, and C(20, 1) represents the selection of one card from the remaining 20 cards in the deck.

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total possible hands:

Probability = Number of favorable outcomes / Total possible hands = 20 / 42,504 ≈ 0.000471

Therefore, the probability of a player receiving all four Jacks in a 24-card deck Euchre game is approximately 0.000471, or about 0.0471%.

## 2. Getting Five Cards of the Same Suit

Probability = Number of favorable outcomes / Total possible hands = 6 / 42,504 ≈ 0.000141

## 3. Getting No Face Cards

Number of favorable outcomes = C(12, 0) * C(12, 5) = 1 * 792 = 792

The combination C(12, 0) represents the selection of zero face cards, and C(12, 5) represents the selection of 5 non-face cards from the remaining 12 cards in the deck.

Probability = Number of favorable outcomes / Total possible hands = 792 / 42,504 ≈ 0.0186

## 4. Getting Only 9s and 10s

## 5. Getting the Joker Card

Probability = Number of favorable outcomes / Total possible hands = 10,626 / 53,130 ≈ 0.200.

Therefore, the probability of a player receiving the Joker card in their hand in a 25-card deck Euchre game is approximately 0.200, or 20%.

## 6. Going Alone and Winning Three Hands

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Copyright 2023 All rights reserved

This product is intended for people over 18 years of age for entertainment purposes. This game includes in-app purchases. Practice or success in social casino gambling does not imply future winnings in real money gambling and gambling in general.

Copyright 2023 All rights reserved

This product is intended for people over 18 years of age for entertainment purposes. This game includes in-app purchases. Practice or success in social casino gambling does not imply future winnings in real money gambling and gambling in general.