I have the following:
Lots of time
Video Poker for Winners
A pencil
Graph paper
To generate a graphical representation of NO:
What statistic do I generate many many times using VPW to make the graph?
What units is on the x axis?
What units is on the Y axis?
It's not clear to me what you are up to, but I'll take the bait.
The most important statistic in gambling is ER.
But many people stop there. Hey, why sweat the details, right?
However, the second most important statistic in gambling is variance. And it is VERY important.
N0 simply combines the two in an interesting way:
N0 = variance / (ER-1)^2
The result being the number of hands that must be played to get at least about an 84% chance of winning a positive expectation gamble.
Example, FPDW: N0 = 26/.0075^2 = 462,222 hands
Other examples:
http://members.cox.net/vpfree/Bank_NO1.htm
My guess is, if you wanted to make graphs, you would put ER-1 on the x axis and variance on the y. There will be various N0 lines, for example you could make one N0 line for 500,000 hands. Then your particular games would be particular datapoints, for example FPDW would be at (+.0075,26). The 500,000 N0 line would intersect .0075 at variance = 500,000 x .0075^2 = 28 . Anything below the N0=500,000 line would have a lower N0.
Another way to combine ER and variance is in the approximation of Kelly Bankroll:
Approx. Kelly Bankroll = variance / (ER-1)
Example, FPDW: Approx. Kelly Bankroll = 26/.0075 = about 3500 bets
Following the Kelly Criterion, you should stop this gamble if your bankroll falls below this value. (Below this value you are increasing your risk and reducing your bankroll growth which is a poor combination, even worse at half level there is no bankroll growth at all). And if you want to know what else came out of Bell Labs, watch these videos:
http://www.youtube.com/watch?v=IFfdnFOiXUU
http://www.youtube.com/watch?v=k9e3dTOJi0o
Yet another way to combine ER and variance is in the Sharpe Ratio:
Sharpe Ratio = (ER-1) / sqrt(variance)
The Sharpe Ratio is used to rate various gambles (or "investments"). A higher positive number is better.
--- In vpFREE@yahoogroups.com, "deuceswild1000" <deuceswild1000@...> wrote:
I have the following:
Lots of time
Video Poker for Winners
A pencil
Graph paperTo generate a graphical representation of NO:
What statistic do I generate many many times using VPW to make the graph?
What units is on the x axis?
What units is on the Y axis?
No bait, just trying to visulize it. Remember you are trying to explain to someone who has much less statistical knowledge than you. Stay in teacher mode not in short cut mode.
Lets use FPDW with an ER of 100.76% with zero cashback when played perfectly. I further think I understand that it would take 446,000 hands to expect to be 84% sure of being even or positive.
So I visulize a graph with ER on the X axis and a frequency of occurrence on the Y axis. I further visualize an approximate bell curve sitting on the X axis with Zero ER setting at the negative one std dev of the curve. To the right of this point would be the positive values of ER. The area under the curve to the right of zero ER would be 84% of the total area of the curve. In order to generate a curve of this mean and std dev. would require that 446,000 hands be played perfectly. The mean would be 100.76% and the std dev of the curve would be 0.76. The positive 3 std dev value would then be 100.0% +(4*0.76)% = 103.4%.
If this visulization is correct, then my question is how do I generate the distribution. How do I get the different ERs and I guess if I can get them I can accumulate them on the Y axis.
I do not want to get the numbers using mean and std dev as given for that game but would actually like to generate the curve in histogram form. So again if the visualization is correct how do I make the curve graphically not mathematically?
--- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <nightoftheiguana2000@...> wrote:
It's not clear to me what you are up to, but I'll take the bait.
Sounds like you're talking about a PDF (Probability Density Function). I don't know of an easy way to generate it. You can goggle it for more information:
http://www.google.com/search?q="Probability+Density+Function"
Jazbo's curves are PDF's, I don't know how he generated them:
http://www.jazbo.com/videopoker/
--- In vpFREE@yahoogroups.com, "deuceswild1000" <deuceswild1000@...> wrote:
I do not want to get the numbers using mean and std dev as given for that game but would actually like to generate the curve in histogram form. So again if the visualization is correct how do I make the curve graphically not mathematically?
deuceswild1000 wrote:
No bait, just trying to visulize it ...
