Aaron326
Aaron326
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May 11th, 2024 at 6:03:11 PM permalink
Hello,

I have a question for someone that can help me with maths.

What would be my advantage if I get on my first card 47% of 10 or AS instead of 5/13 ?

Thank you
ThatDonGuy
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May 12th, 2024 at 7:36:11 AM permalink
I assume you are asking about what happens if, 47% of the time, the first card is a 10-value card or an Ace.

What game?

If it's blackjack, what are the conditions of the game?

When you say "a 10 or Ace 47% of the time," is it still four times as likely to be a 10 as it is an Ace, and if not, how much more likely is it?

That question has many different possible answers depending on the details.
Aaron326
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May 12th, 2024 at 7:44:29 AM permalink
Thank you for your answer,

The game is blackjack with 6 decks

Yes letís assume itís still 4 times as likely to be a 10 as it is an ace. So letís say something like 9.4% Ace and 37.6% 10 instead of 7.69% Ace and 30.76% 10.

Thank you very much and also if someone has the answer maybe he would be so nice to post the calculations ?
I just know getting always 10 gives 13% edge and always Ace gives 52% edge.

Thank you !
Aaron326
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May 12th, 2024 at 7:47:20 AM permalink
My question is how much advantage those conditions would add to the House Edge ? +2% ? +5% ? +10% ?

Thank you again
AZDuffman
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May 12th, 2024 at 1:28:44 PM permalink
My question is why do some cultures use it plural "maths" vs "math" in USA?
All animals are equal, but some are more equal than others
ThatDonGuy
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May 12th, 2024 at 1:32:12 PM permalink
Quote: AZDuffman

My question is why do some cultures use it plural "maths" vs "math" in USA?
link to original post


In the UK and Australia, since it is short for "mathematics," they use the plural.

The question that needs to be asked is, "In that case, why is it 'sports' in the USA but 'sport' in the UK?"
Aaron326
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May 12th, 2024 at 2:28:56 PM permalink
You are very helpful :)
If you could stay focus on my subject it would be really nice from you :)
ThatDonGuy
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May 12th, 2024 at 2:36:46 PM permalink
Quote: Aaron326

You are very helpful :)
If you could stay focus on my subject it would be really nice from you :)
link to original post


Unfortunately, I am not well-versed in blackjack enough to know how to solve this. You have to understand that, with a change in the cards, the entire strategy changes. It's not as cut and dried as "knowing what card X will be will change the HE by N percent."

You also didn't answer one of my questions: while you say that "the probability of a 10 or Ace is 47%, is a 10 still four times as likely as an Ace? Is an Ace equally likely as a 10? Is it something else, and if so, what?
aceside
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May 12th, 2024 at 2:38:16 PM permalink
I would like to calculate it for you if you tell me how you know your next card is a 10 or Ace with a certainty of 47%.
Aaron326
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May 12th, 2024 at 2:59:28 PM permalink
Iím just curious but I know itís somewhere between 2 and 7% edge just would like to know exactly
AZDuffman
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May 12th, 2024 at 5:18:28 PM permalink
Quote: ThatDonGuy

Quote: AZDuffman

My question is why do some cultures use it plural "maths" vs "math" in USA?
link to original post


In the UK and Australia, since it is short for "mathematics," they use the plural.

The question that needs to be asked is, "In that case, why is it 'sports' in the USA but 'sport' in the UK?"
link to original post



First part, thanks. I have never had a good answer to that. I am assuming "mathematics" is a less formal word outside the USA? In the USA the full word "mathematics" is only used in the most formal ways, say a department title at a college. "Math" is all most people use.

As to the second part, well, Brits drive on the wrong side of the road as well, we can only help out so much.

On a slightly more serious note, I have been asked why the USA uses a moneyline but everyone else uses odds. I say, "we don't use the metric system, either."
All animals are equal, but some are more equal than others
DogHand
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May 12th, 2024 at 5:36:36 PM permalink
Quote: Aaron326

Thank you for your answer,

The game is blackjack with 6 decks

Yes letís assume itís still 4 times as likely to be a 10 as it is an ace. So letís say something like 9.4% Ace and 37.6% 10 instead of 7.69% Ace and 30.76% 10.

Thank you very much and also if someone has the answer maybe he would be so nice to post the calculations ?
I just know getting always 10 gives 13% edge and always Ace gives 52% edge.

