Blackjack question

Can the house edge of a blackjack game calculate how much bet units or money a player will/lose statistically?
When the house edge is .4% and the player is flat betting $5 for 1000 hands using perfect strat ovi
Is there a formula I am not quite coming up with? or is a simulation of this game the way to figure out the win/lost stats?

Quote: MikeDread

Can the house edge of a blackjack game calculate how much bet units or money a player will/lose statistically?
When the house edge is .4% and the player is flat betting $5 for 1000 hands using perfect strat ovi
Is there a formula I am not quite coming up with? or is a simulation of this game the way to figure out the win/lost stats?

Hi MD,
Calculate? Yes and no.
From the house edge and the average bet size, we can calculate the value of the average amount you would be expected to lose over those 1000 hands. We could also calculate an estimate of the margin of error of that expected loss to certain levels of probability. It goes something like this for Blackjack.

After those 1,000 hands of flat betting $5, your expected loss would be:-

Average expected loss = 1,000 x $5 x 0.4% = $20 lost

BUT
You are unlikely to have lost exactly $20. Maybe you win $5,000. Maybe you lose $5,000 ( Both pretty unlikely )

With 68% probability you will land somewhere in the range
+/- (1000^0.5 x 5 x 1.2) where 1.2 is the standard deviation for one hand of Blackjack

So that's an outcome of $20 lost give or take $190

In my opinion, games won/lost is a bit of a useless stat in Blackjack, because when you win or lose it may be on a doubled or split hand and you may get the occasional Blackjack. There are plenty of tables of numbers on the Wizard of Odds site.

Quote: OnceDear

So that's an outcome of $20 lost give or take $190

imo,
3 standard deviations plus/minus

gives a much better picture of the range one can expect

-$20 +/- 570 =
$550 to -$590
99.73% of the time

so it is still possible to end outside that range
(not including too much to drink and hit your hand until they say you busted)

to have a winning session (after 1000 hands played) is about a 46% chance
average win given a win = ?
have not gone there yet
average loss given a loss = ?

Sally

Hey OD, Thanks this is appreciated

Quote: MikeDread

Hey OD, Thanks this is appreciated

If you go to a crazy progressive,
You can win/lose alot more money, much faster ;-)

As OnceDear showed you, here's the function...

EV = TotalWagered * HouseEdge = (AvgBet*NumHands)*HouseEdge


Your 1-SD for 1 hand is...

OriginalSD = 1.15*AvgBet


Your 1-SD for ANY NUMBER of hands is...

SD(xHands) = Sqrt(xHands) * OriginalSD


...so in your example.... EV = (5*1000)*(-.004) = -20, OriginalSD = 1.15*5 = 5.75, and your SD(1000 hands) = Sqrt(1000)*(5.75) = 181.83... 3SD = 545.49.

With 99%+ confidence, you can expect to lose $20 +- $545.49 after 1,000 hands flat betting $5.