Lets use FPDW with an ER of 100.76% with zero cashback when played
perfectly. I further think I understand that it would take 446,000
hands to expect to be 84% sure of being even or positive.So I visulize a graph with ER on the X axis and a frequency of
occurrence on the Y axis. I further visualize an approximate bell
curve sitting on the X axis with Zero ER setting at the negative
one std dev of the curve. To the right of this point would be the
positive values of ER. The area under the curve to the right of
zero ER would be 84% of the total area of the curve. In order to
generate a curve of this mean and std dev. would require that
446,000 hands be played perfectly. The mean would be 100.76% and
the std dev of the curve would be 0.76. The positive 3 std dev
value would then be 100.0% +(4*0.76)% = 103.4%.If this visulization is correct, then my question is how do I
generate the distribution. How do I get the different ERs and I
guess if I can get them I can accumulate them on the Y axis.I do not want to get the numbers using mean and std dev as given
for that game but would actually like to generate the curve in
histogram form. So again if the visualization is correct how do I
make the curve graphically not mathematically?
NOTI steers your correctly to Jazbo's distributions in reply
http://www.jazbo.com/videopoker/curves.html
When such a graph is charted for the number of hands relevant to "N0" results for a given game, 84% of expected results will be positive and the graph will represent this as showing the large preponderance of outcomes ending in the black.
As you suggest at the outset, VP for Winners can be used to generate these charts. To become comfortable with this, it might be instructive to do a VPW "Analyze/Bankroll" run and duplicate one of Jazbo's charts (for a single game).
------
A good example to take a run at would be the 10,000 hand chart for 9/6 Jacks. The graph is a little more distinctive (with it's isolated "RF" bounce).
Jazbo's range for ending bankroll ("x-axis") ranges from +/- 1000 bets. The VPW chart is in terms of credits ... at 5 credits per bet, this translates to a $10,000 bankroll range when the denomination in VPW is set to $1.
To set the chart up, first set VPW to $1 denomination. Then, under "Analyze/Bankroll", set a $5000 profit cutoff, $5000 Stake, 10000 rounds (hands), and set the display at 52 bars for maximum clarity.
This analysis will duplicate the Jazbo 10,000 hand chart for Jacks. It's scaled a little differently, so appears flatter, but otherwise yields the identical chart. (The VPW chart differs in one respect inconsequentially ... VPW trials that achieve the $5000 profit cutoff are grouped together as a small spike at the right hand side of the chart.)
--------
The desired FPDW "N0" chart can be devised in a similar manner. It will be important to specific profit/stake values that yield a desirably dimensioned chart -- $30K/$30K may be useful as a first pass, where the mean ending bankroll should come in around $47K. The analysis will be set up for 446,000 hands, of course.
When the chart is done, the stated "Chance of Profit" should be approx 84%, with ending bankrolls lying predominantly to the left of the starting bankroll point.
This graph would be a tangible representation of "N0" as it applies to FPDW play, and of the very achievable "long term" profit expectation.
>
> It's not clear to me what you are up to, but I'll take the bait.No bait, just trying to visulize it. Remember you are trying to explain to someone who has much less statistical knowledge than you. Stay in teacher mode not in short cut mode.
Lets use FPDW with an ER of 100.76% with zero cashback when played perfectly. I further think I understand that it would take 446,000 hands to expect to be 84% sure of being even or positive.
So I visulize a graph with ER on the X axis and a frequency of occurrence on the Y axis.
I think there is a problem with your terminology. "ER" is the expected return. If we are talking about the expected return after 446,000 hands, then that is a single value. On your graph, there would be a single point on the x axis at x= 446,000 * 0.76%, y= 100%. The Y-axis value would be 100% because 446,000 * 0.76% is the only possible value of "ER".
What you are calling "ER" is the `return', not the `expected return'. Creating a graph of the return after 446,000 hands makes sense; a graph of expected return after 446,000 hands does not.
I further visualize an approximate bell curve sitting on the X axis with Zero ER setting at the negative one std dev of the curve. To the right of this point would be the positive values of ER. The area under the curve to the right of zero ER would be 84% of the total area of the curve. In order to generate a curve of this mean and std dev. would require that 446,000 hands be played perfectly. The mean would be 100.76% and the std dev of the curve would be 0.76. The positive 3 std dev value would then be 100.0% +(4*0.76)% = 103.4%.
If this visulization is correct, then my question is how do I generate the distribution. How do I get the different ERs and I guess if I can get them I can accumulate them on the Y axis.
I do not want to get the numbers using mean and std dev as given for that game but would actually like to generate the curve in histogram form. So again if the visualization is correct how do I make the curve graphically not mathematically?
