TwelveOr21
TwelveOr21
Joined: Nov 18, 2018
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October 1st, 2022 at 2:10:02 AM permalink
Hi,
The wiz has a calculator on his site called the gambling session calculator.
https://wizardofodds.com/gambling/gambling-session-calculator/

Selecting a game and inputting the required inputs, it returns some numbers - 1% chance to win this much or less, and so on.

My question is, there's no real explanation on the basis of those numbers, i.e. it says I would have a 99% chance of winning 602.48, and a 75% chance of winning 166.11, and a 50% chance of losing -$12.06.
I can't be the only one that is confused with the reference that I somehow, have a 99% chance of winning $602.

That aside, I pulled up the developer tools in Chrome and checked out the source code, hoping for a hint for how those are calculated - and got stuck here..
var z1=-1*ExpectedLoss-2.326347874*TotStdDev;
var z5=-1*ExpectedLoss-1.644853627*TotStdDev;
var z25=-1*ExpectedLoss-0.67448975*TotStdDev;
var z75=-1*ExpectedLoss+0.67448975*TotStdDev;
var z95=-1*ExpectedLoss+1.644853627*TotStdDev;
var z99=-1*ExpectedLoss+2.326347874*TotStdDev;

Those constants, i.e. 0.67448975 - what do they seem to be derived from?
What confidence is there in the numbers provided - i.e. 95% chance to win X figure? Those numbers are always positive, as if you could almost always win, which can't be accurate in my opinion.

My allure to it was to identify what expectations I would have playing a game for 10 hours.
JackSpade
JackSpade
Joined: Aug 26, 2022
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October 1st, 2022 at 2:19:40 AM permalink
I think you'd have 99% chance of winning 602.48 OR LESS and a 1% chance of winning more than that.
OnceDear
OnceDear
Joined: Jun 1, 2014
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Thanks for this post from:
Dieter
October 1st, 2022 at 4:56:01 AM permalink
Quote: TwelveOr21

Hi,
The wiz has a calculator on his site called the gambling session calculator.
https://wizardofodds.com/gambling/gambling-session-calculator/

Selecting a game and inputting the required inputs, it returns some numbers - 1% chance to win this much or less, and so on.

My question is, there's no real explanation on the basis of those numbers, i.e. it says I would have a 99% chance of winning 602.48, and a 75% chance of winning 166.11, and a 50% chance of losing -$12.06.
I can't be the only one that is confused with the reference that I somehow, have a 99% chance of winning $602.

That aside, I pulled up the developer tools in Chrome and checked out the source code, hoping for a hint for how those are calculated - and got stuck here..
var z1=-1*ExpectedLoss-2.326347874*TotStdDev;
var z5=-1*ExpectedLoss-1.644853627*TotStdDev;
var z25=-1*ExpectedLoss-0.67448975*TotStdDev;
var z75=-1*ExpectedLoss+0.67448975*TotStdDev;
var z95=-1*ExpectedLoss+1.644853627*TotStdDev;
var z99=-1*ExpectedLoss+2.326347874*TotStdDev;

link to original post



You can get some clues if you google those values. They relate to the shape of a binomial bell shaped curve.

This is how I THINK it works...

Wizard assumes that the bell shaped chart of the range of possible expected value plotted as x against probability, plotted y is a binomial distribution. He slices that chart up into ranges of expected value where the area of a slice is the probability of your experienced outcome being in that range.
There are two probabilities going on here: The probability y value from the chart and the probability of you experiencing a range of values.
The nature of the shape of the binomial curve is such that when you pace out left or right from the central peak, we know that
1% of the area lives under each of the tails that are 2.326 standard deviations away from the peak, that
5% of the area lives under each of the tails that are 1.64 standard deviations away from the peak and that
25% of the area is under each of the tails that are 0.6745 standard deviations away from the peak.
if you look at the curve just split down the centre at 0 standard deviations, 50% falls under the left side and 50% falls under the right side. I.e. Your experienced outcome has 100% probability of falling under the curve where you walk away with zero or you walk away with the maximum possible outcome.

E&OE. Hope that helps explain those values.
Last edited by: OnceDear on Oct 1, 2022
Psalm 25:16 Turn to me and be gracious to me, for I am lonely and afflicted. Proverbs 18:2 A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
Dieter
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Dieter
Joined: Jul 23, 2014
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October 1st, 2022 at 7:28:00 AM permalink
Quote: TwelveOr21

My question is, there's no real explanation on the basis of those numbers, i.e. it says I would have a 99% chance of winning 602.48, and a 75% chance of winning 166.11, and a 50% chance of losing -$12.06.
I can't be the only one that is confused with the reference that I somehow, have a 99% chance of winning $602.
link to original post



I read these as boundaries.
1% of the time, you might win more than $602.
99% of the time, you shouldn't win more than $602.

