July 17th, 2019 at 6:07:29 PM
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Yes absolutely. When the dealer gets Blackjack (or 21), all of your hands lose (or lose/push). When dealer deals himself a 10, all of your hands will use the same strategy and hit until H17, which causes you to bust more. When dealer's upcard is a 5, all of your hands will be a favorite to win.

The EV is not changed by playing two hands, but the correlation causes your variance to be larger than if you played one hand.

The EV is not changed by playing two hands, but the correlation causes your variance to be larger than if you played one hand.

So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.

July 17th, 2019 at 6:20:07 PM
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The Original Poster’s question was about House edge, aka EV.Quote:gordonm888Yes absolutely.

The EV is not changed by playing two hands, but the correlation causes your variance to be larger than if you played one hand.

Corrélation has no impact on Expectations, only on Variance. More chance to win more and more chance to lose more. The average remains the same.

Reperiet qui quaesiverit

July 17th, 2019 at 7:56:33 PM
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I don't think I saw anyone actually respond to the OP in terms of Expected Value (EV).

OP: If you're planning on playing blackjack today for 2 hours, with just basic strategy your EV will be -$X. If you are forced to play 2 hands, and you in fact play just as long as you planned to play before (2 hours) your EV for the day will now be -$2X. You will, on average, lose twice as much as you'd normally lose since you're essentially playing twice the number of hands.

The house edge itself does NOT change. What changes is your total amount of money wagered, which is figured in to EV.

EV = (AvgBet*NumHands)*(-.005)

AvgBet = your average bet approximated over your course of play. If you're a $10 player, never raising or lowering your bet, then your AvgBet = $10.

NumHands = the number of hands you play in the time span you play. THIS is what is going to change that makes you lose more money.

-.005 is a GENERIC -.5%, which "most" blackjack games are around, but that's also with playing PERFECT BASIC STRATEGY. Thus, if you're playing a slightly poorer game than basic strategy, you might be around -1%, and that 2nd hand is really starting to work on you.

EXAMPLE: using a generic .5% game, $10 flat bet as mentioned above, and an average of 80 hands per hour (pretty typical for your average player)...

*playing 1 hand for 2 hours = 160 hands total)*

EV = (10*160)*(-.005) = -$8

*playing 2 hands for 2 hours = 320 hands total)*

EV = (10*320)*(-.005) = -$16

Now if you're not playing perfect basic strategy for 2 hands

EV = (10*320)*(-.015) = -$48

See how things can go from -$8/hour on average in the long run to -$48/hour on average in the long run? It pays to know basic strategy and bet as little as possible if you're not an advantage player!

OP: If you're planning on playing blackjack today for 2 hours, with just basic strategy your EV will be -$X. If you are forced to play 2 hands, and you in fact play just as long as you planned to play before (2 hours) your EV for the day will now be -$2X. You will, on average, lose twice as much as you'd normally lose since you're essentially playing twice the number of hands.

The house edge itself does NOT change. What changes is your total amount of money wagered, which is figured in to EV.

EV = (AvgBet*NumHands)*(-.005)

AvgBet = your average bet approximated over your course of play. If you're a $10 player, never raising or lowering your bet, then your AvgBet = $10.

NumHands = the number of hands you play in the time span you play. THIS is what is going to change that makes you lose more money.

-.005 is a GENERIC -.5%, which "most" blackjack games are around, but that's also with playing PERFECT BASIC STRATEGY. Thus, if you're playing a slightly poorer game than basic strategy, you might be around -1%, and that 2nd hand is really starting to work on you.

EXAMPLE: using a generic .5% game, $10 flat bet as mentioned above, and an average of 80 hands per hour (pretty typical for your average player)...

*playing 1 hand for 2 hours = 160 hands total)*

EV = (10*160)*(-.005) = -$8

*playing 2 hands for 2 hours = 320 hands total)*

EV = (10*320)*(-.005) = -$16

Now if you're not playing perfect basic strategy for 2 hands

EV = (10*320)*(-.015) = -$48

See how things can go from -$8/hour on average in the long run to -$48/hour on average in the long run? It pays to know basic strategy and bet as little as possible if you're not an advantage player!

Playing it correctly means you've already won.

July 18th, 2019 at 6:49:55 AM
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What is variance?

July 18th, 2019 at 7:53:20 AM
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Quote:Nenuco33What is variance?

Others can explain it more precisely, but

Variance is the mathematical word that accounts for luck or random chance.

It represents the range of deviation in any particular set of win or loss results from the expected average results.

If you play a game of blackjack that has a house edge of .5, (for example) for every $100 you wager using Optimal Strategy, you can expect to lose $0.50. But you will almost never have that result on any particular $100 you spend. Instead, you might win, or lose more than that (variance). Over time, and many $100 wagers, your results will conform to that .5 HE.

Hope that helps.

If the House lost every hand, they wouldn't deal the game.

July 18th, 2019 at 8:36:12 AM
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what are the calculations to calculate the variance?

July 18th, 2019 at 11:16:18 AM
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Quote:Nenuco33what are the calculations to calculate the variance?

Variance is the average of the square of the difference between the mean and the observations.

The race is not always to the swift, nor the battle to the strong; but that is the way to bet.

July 18th, 2019 at 12:56:47 PM
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Quote:Nenuco33what are the calculations to calculate the variance?

À simple example to understand variance is this. Imagine you play Heads or Tails. EV is zero, because in the long run each player wins and loses the same amount.

If you play for €1, the variance is 1€^2 (standard déviation €1)

If you play for €2, the variance is 4€^2 (standard dev €2)

To calculate easily, take the average of SQUARED results, then subtract the square of the expectation.

Reperiet qui quaesiverit

July 18th, 2019 at 3:41:16 PM
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Ratrher than look at the maths consider a number of games you might play. The assumption is you play each games 24 times betting $1 each time and the odds offered are fair. In both these games, in the long term you'll come out even, but consider what might happen over a shorter game.Quote:Nenuco33What is variance?

(i) Heads or Tails

One of the simplest of games is Heads or Tails, depending on the result you will either win $1 or lose $1.

On a series of 24 spins, you are just as likely to come out ahead as come out behind. It is very unlikely you'd lose (or win) more than $10.

(ii) Double 6.

Consider a fairly risky game where you roll two dice. If you roll double 6 you win $35, otherwise you lose $1.

Strangely you are (nearly) just as likely to come out ahead as come out behind, but this time if you come out losing (by not rolling any winner) you lose all $24. On the other side you might roll several winners; you have a 1 in 7 chance of winning $48 or more.

In the first game you're not going to win a lot nor lose a lot - the variance is low.

In the second game you could win big (4% chance of over $120) but also there's a fair chance of losing all your money (51%). Being the more risky game the variance is fairly high.

If you know roulette then the first game is similar to betting Red or Black, and the second is similar to betting one number (although in both cases the casino wins something on any zero).

July 19th, 2019 at 8:35:05 AM
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Discussion of personal insults, profanity, and forum rules has been split off to here:

https://wizardofvegas.com/forum/info/help/33335-forum-insults-and-profanity-split/

https://wizardofvegas.com/forum/info/help/33335-forum-insults-and-profanity-split/

If the House lost every hand, they wouldn't deal the game.