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 02-18-2017, 04:55 PM #1 mervinswerved enthusiast   Join Date: May 2015 Posts: 52 Hold em prop bet question This might be trivial, and then again, it might not be. Two guys at my home game started a prop bet on the sum of the flop cards. They set the over/under at 21 and each took a side (this came out of a discussion on blackjack, hence the 21). All face cards are worth 10, aces are 11, and the numbered cards are worth their face value. For example, a 4 9 K flop equals 23 and the over wins. All 21's are a push. Who has the edge? What's the expected value of the flop sum? Some simple match revealed the average value of one card is approximately 7.3, therefore three cards would be 21.9. It *can't* be that basic, right? This seems like a combinatorics problem, but I don't have the math skills to work it out easily. For what it's worth, the guy with the under played it the right way. They both lost track of the prop after a while and he made a point of only reminding the "over" player when the under hit. Last edited by mervinswerved; 02-18-2017 at 04:56 PM. Reason: Added a postscript
02-18-2017, 05:23 PM   #2
md46135
centurion

Join Date: Mar 2015
Location: where they don't respect my raises
Posts: 160
Re: Hold em prop bet question

Quote:
 Originally Posted by mervinswerved Some simple match revealed the average value of one card is approximately 7.3, therefore three cards would be 21.9. It *can't* be that basic, right?
actually it is. this is how distribution of the sum looks like.
Spoiler:

mean is 21.9231.

total number of flops is 22100. number of strictly lower flops than 21 is 8292, so the chance for under is 37.52%.

 02-19-2017, 05:58 PM #3 heehaww Pooh-Bah     Join Date: Aug 2011 Location: It was an attractive goat in AR Posts: 4,182 Re: Hold em prop bet question Now you just need to know the chance of exactly 21, from which you can deduce P(over) and then the edge.
02-19-2017, 06:34 PM   #4
md46135
centurion

Join Date: Mar 2015
Location: where they don't respect my raises
Posts: 160
Re: Hold em prop bet question

Quote:
 Originally Posted by heehaww Now you just need to know the chance of exactly 21, from which you can deduce P(over) and then the edge.

less than 21: 8292 (37.52%)
exactly 21: 1508 (6.82%)
more than 21: 12300 (55.66%)
total: 22100

i thought OP was just curious which was more likely. and he didn't say the odds for the bet, I guess 50-50? if so, the one who went with over would have 18.14% return on his stake, while the guy with under is losing at the same rate.

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