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average sum of ranks in 5 card hand average sum of ranks in 5 card hand

06-30-2022 , 04:12 PM
In a 5 card draw game where A=1 and number cards are face value and J,Q,K = 10, what would be the average sum of your card's value among 5 cards in a players hand


example: 4 A J Q K = 35
average sum of ranks in 5 card hand Quote
06-30-2022 , 07:28 PM
32.69
average sum of ranks in 5 card hand Quote
07-01-2022 , 09:05 AM
I think what follows is correct but it's been a long time since I dealt with sampling without replacement problems. I think you can simply calculate the average rank and then multiply by 5 to get the expected value of the sum of the ranks of 5 randomly chosen cards without replacement.

Since there are the same number of cards of each rank (Ace-King), we can simply calculate the average of the following numbers: {1,2,3,4,5,6,7,8,9,10,10,10,10} which is 85/13.

Then multiply by 5 to get (5*85/13) or 425/13 which is what statmanhal posted above to two decimal places.
average sum of ranks in 5 card hand Quote
07-01-2022 , 02:41 PM
What whosnext posted is exactly what I did. Then to check my questionable programming ability. I wrote a simple simulation program and got the same answer.
average sum of ranks in 5 card hand Quote
07-01-2022 , 11:25 PM
Quote:
Originally Posted by whosnext
I think what follows is correct but it's been a long time since I dealt with sampling without replacement problems. I think you can simply calculate the average rank and then multiply by 5 to get the expected value of the sum of the ranks of 5 randomly chosen cards without replacement.

Since there are the same number of cards of each rank (Ace-King), we can simply calculate the average of the following numbers: {1,2,3,4,5,6,7,8,9,10,10,10,10} which is 85/13.

Then multiply by 5 to get (5*85/13) or 425/13 which is what statmanhal posted above to two decimal places.
You don't think it behooves you to make clear that your method and the logic behind it does not require the "without"?
average sum of ranks in 5 card hand Quote

      
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