Blackjack's advertised house edge is wrong

[Elmango]

Hi,

I contacted support a while ago asking for the maths behind the .48% house edge and I was told it was based on wizardofodds' calculation, which can be found here:

Wizard's house edge calculation

And the spreadsheet file: https://drive.google.com/file/d/0B2R98Qfvr8GldVlUZVJFeHVLZ1U/edit

I came up with the same number myself so didn't give it a second thought. But today, while playing, I realized surrender is not allowed and that changes everything. The house edge you are advertising stands for the following rules:

- Infinite decks
- Insurance is an optional side bet only available when the dealers reveals an Ace face card
- If the dealer has natural blackjack, game concludes and insurance is paid if taken
- Dealer stands on soft 17
- Double after split is allowed
- You can double on any first two cards
- Split only one time
- Surrender allowed
- Re-splitting aces not allowed

The moment surrender is not allowed, the house edge increases to .57%. That should be pretty easy to verify with Michael Shackleford's spreadsheet (this guy explains how: https://www.youtube.com/watch?v=UEA46N9jl00).

I believe you've been unfairly advertising the wrong house edge for a long time, which sounds like a big deal to me. A .09% difference could probably represent thousands (if not millions) of dollars depending on the wager volume.

* Edit. It seems like the .48% was obtained from Shackleford's calculator (https://wizardofodds.com/games/blackjack/strategy/calculator/) which calculates the house edge for up to 8 decks, not an infinite one. Here's the calculation for an infinite deck with no surrender: https://bit.ly/2LQlluJ, resulting in .57%.

[Dan]

Hi @Elmango,

I am familiar with the calculation, could you show me where the calculation for surrender rule changes that? As you can see below, it is already taken into consideration.

[Elmango]

@Dan, the calculator you are using (https://wizardofodds.com/games/blackjack/calculator/) considers a finite number of decks (8 in your screenshot) and the maths are not the same with an infinite deck. If that's were the .48% was taken from, it is wrong. If you refer to the infinite deck video I posted and change it so that surrender  is not allowed,  you will end up with .57%.

[Dan]

Just now, Elmango said:

@Dan, the calculator you are using (https://wizardofodds.com/games/blackjack/calculator/) considers for a finite number of decks (8 in your screenshot) and the maths are not the same with an infinite deck. If that's were the .48% was taken from, it is wrong. If you refer to the infinite deck video I posted and change it so that surrender  is not allowed,  you will end up with .57%.

Can you please show me how you take the above calculated result of 0.485% (from screenshot) and apply it to an inifinte deck size?

What it sounds like to me, is you do not agree with the calculation shown in my screenshot.

[Elmango]

@Dan. You are right on that, I don't agree. The calculation shown in your screenshot is invalid because 8 != ∞.

This is how you calculate the house edge on an infinite deck: 

 (made by the same guy who made that calculator). He considers surrender, however. Once you don't, you obtain the .57%, which is the real house edge Stake has.

Just to be clear, the number of decks of cards affects the house edge. You can't just take the calculation made for 8 decks and assume it's the same for an infinite deck.

[Dan]

1 minute ago, Elmango said:

@Dan. You are right on that, I don't agree. The calculation show in your screenshot is invalid because 8 != ∞.

This is how you calculate the house edge on an infinite deck: 

 (made by the same guy who made that calculator). He considers surrender, however. Once you don't, you obtain the .57%, which is the real house edge Stake has.

Taking the two current calculations, can you demonstrate the difference of the infinite deck on both of these attached figures. Cheers!

 

Notice how surrender lowers the house edge. I think what you are trying to claim, is wizards of odds (both the video makers, and the website) are wrong?

