Hi all,

If you have ever watched the World Series of Poker it is common nowadays to see a percentage indicating the probability of certain cards that will be an "out" to allow a player to make a hand that will defeat their opponent.

I play a game commonly with friends called Oh Hell, which is a lot like Spades. Its a game of taking Tricks and Trump can be any suit determined at random each hand. So if i have a 7 of clubs, and the Ace of Diamonds is the trump card (diamonds suit is trump), i am often curious about the probability of the cards that can beat that 7 of clubs.

So what can beat that 7 of Clubs? If i lead a hand with the 7 (meaning those with clubs must play a club or can play trump if they don't have clubs) then the 8 - A of Clubs and ANY Diamond can beat it (excluding the Ace which is not part of the deck because it is the trump card). This means that 19 cards could beat that 7 club. So if my amateur understanding of probability is correct, that would mean there is a 37.2% chance of a higher card winning the hand (19 / 51). Is this correct?

Taking it one step further, let us say the there are 3 players and each player has 5 cards in their hand. I have the 7 of clubs, and no other clubs or diamonds in my hand. Does the probability change to consider that at MOST there are only 10 cards that could beat my 7 of clubs? (because worst case scenario i am assuming that my opponents have all higher clubs and/or diamond cards). How would i use math to determine that probability? Also how would one determine the average probability? For example it is very unlikely that my other two opponents have higher clubs and diamonds ONLY in their hand. Is there a way for me to understand the average scenario?

Please note i am only doing this for fun. I just want to utilize basic statistics for me to make more educated decisions when i play.

Kind Regards,

- Brad

If you have ever watched the World Series of Poker it is common nowadays to see a percentage indicating the probability of certain cards that will be an "out" to allow a player to make a hand that will defeat their opponent.

I play a game commonly with friends called Oh Hell, which is a lot like Spades. Its a game of taking Tricks and Trump can be any suit determined at random each hand. So if i have a 7 of clubs, and the Ace of Diamonds is the trump card (diamonds suit is trump), i am often curious about the probability of the cards that can beat that 7 of clubs.

So what can beat that 7 of Clubs? If i lead a hand with the 7 (meaning those with clubs must play a club or can play trump if they don't have clubs) then the 8 - A of Clubs and ANY Diamond can beat it (excluding the Ace which is not part of the deck because it is the trump card). This means that 19 cards could beat that 7 club. So if my amateur understanding of probability is correct, that would mean there is a 37.2% chance of a higher card winning the hand (19 / 51). Is this correct?

Taking it one step further, let us say the there are 3 players and each player has 5 cards in their hand. I have the 7 of clubs, and no other clubs or diamonds in my hand. Does the probability change to consider that at MOST there are only 10 cards that could beat my 7 of clubs? (because worst case scenario i am assuming that my opponents have all higher clubs and/or diamond cards). How would i use math to determine that probability? Also how would one determine the average probability? For example it is very unlikely that my other two opponents have higher clubs and diamonds ONLY in their hand. Is there a way for me to understand the average scenario?

Please note i am only doing this for fun. I just want to utilize basic statistics for me to make more educated decisions when i play.

Kind Regards,

- Brad

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