House Edge with Basic Strategy is not 0.5 % ??

[SerdarHakan]

Hi , that's my first post in this forum. I'd be so happy if i can get some help from you.

I have written a console simulation program to test and develop new strategies.

Rules I've used are :
- Both dealer and player having BJ or 21 , that's a push/tie.
- Dealer stands on soft 17.
- Blackjack pays 3:2
- No hit allowed after splitting aces
- Double on any card is allowed
- Re-split or double on a splitted hand is not allowed.
- If dealer is showing an Ace , asks for insurance.
- If dealer isn't showing an Ace but actually has blackjack , game is played normally.
- If dealer in fact has a blackjack and showing Ace, players are not allowed to make their moves; results are directly calculated.
- 8 decks shoe with 50% penetration.

At that moment , my player in simulation flat bets 1 unit each hand. And I've used these formulas for calculating House Edge.

Player Edge per Hand = ( Final Money - Initial Money ) / Hands Played; ( Negative means a positive house edge )
Player Edge Per Round = ( Final Money - Initial Money ) / Rounds Played; ( Negative means a positive house edge )

Just for clarification , one round is the game between re-dealing cards. Thus,for example if the player splits , he plays 2 Hands , at 1 Round.
I've separeted round and hand just in case I add more players to simulation in the future. For example , when there is one player Hands/Rounds is approximetly 1 ( not exactly because of the split hands ) , and this would be 2 for 2 players since 2 hands are played by these 2 players at each round , etc.

Following is the output of the simulation of almost 380 million hands.

Note : for blackjack rate , only blackjacks that make player win are considered. The real blackjack percent is probably higher since it also includes both player and dealer having a blackjack.


I have included the screenshot of the output of the simulation as attachment.

It says ;

Win Rate = 41.16 % ( pretty accurate , it is usually considered 42%)
Dealer Bust Rate = 27.8 % ( pretty accurate again , it should be 27-29 % )
Player Edge Per Hand = -0.0573 !


Well , when flat betting 1 unit each hand, final minus initial money divided by number of hands is -0.05.
Which says player loses 0.05 unit of each 1 unit bet at each hand , thus house edge is 5 % , isn't it ?
According to other calculations on the internet , house edge with playing basic strategy should be 0.5% ,not 5% .

I'm sure my simulation works correctly since it calculated other results pretty accuretly , like win rate , dealer bust rate etc.

So , what im doing wrong here ? Is my formula for house edge is incorrect ? Can you help me please , thanks

[BJGenius007]

Well , when flat betting 1 unit each hand, final minus initial money divided by number of hands is -0.05.
Which says player loses 0.05 unit of each 1 unit bet at each hand , thus house edge is 5 % , isn't it ?

For S17 game, player loses 0.0046 unit of each 1 unit bet at each hand, the house edge is 0.46%. Your simulation program must be wrong. The coding of BJ is hard. I doubt you can write a program 100% correctly at the first try.

[Freightman]

First, there is good sim siftware out there already.
Second 38 million hands is not an accurate sim.
Third, s17 is good, sp1 fir all pairs is poor. No double after split also bad.
Fourth, I think you mean to say double on any 2.
Fifth, your win loss rate is inaccurate.
Sixth, bj rate, if I read right, is every 33 hands or so which us way to low.
Seventh, edge is a function of rules to overcome and spread.

garbage in garbage out.

[CoopOwnz]

Your House edge calculations don't seem correct.
HE = Amount WonLost / Initial Wager

Your calculation is for something different. You need to be looking at how much the player won or lost in total. Divide that number by the total amount that was initially bet (meaning before any double/splits).
That should give you close to the 0.46% you are looking for.

38 million hands might not be accurate when you are trying to be extremely precise but you should get pretty close with that sample size.

Your BJ rate is low but you mentioned why it is low.

I recently developed a blackjack simulator for android phones so if you have code specific questions you can ask.
https://play.google.com/store/apps/d...ack.allin1.com

The simulator allows for 10 free runs but is only $0.99 to unlock unlimited runs. You can run the exact sim you are looking for and compare results with what your sim is producing. The only limitation is that the sample sizes are not very big due to android processors being kinda slow. Regardless, you can get accurate results from my simulator I've tested it thoroughly.

