Variance of Pass and Don't Pass

What is the variance of betting pass and don't pass at the same time and how does it compare to betting only the pass line (no odds).

(please someone else check my work)

A = Pass+Don't (1 unit each)
B = Pass (2 units total)

EV(A) = 0*(35/36)+(-1)*(1/36)= -1/36
EV(B) = 2*(.4929)+(-2)*(.5071)= -.0284

EV(A^2) = (0^2)*(35/36)+(-1^2)*(1/36)= 1/36
EV(B^2) = (2^2)*(.4929)+(-2^2)*(.5071)= 4

Known fact: Var(X) = E(X^2) - E(X)^2

Var(A) = 1/36 - (-1/36)^2 = 0.027
Var(B) = 4 - (-.0284)^2 = 3.999

I feel much better about my results because this can also be done via using X is bernoulli, and Var(X) = p(1-p). Using that I get the same results

Var(A) = (35/36)*(1/36) = 0.270
Var(B) = (.4929)*(.5071)*(2^2)*(2^2) = 3.999

i got the same results

for n dollars wagered

c+dc->n^2*0.006751543
c->n^2*0.99980002
dc->n^2*0.972036272

a more useful result for comparing the bets to each other is the standard deviation

c+dc->n*0.082167775
c->n*0.999900005
dc->n*0.985918999

Thanks.

All of this proves my point that betting the pass and the don't pass (using a friend to bet the other one) dramatically reduces the risk of ruin allowing one to get free comped drinks.

Quote: longtimelancer

All of this proves my point that betting the pass and the don't pass (using a friend to bet the other one) dramatically reduces the risk of ruin allowing one to get free comped drinks.

It sure does for one small session of play.
Those values are for one bet just one time.

It is true that for a 2 hour session (say 72 bets each session) you have about a 0% chance of losing all your buy-in.
You still buy-in for $200 and make $10 bets, so a 20 unit bankroll.

Now the chances of losing at least 1 unit in a 72 bet session for the *pass line only* = 50.1%
and to bust out = 2.5% (calculated)

*do/dont* = 86.9% the chances of losing at least 1 unit
and about 0% to be totally wiped out.
So, for one session and not wanting to bust out, this looks good.

So, you play 5 sessions about over time. (360 total bets over time. They are independent events)

Now, you will average, with average luck, about 10 units lost with do/dont. Luck is what it is.
you need to plan on it.
Now you have lost 50% on average of your starting $200 after only 5 sessions played
You have $100 left. Guess it is time to pull more cash from the ATM.

The pass line player has lost about 360* -7/495 = 5.09 units after 5 2 hour sessions.
who loses more money the fastest over time?
More than playing just one session.

Still I have not considered the value of feeling good as you play

Feel good and gamble! (the drinks are almost free)

Sally

Quote: mustangsally

Now, you will average, with average luck, about 10 units lost with do/dont. Luck is what it is.
you need to plan on it.
Now you have lost 50% on average of your starting $200 after only 5 sessions played
You have $100 left. Guess it is time to pull more cash from the ATM.

In 1 hour I can drink at least 3 drinks and so can my friend which makes for 6 drinks/$10: a great bargain in Vegas these days.