Thank you !
link to original post


Aaron326,

Since I don't know all the rules, I'll ASSUME the overall player edge based on 6 (regular) decks and the other house rules is -0.5%, or, to put it another way, the house edge is 0.5%. I'll also ASSUME that your values for 1st card X of +13% and 1st card A of +52% are also accurate.

First question: if the 1st card is 2 through 9, what is the average (negative) player edge?

For 6 regular decks (so ignoring for the moment your increased X & A probabilities), the overall player edge E is given by this equation:

E = (prob A)*(A edge) + (prob X)*(X edge) + (prob 2-9)*(2-9 edge)

Solving gives:

(2-9 edge) = {E - (prob A)*(A edge) - (prob X)*(X edge)}/(prob 2-9)

So

(2-9 edge) = {-0.5% - (1/13)*52% - (4/13)*13%}/(8/13) = -13.81...%

Let's call it -14% for a 1st card of 2-9.

Ok, now we can analyze your situation!

Given your probabilities, your edge is

E = (prob A)*(A edge) + (prob X)*(X edge) + (prob 2-9)*(2-9 edge)

E = (0.094)*52% + (0.376)*13% + (1-0.094-0.376)*(-14%) = +2.356%

Woo HOO!!! MAX BET!

Hope this helps!

Dog Hand
gordonm888
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May 12th, 2024 at 6:47:39 PM permalink
I get a player advantage of 3.215% for a case where the tens and aces are 46.67% of the cards in the shoe. Specifically, 300 cards in the shoe, 140 are Ten,Ace and 160 are 2-9.

I assume the player uses standard basic strategy. The player advantage would be higher if he used optimum strategy for this card distribution.
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unJon
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May 12th, 2024 at 7:54:04 PM permalink
Quote: gordonm888

I get a player advantage of 3.215% for a case where the tens and aces are 46.67% of the cards in the shoe. Specifically, 300 cards in the shoe, 140 are Ten,Ace and 160 are 2-9.

I assume the player uses standard basic strategy. The player advantage would be higher if he used optimum strategy for this card distribution.
link to original post



Oh I donít think OP meant to change the deck composition but rather somehow knew with some probability the first card of the shoe only was 47% ten/face or A.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Aaron326
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May 13th, 2024 at 12:56:35 AM permalink
I really thank you very much for your calculations doghand !!!

Last thing, I guess I have to substract HE from the Edge you found ? So E = 2.356 - 0.5 = 1.856 ?

Or 2.356 is already with HE substracted ?
DogHand
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May 13th, 2024 at 5:11:55 AM permalink
Quote: Aaron326

I really thank you very much for your calculations doghand !!!

Last thing, I guess I have to substract HE from the Edge you found ? So E = 2.356 - 0.5 = 1.856 ?

Or 2.356 is already with HE substracted ?
link to original post


Aaron326,

Thank you for your kind words.

The 2.356% I quoted includes the house edge.

Note, though, that you should re-do the calculations yourself with the actual house edge and the actual player edge for each upcard. One way to get these values is to use this website:

https://www.bjstrat.net/cgi-bin/cdca.cgi

Enter the correct rule set, then click "compute" to get the overall player edge (it will be negative, of course). Then set the player hand to have just an Ace and compute to get the A edge. Repeat for 2, 3, ... up to 9, then average those eight results to get the 2-9 edge. Next, set a T to get the X edge. Finally, use the equation I gave to find your actual edge.

Hope this helps!

Dog Hand
aceside
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May 13th, 2024 at 5:20:08 AM permalink
You do not need to substrate the ordinary EV from the edge Dog Hand found, so the 2.356% is the EV.

I thought about this again. A more reasonable question to ask is this, what is the new EV when player knows the next card for him is NOT a face card? This happens when player had a glimpse of this card.

Let me follow Dog Hand calculation to find out.


EV = (prob A)*(A edge) + (prob X)*(X edge) + (prob 2-9)*(2-9 edge)

= (1/10)*52% + (1/10)*13% + (8/10)*(-14%) = +0.18%

Bet minimum!
Aaron326
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May 13th, 2024 at 5:21:39 AM permalink
Thank you dog hand !!

Why canít I just do 2.356% + 0.5 = 2.856% to find my edge without HE or if HE = 0
I thought we always could do this way like knowing our Edge and then subtract the HE to have our real expectation.

