Casino edge

[DonFinuchi]

Hi guys,

A question from a noob

Accourding to the basic strategy engine in a 6 decks, S17, D9, DAS, No Surrender, No Peek game, the casino has a estimated edge of 0.64. Does that mean that the player/casino has a win ratio of 49,36%/50,64% or 49,68%/50,32%? Or am I totally off?

 

[shadroch]

You will win around 43% of the hands played. Your posts does not factor in pushs. The casino will win more hands than you, but your BJs will pay 3-2 and you will have the abilty to double your bets in favorable situations so you will make more per winning hand thand the casino does.

 

[DonFinuchi]

Ok. But how am I supposed to perceive the 0.64 edge exactly?

 

[shadroch]

That, in the long run, for every hundred dollars you bet, you'll get back $99.36
Obviously, you results will differ but if a million people each played a million hands, thats what it would average out to.

 

[DonFinuchi]

Ah... Thx

 

[Sucker]

Advantage is defined as such: Advantage = (wins - losses) / (wins + losses).
What shadrock has described is what's known as EXPECTATION; which is defined as: Expectation = (wins - losses) / (wins + losses + pushes). This differs from Advantage; in that Expectation factors in pushes, while Advantage counts pushes as though the hand wasn't even played. Note that in both cases, we're talking about MONEY won, and not HANDS won.

Because of pushes, in a blackjack game with a house advantage of .64%; for every $100 that you BET, you'll actually get back slightly more than $99.36.

Here's a simple way to help you understand the difference between Advantage and Expectation:

Suppose you have a game where there are 100 marbles in a jar, 99 white ones and 1 black one. If you pick a black one, you win; and if you pick a white one it's merely a push. After 100 hands, you'll have 1 win and 0 losses; so your Advantage is 100%. However, your Expectation will be only 1% (1 win, 0 losses, 99 pushes).

 

[Nynefingers]

I disagree with your definition of advantage. Advantage is figured in one of a couple of ways: based on your initial bet, or based on your total bet. The difference is whether or not the money bet on splits and doubles is considered or only the money you bet at the end of the hand. They are calculated as follows:

Initial Bet Advantage = (wins - losses)/(initial bet)

Total Bet Advantage = (wins - losses)/(total bet)

Those will both be based on expected wins and losses, not your actual results which will be affected by variance.

I generally think of EV in terms of dollars or units instead of percentages, so average bet size and number of hours, hands, etc. comes into play there.

 

[Sucker]

I disagree with your definition of advantage.

This is not MY definition of advantage. It's THE definition of advantage. This EXACT definition has been published in countless books, it's agreed upon by ALL scholars of probability; and it's CERTAINLY the definition which was used by the writers of the basic strategy engine.

You're entitled to your opinion. You're NOT entitled to the facts. :whip:

I sometimes believe that if I claimed that the sky is blue, I'd get 10 people telling me why I'm wrong. :laugh:

 

[sagefr0g]

well, for some of i think it's Don S's stuff and QFIT's cvcx stuff i have:

EV = #ROUNDS X AVG. BET X W/L%

where W/L% is the Initial Bet Advantage

Initial Bet Advantage is the amount won or lost divided by the initial bet.

 

[London Colin]

If there's a technical distinction between advantage and EV, then I'm pretty sure it is not one that is ever applied in this context. The terms 'House Edge', 'House Advantage', and EV are interchangable, as far as I am aware. And the definition that applies is that of EV. (For that matter, the word advantage does not appear on the Basic Strategy Engine, nor in DonFinuchi's question.)

The only thing to watch out for is the sign. EV often means player EV, in which case the sign is opposite to the house edge.

As for the definition, we are talking about a single hand of blackjack. The fundamental definition of EV is simply that it's the sum of all the possible payoffs (-1 when you lose, +1 when you win, +1.5 when you get a natural, -2 when you lose a double or two split hands, etc.), each multiplied by it's probability.

The above definition represents how you do the calculation by Combinatorial Analysis: you consider every possible player/dealer hand combination, its probability and its payoff.

