<t>Set up a system of equations where the variables are the expected number of tosses to reach the desired state. For example, for A, you have the states T (original state or last two tosses were tails), H, HT, and HTH, where HTH = 0.T = .5(T + 1) + .5(H + 1)H = .5(H + 1) + .5(HT + 1)HT = .5 + .5(T ...

Bass is an acceptable plural of bass. You only add "-es" to make most fish plural if there's more than one species.

No, that's not a problem.

<t>QuoteOriginally posted by: BobMurphyAh okay, thanks! Does it then follow that, as interest rates go to zero, you wouldn't exercise the American put early, either? (Since you're losing the exercise value but not getting much benefit in earlier strike price.)Consider an American put with S=.1, K=10...

Best to think of the dividends case with an exaggerated example. Consider S=15, K=10, time to expiry = 1 week, and there is a $10 dividend in a couple days. You obviously want to exercise before the dividend.

Is what you're going for the fact that when the bubble merges with the top part, the overall surface area increases?

The wording of the question seems to imply that air bubble is trapped in a portion of the cylinder which isn't as pressurized, so I would assume the pressure would decrease when the two portions merge.

(1 oz/673.7 dollars)*(31.10g/oz)*(1mol/196.9665g)*(6.022*10^23 atoms/mol)*(1 dollar/100 cents) ~= 10^18

And we rightfully blame all of this on Logan.

QuoteOriginally posted by: DCFCBeing an ally of America is not a rational decision. When Britain was last attacked not one American came to help.Are you talking about the Argentinians?

<t>I think anything that has an improper rotation axis (S_n operation -- can be transformed onto itself by a 2*pi/n radian rotation followed by reflection through a plane) but no plane of symmetry would work here. Another example is tetramethylcyclooctatetraene, which has S_4 symmetry. The C_i point...

<t>QuoteOriginally posted by: newtoquantBesides, isn't the expected pay off $2.5 =( 6+5+4)/6 , with your first part and not 5?The stopping time strategy I posted says that he will take the payout (and not reroll) if he gets a 4, 5, or 6, so half the time he gets an average of $5. The other half the ...

<t>QuoteOriginally posted by: newtoquantBesides, it would make sense to not pay any money for the first roll, if the person wants to roll over.A casino would quickly go out of business if they let people decide if they wanted to bet after seeing the outcome!!! The 5 is just the expected payout given...

I get the following. The player adopts a strategy of stopping after one roll if he gets a 4, 5, or 6 and continues otherwise. This means that the expectation is .5*5 (payout if game stops after one roll) + .5*3.5 (payout if player opts for a second roll)= 4.25.

I don't think I understand the rules of this game. How would this be any different than just playing the original game twice in a row?