Let me know if you need help with your code.

[SerdarHakan]

Well ,Eventhough that's the third version of my program, I can't still say it's 100% correct. However, let me explain types of bugs and their effects you can expect in such a program.

As an example from earlier versions : A-A hand was understood as a soft-12 hand and not an Ace pair. Since getting an A-A pair is not so likely, this kind of unexpected behaviour only changed my win rate slightly. It was giving 40.5 % instead of 41-42%.

According to Wizard Of Odds, correct win and lose rates are following ( when played with basic strategy )
Reference : http://wizardofodds.com/games/blackjack/appendix/4/

Accepted Win Rate = 42.2 % -------- My Win Rate Result : 41.2 %
Accepted Lose Rate = 49.1 % --------- My Lose Rate Result : 50.1 %

It looks like only 1% of the games in the simulation is kinda bugy, misinterpreted etc. , and i lose them instead of win , which reduces my win rate and accuracy.

However, considering this , my results are still pretty accurate. Let me give you relative error percentages of win and lose rate.

Relative Error % = abs( Measured Value - Accepted Value ) / Accepted Value * 100;

Win Relative Error % = 2.3 %
Lose Relative Error % = 2.0 %


Now , let me assume correct value of the House Edge is 0.5 % and my measured value is 5 % .
House Edge Relative Error % = 900 % !!!!

See, it can't be. Eventhough i accept my simulation doesn't work correctly in the 1% of the games. It's impossible to get 900% error while getting other data almost correct.

Let me also give you the House Edge for basic strategy excluding double. This is the result when you only flat bet and hit or stand.

Let , Flat bet amount = 1

Expected Value = 1.(42.2%) - 1.(49.1%)
Expected Value = - 6.9 %


Which means, when playing blackjack with stated win and lose rates , You are expected to lose 6.9% percent of each bet. Which implies 6.9% House Edge.

The way basic strategy reduces this, as we all know and should know , it doubles when player has a hand that is likely to win. Thus, eventhough you are still winning 42.2 % of the total games , amount of money you win at those hands is increased thus House Edge is reduced.

But hold on a second. Do you really think doubling one in a while can reduce house edge from 6.9% to 0.5% !! It clearly should be 5 % .

So what is happening ? 0.5 % House Edge is just a misunderstood statistic ? One wrote 0.5 instead of 5 and it stayed that way without questioning it again ?

------------------------------------

For the house edge formula, i assume this formula is a hand specific. What i means is , you get a value for each hand , which is ( win or lose ) / initial bet.
For a win hand where you bet 1. it is 1. For a win hand where you doubled it's 2 , and for a lose its -1.
Then after millions of simulations you get the average of them to find House Edge right ? It is actually the same expected value calculation i've done above with doubling excluded, so returns were only 1 and -1.

When you add up all the numerator , which are 1,-1 or 2 for millions of games. You exactyl get final money - initial money.
And when you add up all the denominator, which is sum of all bets done at millions of hands. (with 1 flat bet ) it is the number of hands.

[Freightman]

You're still making fundamental errors. If your program doesn't recognize the proper basis decision, as in split aces, house edge on what would normally be a .5% house edge will actually be higher. Also, though not totally sure, I kinds sorta think you are ignoring the effect of different rules on house edge.

Your goal is to develop a strategy that will make money. That means perfecting basic, incorporating deviations that will enhance your basic decisions, and a ramped betting scheme that will recognize the strength or weakness of remaining deck composition.

I guess the point I'm trying to make, is that I don't understand what it is that you are trying to accomplish.

[CoopOwnz]

So if every hand is wagering $1 then your total INITIAL wager will be the number of INITIAL hands. Your total hands cannot include split hands.
Assume you have 100 INITIAL hands played. After all was said and done you came out positive $5. The House Edge calculation would be 5/100 = 0.05
If you are doing that exact calculation then you are doing it correctly. I would recommend running a very small simulation to test this.

