Can Someone Help with House Edge?

[Sonny]

do either of u get 1,999,872 ways of getting a pair of queens with a dealer BJ?

I used a little shortcut to calculate the Q,Q hands:

Q,Q BJ = (combin(32,2)/combin(416,2))*DealerBJ
Q,Q No BJ = (combin(32,2)/combin(416,2))*(1-DealerBJ)

where

DealerBJ = 128/416*32/415+32/416*128/415

so

Q,Q BJ = (496/86320)*.0474 = .00027
Q,Q No BJ = (496/86320)*.9526 = .00547

-Sonny-

 

[miplet]

I used a little shortcut to calculate the Q,Q hands:

Q,Q BJ = (combin(32,2)/combin(416,2))*DealerBJ
Q,Q No BJ = (combin(32,2)/combin(416,2))*(1-DealerBJ)

where

DealerBJ = 128/416*32/415+32/416*128/415

so

Q,Q BJ = (496/86320)*.0474 = .00027
Q,Q No BJ = (496/86320)*.9526 = .00547

-Sonny-

Close Sony, but if the player has 2 queens, that leaves only 126 tens and 414 cards for a dealer blackjack.
dealer bj =(126/414)*(32/413)*2= 0.047162859

do either of u get 1,999,872 ways of getting a pair of queens with a dealer BJ?
And 40,403,664 ways of getting a pair of queens without a dealer BJ?

Yes, I get exacly 4 times those numbers because I used A,9 as a differant hand than 9,A for both the dealer and player hands. Here is what I get for all the payouts. I already divided them by 4.

Pair of Qs BJ	1999872
Pair of Qs 	40403664
Matched 20 	28724976
Suited A,9	21885696
Suited x,x	160039152
Any A,9		65657088
Any x,x		463703184
other		6597169488
Total		7379583120

 

[Kasi]

Thanks Mip. I knew you were using permutations and that we agreed on the first two numbers.

I'm surprised I got that far actually!

Maybe I'll try the rest, somewhat easier for me now (maybe!) that I know what the right answer is lol.

Such is my faith

I like your spreadsheet method - I hate all this "combin" stuff lol.

Tlop - pay the man!

 

[Sonny]

Yes, I get exacly 4 times those numbers because I used A,9 as a differant hand than 9,A for both the dealer and player hands.

Ooooh, I forgot about the soft twenties! I thought only the hard twenties payed out for this side bet. That makes the situation even more interesting…

-Sonny-

 

[miplet]

oops

I made some errors. I was overlapping Matched 20 and Suited 20, and who knows what else. I am now getting a player EV of -0.08193495 (House advantage 8.19%)
http://www.miplet.net/bj/luckyladiesnsqv2.xls

Hand       	Pays	Probability	Return
Pair of Qs BJ	250	0.000271001	0.067750169
Pair of Qs 	25	0.00547506	0.136876512
Matched 20 	25	0.003892493	0.097312326
Suited A,9	10	0.002965709	0.02965709
Suited x,x	10	0.017794254	0.177942539
Any A,9   	4	0.008897127	0.035588508
Any x,x   	4	0.066728452	0.266913809
other      	-1	0.893975904	-0.893975904
Total      	 	1            	-0.08193495

Combining  A,9 and x,x
any suited	10	0.020759963	0.207599629
any 20    	4	0.075625579	0.302502317

 

[miplet]

Ooooh, I forgot about the soft twenties! I thought only the hard twenties payed out for this side bet. That makes the situation even more interesting…

-Sonny-

When I change the payout to -1 for soft twenties, I get an EV -0.159043384 which worse than your -0.144. Do you have any other errors, or do I? :+)

 

[Kasi]

http://www.miplet.net/bj/luckyladiesnsqv2.xls

 [/QUOTE]

All I can add tonight is I agree with the number of permutations for your "non-20's" in the above sheet lol.

Not sure but, in your "matched 20's", have you subtracted the chances of matched queens with a dealer BJ that would have the higher 250-1 pay-off?

It almost seems like maybe you ignored queens completely? Like wouldn't QK suited qualify for matched 20?

Just a question - pretty much why I don't feel like figuring it out lol.

 

[miplet]

All I can add tonight is I agree with the number of permutations for your "non-20's" in the above sheet lol.

Not sure but, in your "matched 20's", have you subtracted the chances of matched queens with a dealer BJ that would have the higher 250-1 pay-off?

It almost seems like maybe you ignored queens completely? Like wouldn't QK suited qualify for matched 20?

Just a question - pretty much why I don't feel like figuring it out lol.

"Matched 20" normaly is the exact same card twice like two kings of spades, or two jack of hearts. I didn't use any queens because they would be in the pair of queens payout. King and queen of diamonds would be a suited 20. An ace and 9 of clubs would also be a suited 20.

 

[tlop]

Answer

So do we think we an accurate answer? If so, what is it? And what is your PayPal address?

Thanks again for all of your help.

Oscar

 

[Kasi]

"Matched 20" normaly is the exact same card twice like two kings of spades, or two jack of hearts. I didn't use any queens because they would be in the pair of queens payout. King and queen of diamonds would be a suited 20. An ace and 9 of clubs would also be a suited 20.

Since I got this far down tonite, I agree with all your pemutation numbers in spreadsheet 2 except for, I think, as best I can remember, the unsuited x,x,

But I think I'm still double-counting some stuff (I'm having trouble pulling your sheet up tonite for some reason).

So, basically, as usual, I believe your numbers alot more than mine lol.

All I can remember now is I agreed with every number but one lol. And I'm surprised i got that far lol.

If I get back to it, I'll let u know.

 

[miplet]

Since I got this far down tonite, I agree with all your pemutation numbers in spreadsheet 2 except for, I think, as best I can remember, the unsuited x,x,

But I think I'm still double-counting some stuff (I'm having trouble pulling your sheet up tonite for some reason).

So, basically, as usual, I believe your numbers alot more than mine lol.

All I can remember now is I agreed with every number but one lol. And I'm surprised i got that far lol.

If I get back to it, I'll let u know.

unsuited x,x
There are 96 cards (10,j,k) posible for the first card. If it was a jack of clubs, that would leave all the 10,j,q,k that are not clubs for the second card. That also happend to be 96. 96*96 = 9216
The first card could also be a queen (32 cards). If it was a queen of diamonds, that would leave all the 10,j,k that are not diamonds for the second card. That number is 72. 32*72 = 2304.
9216+2304 = 11520. There are 172640 posible 2 card hands(416*415). 11520/172640 = 0.066728452. That matches what's in my spreadsheet.

So do we think we an accurate answer? If so, what is it? And what is your PayPal address?

I get a house edge of 8.193495% . I hope it is accurate, but it wouldn't be the first time I messed up. I'll pm you my paypal address as soon as I figure out what it is. Haven't used it in years.

 

[Kasi]

I'll pm you my paypal address as soon as I figure out what it is. Haven't used it in years.

Tlop - pay the man

Thanks Miplet - finally got my duplicate queens straightened out lol.