Expected win rate

[Guy]

Hi all,

Can anybody tell me, if I play one hour with one hand (IE 100 hands) and expect to win X if it is true to say that if I play one hour with two hands (IE 200 hands) that my expected win rate is 2X, assuming of course I bet the same amounts at the same counts in both cases?

Guy

 

[The Mayor]

This is false. The reason is "covariance" -- the two hands are not independent. They both win/lose together quite often (e.g. if the dealer busts they both win, if the dealer gets BJ, they both lose).

The correct "equivalence" taking covariance into consideration is that 1 hand at $30 is the same as 2 hands at $20 each.

 

[Guy]

Thanks Mayor,

Sorry if I'm being thick with this.

I can understand how covarience effects the SD and therefore the optimal bet for size of bank roll.

But am struggling with how the number of hands in play effects the expected win/loss rate per hour of play (not per hand).

For example if I flat bet $10 using just basic stratergy I would expect to loose at about 0.5% per hand or 5 cents per hand, right. So if I play two hands would I not expect to still loose at about 0.5% 5 cents for each hand ?

You comments greatly appreciated.

Guy

 

[Cyrano]

I'm not sure I follow, Mayor. Perhaps I've misunderstood, but it would seem to me that the win rate would exactly be 2X. However, the deviation would be less than what the 2X deviation would be, since covariance is not a function of win rate, rather, a function of departure.

In the example you've given, I would contend that if you doubled 1 hand at $30 to 2 hands of $30, it's effectively the same as betting $60, with the win rate of $60. The only difference is, your fluctuations would be lower than the normal 1 hand of $60.

 

[The Mayor]

The circumstance of playing two hands at once against the same dealer hand is not the same as playing two hands on two different tables. In the second case they are independent events, in the first case they are not. That's all there is to it.

--Mayor

 

[The Mayor]

If you play 2 hands of $30 -- then

1) The two hands will win/lose together quite often based on the dealer's result (not the players). This is covariance.

2) The composition of one hand will affect the odds for the other hand. This is another aspect of covariance. For example, playing two hands in single deck, suppose you are dealt 7-7 to both of your hands against the dealer's T? Are you going to catch a 7? THis is an extreme example, but it underscores the hands effect on each other.

--Mayor

 

[Cyrano]

I don't dispute what covariance is. A covariance of 1=the results are locked, where a covariance of 0=the hands are independent of each other (p. 202 of Professional BJ). 2 hands at the same table lies somewhere in between, according to PBJ, somewhere between 0.4-0.5. However, this does not impact EV--only volatility. Perhaps this site would explain my position better: (Dead link: http://www.customstrategycards.com/online_bj-br.htm) --"When more than one hand is played concurrently, all the player hands hinge on a single dealer hand. The statistical measure of this relatedness is termed covariance, and it causes a substantial increase in volatility for each additional hand played."

I don't quite understand your second example, since your win/loss are not dependent of how many 7's you've used--it's dependent on what the dealer draws.

If you play 2 hands of $30 -- then

1) The two hands will win/lose together quite often based on the dealer's result (not the players). This is covariance.

2) The composition of one hand will affect the odds for the other hand. This is another aspect of covariance. For example, playing two hands in single deck, suppose you are dealt 7-7 to both of your hands against the dealer's T? Are you going to catch a 7? THis is an extreme example, but it underscores the hands effect on each other.

--Mayor

 

[Guy]

I Feel like I'm getting a bit out of my depth here, but for what it's worth here is my two penneth worth:-

I think I have read that other players at the table and their actions will not effect my expected win rate, if this is true how can a second hand played by myself have a different expected win rate than a hand played another player at the table, surley the cards don't know who's brain is making the descisions ;-)

Clearly I'm missing somehting here ?

Guy

 

[Cyrano]

Extra players do not have an effect on your advantage (you will still win, say, 2 bets/100 hands played). They do, however, have an affect on your win rate, since you won't get in as many hands/hour (instead of playing 100 hands/hour, you're playing 50 hands/hour, it will take you twice as long). Hope this makes sense.

______

I Feel like I'm getting a bit out of my depth here, but for what it's worth here is my two penneth worth:-

I think I have read that other players at the table and their actions will not effect my expected win rate, if this is true how can a second hand played by myself have a different expected win rate than a hand played another player at the table, surley the cards don't know who's brain is making the descisions ;-)

Clearly I'm missing somehting here ?

Guy

 

[CC-Management]

Welcome to CC.COM. We would like to invite you to sign up and create a profile. Join our group! It's free! We are united in playing 21 with skill and knowledge

 

[Guy]

Thanks Cyrano,

So we seem to be agreed that the expected win rate per hand stays constant regardless of the number of concurrent hands being played, what does change however is the Standard Deviation and therefore the optimal bet compared to size of bank roll.

This is what I had initially supposed and had been playing on that basis, I was looking for somebody to confirm my assumptions which you have, thankyou.

Guy

 

[Hinoon]

Just a quick not to say that this whole thread is an example of why this is one of the best places to learn BJ. Civil discussion, thorough answers, and accessible language. I learned a lot from this thread.

Thanks to all of the contributors.

 

[Guy]

Thank you!

Guy

 

[Guy]

Hmm, ran some sims, and the mayor was right, I dont understand really, but the expected win rate DOES NOT double if you run two hands simultaneously!

Guy