[Elmango]

@Dan, I'm not sure I understand your question. We can't use that calculator as a reference, unless the game had 8 decks. Here's my updated spreadsheed (for an infinite deck and all stake's rules) so that you can see where the .57% comes from:

https://docs.google.com/spreadsheets/d/e/2PACX-1vT5Z0fiezIms05v4vOuQjFjabFqzG4woYwhCFJ8xtwJqBzC8N71ron6Axq9j-dtKg/pubhtml

[Dan]

The easiest way to solve this is to calculate how much of an impact the difference between 8 decks and an infinite deck has on the EV. 

In an 8 deck game, the first ace is 16/208 and the second is 15/207.

In an inifinite deck its technically 1/13 and 1/13.

 

Just now, Elmango said:

@Dan, I'm not sure I understand your question. We can't use that calculator as a reference, unless the game had 8 decks. Here's my updated spreadsheed so that you can see where the .57% comes from:

https://docs.google.com/spreadsheets/d/e/2PACX-1vT5Z0fiezIms05v4vOuQjFjabFqzG4woYwhCFJ8xtwJqBzC8N71ron6Axq9j-dtKg/pubhtml

Do the calculation with pruely the rules above in my original image.

No surrender and 8 decks. Are you saying that with no surrender and 8 decks, its not 0.485%?

[Elmango]

@Dan, it's not that simple. Please watch this video: 

It was made by the same person who made the calculator.

[Dan]

Just now, Elmango said:

@Dan, it's not that simple. Please watch this video: 

It was made by the same person who made the calculator.

Before we can continue, please provide the correct calculation for 8 decks and no surrender. 

 

[Elmango]

8 minutes ago, Dan said:

The easiest way to solve this is to calculate how much of an impact the difference between 8 decks and an infinite deck has on the EV. 

In an 8 deck game, the first ace is 16/208 and the second is 15/207.

In an inifinite deck its technically 1/13 and 1/13.

 

Do the calculation with pruely the rules above in my original image.

No surrender and 8 decks. Are you saying that with no surrender and 8 decks, its not 0.485%?

No, I agree 100% on what your calculator says - the calculation is correct. What I'm saying is that it doesn't stand for an infinite deck, the calculation is different (use the video as a reference). Here's the first part:

 

[GKD09]

Love how these are your first 4 posts lol. But really interested to see where this ends. I'm too lazy to do my own research on my only weekend

[Dan]

@Elmango Using your spreadsheet, i configured it for 8 decks and no surrender, but it doesnt equal 0.485%

Whats wrong with your spreadsheet? Or is there a problem with the wizard of odds calculator?

[Elmango]

@Dan, what do you mean you configured it?. It's made for a infinite deck only. You'd need to make one for a finite number of decks, the maths are different. The assumption when using infinite decks is that the cards you have do not affect your chances, however when considering 8 decks or less then your cards do have an influence. For instance, with a single deck you stand on 7-7 vs 10 because there are now only two 7s left in the deck, reducing your chances of getting 21 and reducing the chances the dealer has 17. So the same type of tables using finite decks would require all combinations of cards that can make up each total.

Anyway, my spreadsheet, your calculator and the videos I posted were made by Michael Shackleford, an expert in probability (he's been the blackjack reference for over a decade). I checked his maths on the infinite deck part and they are correct. I haven't done it for 8 decks though but I don't see how that's relevant. Do you work for Stake? - I still don't know where the .48% they advertise came from. 

There's nothing wrong with the calculator nor the spreadsheet. AFAICT the only thing that is wrong is the advertised house edge by Stake, which should be .57% according to my calculations and Shackleford's. I imagine Stake mistakenly either 1) assumed the house edge of a finite and infinite deck was the same or 2) correctly calculated the house edge for an infinite deck but forgot to adjust it so that surrender is not allowed.

[Elmango]

12 hours ago, GKD09 said:

Love how these are your first 4 posts lol. But really interested to see where this ends. I'm too lazy to do my own research on my only weekend

Yeah, I feel you. The only reason I did more research is that I had the rules for a .48% in the back of my mind. So the moment I was playing and wasn't offered surrender I knew something was off  😄

[blueprints]

 Dan hasn't really acknowledged a good chunk of what Elmango has been explaining. 

