GingerAle

I MUCKED this up when I edited it to make it neat. I can't blame it on a banana allergy.

The sums were/are correct for the correct values, so the answer stays the same

Here's the corrected version.

Black Ball probability 0.80

                                $1 Ball drawn probability 0.75    Expected Value = 0.80 * 0.75 * 1 =  $0.60 

                                $7 Ball drawn probability 0.25    Expected Value = 0.80 *0.25 * 7 =   $1.40

                                                                                                                          Sum         $2.00

White Ball probability 0.20

                                $8     Ball drawn probability 0.889    Expected Value = 0.20 * 0.8889 * 8    =    $1.42

                                $500 Ball drawn probability 0.111    Expected Value = 0.20 * 0.1111 * 500 =   $11.11

                                                                                                                                          Sum       $12.53

                                                                                 Sum of expected values   2.00 + 12.53 = 14.53

Expected win per play $14.53

I'll explain the logic below.

A few years ago, I was in a sports lounge watching a football (American) game. One of the teams was kicking for a field goal and an intoxicated patron bet $10 the team would be successful. They weren’t.  The ball hit the goalpost and bounced off. 

A minute later, a replay came on and the patron made the same bet. He, of course, lost. When asked why he’d make such a bet, he replied that he couldn’t believe they do the same thing twice.   

EP what you write here really can’t be true.

If it starts at 1 and doubles everyday:

.01 on day 1

. . .

If the amount (a penny on day one) doubles everyday how can you have the same amount? It did not double on day one.  (This reminds me of a few crooked bankers).

Start with a penny on day “zero.” The decimal counting system starts with zero, not one (1). If you look at it this way, it’s more clear.

            _{(Expanding the window will align the text and numbers)}

                                                                    Comparsion to

Day               2^(day number)                      Total grains (of rice) on a chess board,

                                                                    where the previous square’s amounts are added.

                                                                    Note the first square is square zero.

 0                             1                                             1

1                              2                                             3

2                              4                                             7

3                              8                                            15

4                              16                                          31

 . . .                         . . .                                          . . .

28                           268435456                           536870911

29                           536870912                           1073741823

30                           1073741824                         2147483647

--------------------------

Remember: “A penny learned is a penny earned”

(Assuming the player pays nothing to play)

Black Ball probability 0.80

                                $1 Ball drawn probability 0.75    Expected Value = 0.80 * 0.75 * 1 =  $0.60 

                                $7 Ball drawn probability 0.25    Expected Value = 0.80 *0.25 * 8 =   $1.40

                                                                                                                          Sum         $2.00

White Ball probability 0.20

                                $8     Ball drawn probability 0.889    Expected Value = 0.20 * 0.8889 * 1    =    $1.42

                                $500 Ball drawn probability 0.111    Expected Value = 0.20 * 0.1111 * 500 =   $11.11

                                                                                                                                          Sum       $12.53

                                                                                 Sum of expected values   2.00 + 12.53 = 14.53

Expected win per play $14.53

-------------------------------------------------

I like to play the ponies. It’s a great venue to apply statistics and probability, and it is a lot of fun. It’s even more fun when you win more often.  A basic understanding of statistics helps to separate the whinnies from the neighs.

When the Troll-Master was tutoring me in statistics, he sent me links to two vids that parody the sport.

Classic Spike Jones with one of his many classical music parodies.

Your banana daiquiri is waiting for you at the top of the this tree.

For Miss Melody, Headmistress of web2.0calc, one Banana Daiquiri fit for a Queen.

This banana daiquiri is blended using a recipe by LancelotlLink’s personal chef. It contains 600 imperial minims of the finest rum and your very fine banana, pureed using modern kitchen appliances. (No spit. No peal.)   These are what I make for Lancelot when he comes home to his favorite tree house.

I think your answer is very close.  Negative bitterness is sweetness. It’s sort of like the logarithms of the PH vs. POH thingies in chemistry. 

I will make you a banana daiquiri as soon as Churgeon Morgan Tud’s ghost-exorcising program finishes its magic.  This crystal sphere is hanging in the distant past for minutes after each command.  It not only has ghosts, they are trolling me. 

I’m having a banana daiquiri now. I only put about 150 imperial minims of rum in it –just enough to flavor it. No more hangovers for me until Christmas. 

Hi Miss Melody,

The Troll Master taught me how to modify session cookies to allow editing even after about 2 to 3 hours. As long as the main cookie is still valid and hasn’t been renewed, which can happen at random times. (There is also something about an ID code injection that will allow you to edit for about 12 hours until it “hard locks,” but I don’t understand it).  

The Troll Master knows a great many “tricks” on here.  One of them was he could read most any blanked post (if he could find it), but he often lamented that he never figured out how to “unblank” a post. He always wanted his Scooby Snacks back. LOL

Then there are the point scores.  The Troll Master is among the very few internet trolls who could actually collect his tolls –at least on this site.  God, some of the toll collecting was just drop-dead funny (The Unicorn “Fairy” post).  What he “did with the points” was often cool.  He called it “correcting a statistical injustice.”   Heir Massow probably called it something else when he modified the code and “dulled the troll’s teeth” 

One interesting thing, he rarely gave himself points, even for his legitimate math posts, but he did sometimes give himself negative points if a troll post had negative points from his target, but became positive because of "appreciation by his fans.”  –He always seemed to have a few fans. I was/am one, for sure!

Thank you, Sir Alan.

My preview also displayed what I typed instead of the rendered code.

I just made an edit and posted it as if it will work. It did.

It means the exponent value is in the positive range. 

Examples:

3.0 * 10³   = 3000  This is a positive index (exponent).

3.0 * 10^-3  =1/3000 This is a negative index (exponent).

I would show you in LaTex, but for some blŏŏdy reason it will not render on my computer.

EDIT . . . . Append . . . .

\(3.0 \times 10^3 = 3000 \leftarrow \text { This is a positive index (exponent).}\\ 3.0 \times 10^{-3} = \dfrac{1}{3000} \leftarrow \text { This is a negative index (exponent).}\\\)