buzzpaff
buzzpaff
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September 14th, 2011 at 9:23:51 AM permalink
OK So I figured out the math for my game. Figured out how to protect jackpots from counters. Working on provisional patent when PANIC struck. Now I have no idea how to do the math for this question :
With all 4 Aces removed from a single deck, what would the house edge then be? I mean no one gets a BJ, no soft total to double down on, no worry about a dealer hitting a soft 17. Double after split, double down any number of cards or any total. No
worry about insurance, no surrender ! No worry about splitting Aces. Who has the advantage and how the hell would I figure it out ?? Sure can't use any on line calculator. And with no Aces in the deck, how would basic strategy be affected ? I would mean, still hit 16 against a 10. I think not.
But key word is THINK ! HELP !!!!!!!!!!!!!!!!! PLEASE !!!!!!!!!!!!!!!!!!!!!!!!
buzzpaff
buzzpaff
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September 14th, 2011 at 9:58:29 AM permalink
Not expecting anyone to actually do it, just head me in the right direction !
buzzpaff
buzzpaff
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September 14th, 2011 at 10:40:23 AM permalink
.....
Switch
Switch
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September 14th, 2011 at 11:49:27 AM permalink
Here's a start Buzz:-

https://wizardofodds.com/blackjack/appendix7.html

I'm not sure if it's as simple as multiplying -0.005816 by 4 to get the same effect as removing 4 aces but, if it's close, then it comes out to around a 2.3% added house edge (which is actually the same edge gained by paying Blackjacks at 1/1 rather than 3/2).

I think that the 3rd Ace (due to splitting gone) and 4th Ace (due to no 'Blackjacks') will have a greater effect than removing the first 2 although I'm not sure and I wouldn't like to guess what that would be.
ThatDonGuy
ThatDonGuy
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September 14th, 2011 at 12:09:21 PM permalink
There is no "easy way" to calculate best strategy (and, thus, house edge) in blackjack.

What I ended up doing was, first I calculated the probability of the house getting 17, 18, 19, 20, 21, and bust for each possible up card (counting all 10s the same), excluding two-card 21s; then, for each up card, I calculated the expected value of the player standing on each number against hitting (you have to start with 21 and work down).
weaselman
weaselman
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September 14th, 2011 at 6:55:31 PM permalink
I have not checked my calculations very thoroughly, so, something may be off ... But I am getting a HE of 2.96% in an infinite deck without aces.
Basic strategy seems the same as normal, with the following exceptions:
- Surrender a pair of 8s against a 10, but NOT 16 against 9 (hit it)
- Hit 9 vs 3 (do not double)
- Stand on 16 vs 7, and 12 vs 3
- Split 3,3 against 8

Edit: Just realized, I did not take "double on any number of cards" into account ... That will lower the HE somewhat, but I am too tired now to go back to the calculations.

Oh, and without surrender ... the first line above changes to
- Stand on 16 against 10, including a pair of 8s.

The house edge without surrender is 3.045%
"When two people always agree one of them is unnecessary"
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