7craps
Joined: Jan 23, 2010
• Posts: 1977
October 20th, 2012 at 2:48:38 PM permalink
Quote: 7Craps

Your actual \$\$ losses will be close to the house edge as a %
but variance still controls the actual EV (real \$\$s) in absolute values.

Quote: AcesAndEights

I'm not going to pretend that I understand everything you just said,
but it seems like that point is the most important.

#1) Over time, as you play more and more, the absolute difference of your results compared to the expected result won't converge to zero, they will continue to swing wildly above/below expectation.

Yep.
Everyone needs to understand this point or the Law, and the reason why it happens.
(EV = total \$ wagered * (net \$ gain / total \$ wagered)
or
(EV = total \$ wagered * (House edge)
becomes infinitely large, and it actually makes larger and larger fluctuations above and below your EV."

Most ALL gambling writers and public opinion/belief is the FALSE belief that
HE AND EV both will converge to expectation.
That is a % and actual \$s lost.
A total misunderstanding of the Law of Large Numbers.

Now, the EV is an absolute value expressed in \$s. -\$1500 for example.
Not a percentage.
The Law of Large Numbers does not deal at all with absolute values, only Relative Frequencies, in other words, ratios or percentages.
Again for all that will read this far into the future
House edge is simply a ratio (expressed as a % of \$s)
HE = net \$ gain / total \$ wagered
EV = net \$ wagered * (\$ gain / total \$ wagered)
EV = net \$ wagered * HE
EV = actual \$s
EV is not a ratio, it is a product, an absolute value.

Quote: AcesAndEights

#2) But as you play more and more, if you divide that difference by your number of rolls/samples/whatever, THAT number will approach zero.

yes, because you are now converting actual \$s, EV, into a ratio of actual \$s of rolls/samples/whatever.

Now, The percentage converges, not actual \$s, the EV, for whatever unit you so desire.

Quote: AcesAndEights

#3)So the more you play, the closer you will be to expectation
taking into account how long you have been playing. Does that sound about right?

Only by comparing percentages to percentages.
the closer you will be to the HE expectation and NOT the EV expectation.
An EV is NOT a percentage.
It is in \$units
In the real world, NO ONE EVER converts EV to percentages for common casino games.
It is always stated as EV = X\$s

One gets closer to the HE the more one plays and not the EV, when EV is expressed in \$s.
Because the HE is the ratio between \$net/\$action
House edge is an apple
EV is an orange
becomes infinitely large, and it actually makes larger and larger fluctuations above and below your EV."

This is why many get stuck about actual gambling losses.
They THINK and come to a conclusion, incorrectly, because of the EV value and that value only.
Standard deviation shows how far one can be after many bets or a long time of play,
and that distance has a way higher probability of being FURTHER from expected EV than closer to IT.

But the math for variance and standard deviation is way harder to do for most than
EV = HE * \$Bet * # of Bets

But the effort to calculate var/sd, IMO, is worth it at least 1 billion times more than EV,
since the results from both EV and SD now paints a very useful and more complete
picture, in most cases, of what one can expect after any length of play.

================================
It is like players crying at a Craps table
"The shooter just Crapped out. He rolled a 7"

truth is, he roiled a 7 while a point was established.
But the incorrect public and many dealers,
say that shooter "Crapped out" instead of the correct "Sevened Out"
This example does not cause confusion in what actually happened.
The shooter lost his point and a new shooter starts.

When EV is thought of incorrectly,

"the EV was ONLY -\$50" and the result was
"But I lost a fu**ing \$1000 playing this game with the best bests and strategy"
now that player just says "FU** everyone, I do as a please from now on",
This player believed in the MYTH of EV only,
Myth = the longer one plays the closer the actual EV will get to the expected EV.

and did not understand or did not want to understand
the possible range of wins and losses from variance.

Looks like the Wizard also might believe that HE and EV are the only guiding lights...
both converges to expectation
from the last question on this Ask the Wizard.
Of course, he has a few weasel clauses in there too.
I would have answered that Craps Q way differently... and will
Yeah, I do that Craps Q next thread next week while on vacation...
winsome johnny (not Win some johnny)
teddys
Joined: Nov 14, 2009
• Posts: 5514
October 20th, 2012 at 3:00:12 PM permalink
Quote: 7craps

Looks like the Wizard also might believe that HE and EV are the only guiding lights...
both converges to expectation
from the last question on this Ask the Wizard.
Of course, he has a few weasel clauses in there too.
I would have answered that Craps Q way differently... and will
Yeah, I do that Craps Q next thread next week while on vacation...

The Wizard worships at the altar of H.E. and E.V. True, that is the most important thing, but I feel variance and standard deviation are somewhat neglected. (He does have a very good page on SD/V in Video Poker and also the SD/V of most table games.) It could be because the math is somewhat more advanced for those elements. A beginner would do well to evaluate a game/bet by E.V./"Element of Risk" alone at first.

The fact of the matter is that none of us are going to play enough craps to see the 98.59% return materialize on all of our pass line bets. (For \$1m wagered, that's a loss of \$14,100!) Better just to play the free odds and hope you get enough positive variance to stay above water. Its hard for craps players to admit we are playing a losing game.
"Dice, verily, are armed with goads and driving-hooks, deceiving and tormenting, causing grievous woe." -Rig Veda 10.34.4
odiousgambit
Joined: Nov 9, 2009
• Posts: 8807
October 21st, 2012 at 1:41:20 AM permalink
Quote: 7craps

Looks like the Wizard also might believe that HE and EV are the only guiding lights...
both converges to expectation
from the last question on this Ask the Wizard.
Of course, he has a few weasel clauses in there too.
I would have answered that Craps Q way differently... and will
Yeah, I do that Craps Q next thread next week while on vacation...

Hoo-hoo! Calling out the Wizard! He don't like that!

Let's take a look at that ask-the-W. The part about a system being worthless to try to increase, reliably, losses instead of gains would be correct, except I would say often you do lose more *if* the system makes you risk more money, which it would seem to me a normal Martingale does. However, the parameter stated is wagering overall \$1 Million exactly, so I would say the Wiz is on solid ground so far.

The last sentence by the questioner:

Quote: Peter K. from Bellevue NE

Is he doomed to only give the house roughly 0.18% or \$1800?

To instantly say Yes! as the Wizard did, would seem to validate the amount as well as the percentage, so I would guess Michael did not intend that validation, but intended to sort of ignore that part of the question, not realizing what it would look like. Huge variance was afoot, what with the stipulation that the 10x odds would be maxed. One complication, though, is that the \$1 million would include the odds portion, so the player would be making only about 1200 or so line bets I'm guessing.

Running a Wincraps test on that now.

Quote: teddys

The Wizard worships at the altar of H.E. and E.V.

Ouch! I can feel the Wizardly wrath building way over here 2000 miles away!

Quote: teddys

It could be because the math is somewhat more advanced for those elements.

Teddy!

Well, maybe the Wizard will not see this if you get lucky.

Quote: teddys

For \$1m wagered, that's a loss of \$14,100!

If the player made no other bets than pass line without odds. I'll see what happens with Wincraps on that too.

PS: I am finished with Wincraps, see my blog post
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
24Bingo
Joined: Jul 4, 2012