If, instead of CA, you run a simulation of many, many hands then it becomes a case of dividing the money won by the number of initial bets made. If you've lost $1 after playing 1000 rounds of blackjack at $1 per hand, then you've arrived at a current estimate of your EV to be -0.1%. (i.e. a House Edge of +0.1%) You don't ignore the pushes.

 

[Mr. T]

With due respect to Guru London Colin my answer to the OP question would be that " if you bet $100 you would expect to lose 64 cents".

 

[Nynefingers]

This is not MY definition of advantage. It's THE definition of advantage. This EXACT definition has been published in countless books, it's agreed upon by ALL scholars of probability; and it's CERTAINLY the definition which was used by the writers of the basic strategy engine.

You're entitled to your opinion. You're NOT entitled to the facts. :whip:

I sometimes believe that if I claimed that the sky is blue, I'd get 10 people telling me why I'm wrong. :laugh:

I don't really care enough to dig up a whole bunch of references right now, but I will provide one that I think everyone here would consider reputable. Per the Wizard of Odds:

Player Advantage: This is the ratio of net player win to total initial bets.

From this link and surely others as well.

Also, QFIT's products report the advantage as both Initial Bet Advantage and Total Bet Advantage.

Many folks (QFIT included) use edge, advantage, and EV interchangeably, with all referring to a number expressed as a percentage of your bet. I prefer to use edge or advantage to refer to the percentage number and EV to refer to dollars or units for a given amount of time or hands. I consider that merely a preference as the term EV is frequently used both ways.

Oh, and the sky is most definitely not blue here at the moment. Maybe later though :laugh:

 

[London Colin]

With due respect to Guru London Colin my answer to the OP question would be that " if you bet $100 you would expect to lose 64 cents".

Mine too. My answer was more aimed at refuting Sucker's post than anything else.

 

[Nynefingers]

Mine too. My answer was more aimed at refuting Sucker's post than anything else.

I agree with this interpretation for sure. The only question is are we betting $100 total including doubles and splits, or just $100 at the beginning of the hand. That's the only difference between TBA and IBA.

 

[London Colin]

I agree with this interpretation for sure. The only question is are we betting $100 total including doubles and splits, or just $100 at the beginning of the hand. That's the only difference between TBA and IBA.

But you can assume it's IBA unless told otherwise, I would think.

I just dug out my copy of 'Gambling Ramblings', a collection of articles by Peter Griffin. He mentions both issues: IBA vs TBA, and whether or not to throw out ties (in reference to baccarat and craps). It's an interesting read.

He shows that, if you go down the TBA route, it can actually imply differences in Basic Strategy, under certain rules.

Regarding advantage, and whether or not to include ties, he says 'There is no common agreement even among mathematicians about which description is preferable'. So I guess we shouldn't expect to find agreement on an internet forum.

 

[Renzey]

Accourding to the basic strategy engine in a 6 decks, S17, D9, DAS, No Surrender, No Peek game, the casino has a estimated edge of 0.64. Does that mean that the player/casino has a win ratio of 49,36%/50,64% or 49,68%/50,32%? Or am I totally off?

I think this is the answer you're looking for. Although your wins and losses will be far from 50-50 due to blackjacks, doubles, pushes, etc., those factors will flatten out your effective win/lose odds to 49.68%/50.32%. That is, it's the total difference between wins and losses that determine the expected win or loss.

 

[NeoQuaker]

Speaking of the casino edge, can someone say what exactly gives the casino an edge in Blackjack? For example, in Roulette, its the 0 and 00 that create that edge. But in Blackjack, I don't see it. Seems like it would be a 50/50 game. Why is the dealer more likely to get a higher hand than players?

Sorry if this might be a bit off topic, but I believe the OP's question has been answered.

 

[shadroch]

The house edge comes from the player going first. If a player bust, house wins even if they also bust.

 

[NeoQuaker]

Thanks shadroch, forgot about that.