I will have a look of your link thank you :)
aceside
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May 13th, 2024 at 5:32:51 AM permalink
There is a little confusing here. The house edge is about +0.5%. Itís positive. The number +2.356% is a player edge.
Aaron326
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May 13th, 2024 at 5:36:30 AM permalink
Yes sorry for confusion in my words :)

I meant why not calculate my player edge independently than the HE and then just substract the HE from the edge.
So imagine player edge 2.856% -0.5 (=HE) = 2.356%
I always thought doing this way was the right way but maybe I was wrong Ö
We cannot do it this way at all ? (Ignore HE for calculations and then substract the HE at the end)

Thanks !
aceside
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May 13th, 2024 at 5:42:59 AM permalink
You can just say, player gains an edge of 2.856% = 0.5% +2.356%. This is correct.
Mental
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May 13th, 2024 at 5:47:50 AM permalink
Quote: aceside

You do not need to substrate the ordinary EV from the edge Dog Hand found, so the 2.356% is the EV.

I thought about this again. A more reasonable question to ask is this, what is the new EV when player knows the next card for him is NOT a face card? This happens when player had a glimpse of this card.

Let me follow Dog Hand calculation to find out.


EV = (prob A)*(A edge) + (prob X)*(X edge) + (prob 2-9)*(2-9 edge)

= (1/10)*52% + (1/10)*13% + (8/10)*(-14%) = +0.18%

Bet minimum!
link to original post

Why bet minimum with a +EV game?
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aceside
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Mental
May 13th, 2024 at 5:53:43 AM permalink
But I am thinking about this situation when player had a glimpse of the next card for him and was certain that it was not a Jack, Queen, or King with a lot of paint.
aceside
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May 13th, 2024 at 5:56:00 AM permalink
Quote: Mental

Quote: aceside

You do not need to substrate the ordinary EV from the edge Dog Hand found, so the 2.356% is the EV.

I thought about this again. A more reasonable question to ask is this, what is the new EV when player knows the next card for him is NOT a face card? This happens when player had a glimpse of this card.

Let me follow Dog Hand calculation to find out.


EV = (prob A)*(A edge) + (prob X)*(X edge) + (prob 2-9)*(2-9 edge)

= (1/10)*52% + (1/10)*13% + (8/10)*(-14%) = +0.18%

Bet minimum!
link to original post

Why bet minimum with a +EV game?
link to original post


Good catch! Actually you are right. Player may bet maximum.
Aaron326
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May 13th, 2024 at 6:03:07 AM permalink
Quote: aceside

You can just say, player gains an edge of 2.856% = 0.5% +2.356%. This is correct.
link to original post



This I know but I was just thinking if we could do the calculation for player edge without HE first and then just subtract the HE.
It would be easier in case I would like to do same calculation just removing surrender rules etc Ö
Here Doghand (that I respect for his answer) ask me to do calculation again and maybe he has a good reason.
I was just wondering if we could do it the way I asked.

When I read first the calculations of doghand it didnít look like the HE of 0.5 was in the equation ? Unless I didnít read properly all his calculation.
Aaron326
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May 13th, 2024 at 6:06:25 AM permalink
Where does the HE of 0.5 appears in the calculations of doghand ?
Aaron326
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May 13th, 2024 at 6:09:01 AM permalink
Ok I think I got it 52% for Ace and 13% for Ten are the edge for a game at HE = 0.5
So I need to get those new numbers for the HE I will want
aceside
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May 13th, 2024 at 6:10:42 AM permalink
Dog Hand calculation is just a shortcut demonstration. I believe you cannot calculate the way you speculate because Blackjack EV components are all entangled together. It is inaccurate to separate out different EV components and say their contributions.
Mental
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May 13th, 2024 at 6:13:22 AM permalink
Quote: Aaron326

Where does the HE of 0.5 appears in the calculations of doghand ?
link to original post

That is like asking where the HE of baccarat appears in the calculation. The game you describe is a completely different game compared to ordinary BJ. You don't need to use the ordinary game HE as a starting point for your HE calculations. You might be used to people stating that such-and-such a rule change adds X % to the HE. But this is normally computed by doing a completely new calculation of the house edge and subtracting.
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aceside
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May 13th, 2024 at 12:24:00 PM permalink
I just checked my calculation again with the situation that player had a glimpse of the next card for him and was certain that it was not a Jack, Queen, or King with a lot of paint.

EV = (prob A)*(A edge) + (prob X)*(X edge) + (prob 2-9)*(2-9 edge)
= (1/10)*52% + (1/10)*13% + (8/10)*(-14%) = -4.7%

Bet minimum!
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