Remember, Expected Value and House Edge are different formulas. My simulator shows both House Edge and Expected Value. They are close but different. Expected value will be your Amount WonLost / TOTAL Wager. House Edge is Amount WonLost / INITIAL Wager.

[SerdarHakan]

Yes, im not including split hands in the result showed as Player Edge Per Round in my data.

I have just tried your formula . Let me explain my implementation. After each round , i took the change in the player money , which is Win or Lost . I've divided that with my Default Bet.

-----------
CoopOwnz, i assume you've recommended small test because of the reason that my first calculation were using final money - initial money; which has a chance of underflow for final money. It was checked for that. So , that was not a problem. Besides, with this new approach , I have set to player money 0 at the beginning of each hand , and took the final money as the change in money , thus underflow risk is not an issue anymore.

------------

And for millions of games, i kept taking averages of this values to see where they're approching.

Let
HE of the Hand = Change in Money / Default Bet;
Sum Of Previous HE = House Edge * Rounds played;
House Edge = ( House Edge + HE of the hand ) / (Rounds played + 1);


The result is approximetly 0.05 , which is 5 % again.

I really started to think 0.5% house edge is just a misunderstanding on internet.

What your simulation shows for House Edge CoopOwnz ? 0.05 ( 5 % ) or 0.005 ( 0.5 %)

For the ones that asks what i'm trying to accomplish , i'm trying to understand what will i lose in the long run per my bet.

If you bet 100 unit each hand , you lose 5 unit ( as i claim ) or you lose 0.5 unit ?

After 100 rounds , do you expect to lose 50 units or 5 units ? That matters and changes everything a lot !

[Freightman]

Think in terms of dollars, not units. If you flat bet $100 per hand, your long term loss is .50 per hand playing oerfect basic, and assuming a one half of one percent house edge which I don't know youre simulating. Any profit after 100 hands is positive variance.

A 5% edge that you are querying can't be overcome.

[BJGenius007]

You're still making fundamental errors. If your program doesn't recognize the proper basis decision, as in split aces, house edge on what would normally be a .5% house edge will actually be higher. Also, though not totally sure, I kinds sorta think you are ignoring the effect of different rules on house edge.

Your goal is to develop a strategy that will make money. That means perfecting basic, incorporating deviations that will enhance your basic decisions, and a ramped betting scheme that will recognize the strength or weakness of remaining deck composition.

I guess the point I'm trying to make, is that I don't understand what it is that you are trying to accomplish.

As Freightman said, your program is not fundamentally correct if your program treats the pair of aces as soft 12. Even the ploppy knows you always split the aces!

[CoopOwnz]

Okay I'm still confused why you are not following the calculation for House Edge. If you are trying to get the house edge of a game of blackjack it is done this way: AMOUNT WONLOST / INITIAL WAGER. What you are doing by calculating the HE per hand and multiplying it by the number of rounds is NOT the correct way to calculate House Edge. Here is what you should do:

After every hand your simulator plays you subtract or add the win or loss to a variable. Once your simulation is over you simply take this number and DIVIDE by the TOTAL INITIAL ROUNDS played (this is the same as initial wager in your case since the bets are $1 each time). THAT is how you calculate HOUSE EDGE. Stop doing that other nonsense and asking why it doesn't match other House Edges.

I really started to think 0.5% house edge is just a misunderstanding on internet.

Don't be naive. I have spent many months testing simulators and running hundreds of billions of hands. When I first started trying to get HE and EV values from my own simulator I was also off by a lot like you are. In this case you are not calculating the HE correctly you are doing some other calculation that I don't understand. If the actual House Edge was 5% then there would be no counting cards because you could never win.

My simulator House Edges match those of Norms simulator with a Standard Deviation of about 1/1000th of a percent if both running 3 billion hands everything the same.

[Sharky]

..Seventh, edge is a function of rules to overcome and spread.....

incorrect, edge is a fn of rules and cards played....NOTHING to do w/ your spread...spread is what you make, or don't, of your edge

[Freightman]

incorrect, edge is a fn of rules and cards played....NOTHING to do w/ your spread...spread is what you make, or don't, of your edge

Semantics. You're right of course for house edge definition. A players edge is a function of rules, spread, indices - in other words, your second sentence.