Blackjack: Standard Deviation per 100 hands?

[DavidC]

Hey guys.

I'd like to know, if I played perfect strategy, what my expected loss would be on 100 hands of blackjack, and what my standard deviation would be over that period of hands.

Obviously, this would depend on the exact rules of the game, but something rough would be great, or info as to how specific rules affect the SD.

--Dave.

[MentalNomad]

STFW. /images/graemlins/grin.gif

I have a book called "Blackjack: A professional reference," or something like that. I just looked it up -- compiled by Michael Dalton: http://www.amazon.com/exec/obidos/tg/detail/-/1879712016/qid=1123541391/sr=8-5/ref=sr_8_xs_ap_i5_xgl14/104-3124015-3732706?v=glance&s=books&n=507846. It has basic startegy for various game variants (number of decks, redoubles allowed, double after split allowed, etc.) You can also calculate you expectation playing basic against any game type.

You can probably find it all online; I haven't looked. Been out of the BJ scene for a long time.

[MentalNomad]

Oh, and your basic disadvantage will run between .5% and 2%. Around 1% is common online, as far as I can recall. Can't recall variance figures. Too lazy to go over to bookshelf and check under the dusty books.

[cardcounter0]

SD of 1.23 would probably be a good rule of thumb to use.

[DavidC]

[ QUOTE ]
SD of 1.23 would probably be a good rule of thumb to use.

[/ QUOTE ]

Umm... /images/graemlins/smile.gif

Okay, a guy said that the HA was maybe 2% dep on the rules you're using.

and you said 1.23 std dev / 100 hands?

Meaning that over 100 hands we can expect to get a return of 98.

Your std dev indicates 100 hands to return between 99.38 and 96.77, 67% of the time? /images/graemlins/smile.gif

do you mean 1.23/hand?

meaning that 100 hands of bj would yeild between

221 units and -125 units 67% of the time?

--Dave.

[cardcounter0]

for your type of calculations use
1.1 * sqrt (n)
where n = number of hands played.

and a better approximation of a 1 SD interval is 68.3

[DavidC]

[ QUOTE ]
for your type of calculations use
1.1 * sqrt (n)
where n = number of hands played.

and a better approximation of a 1 SD interval is 68.3

[/ QUOTE ]

Firstly, thanks on the correction to 68.3.

Assuming 1000 hands, then: the SD will be 1.1 * 31.6 units... 34.875 units.

$1 per hand gives us a return of $980 after 2% House Edge.

~68% of the time, we'll be between $1014 and $945?

The next standard deviation jump is to 95% of the time, right? (http://www.robertniles.com/stats/stdev.shtml)

So that will result in between $1049 and $910.

(I'll add in the bonus to this later, it's pretty simple stuff.)

Going to break this down a bit, further, though:

Over your 1000 hands, you expect:

2.5%: really good
2.5%: really bad
34%: +$14
34%: -$55
13.5%: +$49
13.5%: -$90

(Without bonuses)

[cardcounter0]

Yes, these calculations are correct.

(nit: 2 SD = 95.4)
/images/graemlins/grin.gif