(Switching to default blackjack, .0048he, 72hph, $25, 4h, 1.15sd)
I want to play blackjack for 4 hours at $25 table minimum.
The calculator says:
1% -1169.59
5% -837.09
25% -363.65
50% -34.56

So,
99% of the time, I should lose less than $1169,
95% of the time, I should lose less than $837,
75% of the time I should lose less than $363.

Since I usually bring 40 units ($1000) to the table, I think I'll probably survive for 4 hours.

OD has a much better technical explanation.
I'm trying to share my thought process, and how I use the tool.
May the cards fall in your favor.
TwelveOr21
TwelveOr21
Joined: Nov 18, 2018
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October 1st, 2022 at 1:37:05 PM permalink
Thanks OD and Dieter for your replies.
That makes sense - I had already drawn the conclusion that typical results should fall in that middle range.

The text on the page though, and why I thought I needed to better understand it, reads '99% of the time you should win this much or less'.. it doesn't say of the time, it says 99% chance.

Now, if you were presented that text as is, on a game such as Blackjack - you have a 99% chance to win 1169, that is actually incorrect.
The page should present it as described by OD in my view, the results at 99% are actually outliers, making them more of a 1% chance of winning that much or less. They are after all 2 standard deviations away, so they aren't what you'll see 99% of the time.
And far more likely are the results between 25% and 75%.
And whilst we are here noting it - Probability win reads 0.48.. I would multiply that by 100 and add a % sign after it.
Ace2
Ace2
Joined: Oct 2, 2017
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October 1st, 2022 at 1:42:42 PM permalink
Quote: TwelveOr21


The text on the page though, and why I thought I needed to better understand it, reads '99% of the time you should win this much or less'.. it doesn't say of the time, it says 99% chance.
N

Whatís the difference?

If you played a million sessions, very close to 990,000 will fall within the expected range
Itís all about making that GTA
TwelveOr21
TwelveOr21
Joined: Nov 18, 2018
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October 1st, 2022 at 1:58:55 PM permalink
Quote: Ace2

Quote: TwelveOr21


The text on the page though, and why I thought I needed to better understand it, reads '99% of the time you should win this much or less'.. it doesn't say of the time, it says 99% chance.
N

Whatís the difference?

If you played a million sessions, very close to 990,000 will fall within the expected range
link to original post



I'll phrase the question differently.

If you saw a page that described a game, and it noted -
1% chance to win this much or less.
5% chance to win this much or less.
50% chance to win this much or less.
99% chance to win this much or less.

Wouldn't you expect the results to end up in the 99% bucket, 99% of the time?

The page to me reads, the results at 99% are far more likely to happen then the results at 1% - because 1% has a 1% chance of happening, and 99% has a 99% chance of happening.
In actuality, the more likely occurrence (chance), i.e. the one that has a higher chance or higher likeliness of happening, is the 50% chance..
Dieter
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Dieter
Joined: Jul 23, 2014
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October 1st, 2022 at 6:04:28 PM permalink
Quote: TwelveOr21

Quote: Ace2

Quote: TwelveOr21


The text on the page though, and why I thought I needed to better understand it, reads '99% of the time you should win this much or less'.. it doesn't say of the time, it says 99% chance.
N

Whatís the difference?

If you played a million sessions, very close to 990,000 will fall within the expected range
link to original post



I'll phrase the question differently.

If you saw a page that described a game, and it noted -
1% chance to win this much or less.
5% chance to win this much or less.
50% chance to win this much or less.
99% chance to win this much or less.

Wouldn't you expect the results to end up in the 99% bucket, 99% of the time?

The page to me reads, the results at 99% are far more likely to happen then the results at 1% - because 1% has a 1% chance of happening, and 99% has a 99% chance of happening.
In actuality, the more likely occurrence (chance), i.e. the one that has a higher chance or higher likeliness of happening, is the 50% chance..
link to original post



The 75% of the time results are part of the 99% of the time results, as far as I know.

I agree, the specific wording is confusing until you wrap your head around the nuances.

The 5% lower limit and the 95% upper limit are the expected bounds of most of your play sessions.
May the cards fall in your favor.

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