On 12/12/2019 at 10:58 PM, Dan said:

Taking the two current calculations, can you demonstrate the difference of the infinite deck on both of these attached figures. Cheers!

 

Notice how surrender lowers the house edge. I think what you are trying to claim, is wizards of odds (both the video makers, and the website) are wrong?

He is saying the infinite deck makes a difference. Even i can understand that. I mean do you see a option for Infinite decks besides the number 8 on "number of decks of cards used"

If you go to stake.com and click on blackjack and then click on the "Rules" The first line on the rules is "

Unlimited decks in play 

bThe calculator your using Dan to defend steak's 0.48% claimed house edge on steak is not valid because there is no option for infinite decks. only 1-8. he showed you how to get the house edge for infinite amount of decks but your ignoring it, prolly because you work for steak. well it really doesnt make the site look good when a newbie comes and makes one of you have to get this defensive and evasive on valid points.  

[Shekhar1992GL]

Whats going on here guys,

@dan why u entertaining that noob,
Won't u think person who start first post and make wager like 0.00000035 is aware of anything about gambling and house edge.

What u want know @Elmango about gambling.
If u want to know about calculation or what ever u can ask support.

[Elmango]

23 hours ago, Shekhar1992GL said:

Whats going on here guys,

@dan why u entertaining that noob,
Won't u think person who start first post and make wager like 0.00000035 is aware of anything about gambling and house edge.

What u want know @Elmango about gambling.
If u want to know about calculation or what ever u can ask support.

I work in the gambling industry, @Shekhar1992GL. I'm very familiar with these calculations 😄. Anyway, I don't see how me not gambling huge amounts makes my arguments less valid. I encourage you to go through the maths. 

Just for the record, I'm not the first one suggesting the house edge is wrong but it seems I'm the first one showing how it should be calculated. Here's another post: 

 

[nuuuitsjdragon]

On 12/21/2019 at 12:24 PM, Shekhar1992GL said:

Whats going on here guys,

@dan why u entertaining that noob,
Won't u think person who start first post and make wager like 0.00000035 is aware of anything about gambling and house edge.

What u want know @Elmango about gambling.
If u want to know about calculation or what ever u can ask support.

Oh look, a common troll. 

1) If you’re not aware of what is going on, please refrain from making blasé comments. 

2) Without having researched the topic to any depths and thus, having insufficient knowledge - You automatically lose the right to educate someone else on what the next step should be. 

3) Your shallow (and insensitive) views invite judgement as a stereotypical fool.

TL;DR “Even a fool is thought wise if he keeps silent, and discerning if he holds his tongue.”

Learn to observe. 

On 12/21/2019 at 12:11 PM, blueprints said:

 Dan hasn't really acknowledged a good chunk of what Elmango has been explaining. 

He is saying the infinite deck makes a difference. Even i can understand that. I mean do you see a option for Infinite decks besides the number 8 on "number of decks of cards used"

If you go to stake.com and click on blackjack and then click on the "Rules" The first line on the rules is "

Unlimited decks in play 

bThe calculator your using Dan to defend steak's 0.48% claimed house edge on steak is not valid because there is no option for infinite decks. only 1-8. he showed you how to get the house edge for infinite amount of decks but your ignoring it, prolly because you work for steak. well it really doesnt make the site look good when a newbie comes and makes one of you have to get this defensive and evasive on valid points.  

Word. 

I don’t understand why the back-and-forth was required between Dan and the OP, much less assuming a hostile position. 

The questions are well-phrased, concise and supported with strong evidence...

I’m no mathematical genius but even I, like Blueprints, can fully understand the context. 🙄

[Elmango]

@Dan I noticed the house edge has been changed  from .48% to .5% but as far as I can tell the rules haven't changed so it should be .58%. Any comments?