If you want to see what the distribution of RETURN looks like after 446,000 hands of FPDW, Dunbar's Risk Analyzer for Video Poker can give you the kind of histogram you describe. Use the "Calc Short-term RoR" button. A good number to use for bankroll for FPDW is 1700 bets, because (1) that's enough so that you won't go broke and (2) it's also ½ of the ER (and therefore ½ of an SD).* (see footnote)
Like NOTI and Harry, I don't know how to generate the graphs mathematically. (I do it by brute force in DRA-VP)
--Dunbar
* The ER after 446,000 hands of FPDW is 0.76% * 446,000 = 3398. The standard deviation after 446,000 hands is the square root of the variance. And the variance after 446,000 hands is 446,000 * 25.8 = 11,523,712. So, the SD is the square root of 11,523,712, which is 3395. Note that ER = SD (or close enough!)
--- In vpFREE@yahoogroups.com, "deuceswild1000" <deuceswild1000@...> wrote:
--- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <nightoftheiguana2000@> wrote:
NOTI
I do not see how a 10,000 sample size relates to the 400,000 plus
Harry,
Your step by step instructions is just what I am looking for. Lets for the sake of discussion pretend that all I have is a regular deck of cards and lots of time.
Run the steps from there or their VPW or Winpoker equivalents. I do not want to do an analyze bank roll, as that is not telling me how to get the individual data points on the x axis that I then accumulate via the y axis and thus make a histogram. The analyze bank roll is already doing the histogram, but I do not see where it is getting its data points.
Also, your comments on relating 10,000 hands to NO number of hands would be appreciated also. Instruction wise if it is possible.
No cocktail napkins are allowed, but if you would prefer going private email, ok, but nobody else would learn. I go on the basis that there is at least one other person out there that would also like to know, but is to reluctant to ask in front of thousands of reader. I am not ashamed to ask to be taught something.
Further, I will put forth a guess as how to generate a Jazbo curve/histogram using VPW. Run 10,000 hands, record ending bankroll in terms of ER. Do this many times. Accumulate the data on an x axis that has ER values running from negative on the left to positive on the right. The y axis would be simply frequency of occurrence. Of course, seeing we are making a histogram, there would be a need for equal cell intervals in which to accumulate each indvidual data point. Is this correct? Yes/No. If not, then step by step how would you do it, like asked above.
And then reiterating, how does this relate to NO numbers of hands?
NOTI, feel free to respond also, but please break it down. Pretend you are teaching a class of beginners
If this is too time consuming for either, please excuse yourselfs, as we will never get together face to face, which would be much more productive and meaningful, but not practical,even though it would be my choice also.
--- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <nightoftheiguana2000@...> wrote:
Direct link to Jazbo's (PDF) curves:
http://www.jazbo.com/videopoker/curves.html
Yes, I should have said R not ER. Avg R should equal ER as I understand it.
Yes, I saw that std dev had to equal avg R minus 1.0.
So, in essence are you saying that it takes 446,000 hands to make std dev equal to avg R minus one in ths example?
If so, that is pretty simple.
" Creating a graph of the return after 446,000 hands makes sense; a graph of expected return after 446,000 hands does not."
I do not understand the above. Like I asked in another post, lets say I do not have any bank roll prgram, Just a deck of cards or Winpoker how do I create the histogram and do I have to run 446,000 hands TOTAL or 446,000 many many times to get the end point value.
NO implies (to me) that if I played 446,000 hands I would expect to see ending bankroll fall on a curve that has 84% chance of positive or breakeven outcome. If this is correct what are the units on the x axis?
What are the units on the x axis and how do I obtain them manually? I think my question boil down to that. Also how do Jazbo's 10,000 hand curve relate to 446,000 , or was it just an example saying it would look like that, but each sessin would be 446,000 hands. I think that is another way of putting it.
--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@...> wrote:
--- In vpFREE@yahoogroups.com, "deuceswild1000" <deuceswild1000@> wrote:
>
> --- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <nightoftheiguana2000@> wrote:
> >
> > It's not clear to me what you are up to, but I'll take the bait.
>
> No bait, just trying to visulize it. Remember you are trying to explain to someone who has much less statistical knowledge than you. Stay in teacher mode not in short cut mode.
>
> Lets use FPDW with an ER of 100.76% with zero cashback when played perfectly. I further think I understand that it would take 446,000 hands to expect to be 84% sure of being even or positive.
>
> So I visulize a graph with ER on the X axis and a frequency of occurrence on the Y axis.I think there is a problem with your terminology. "ER" is the expected return. If we are talking about the expected return after 446,000 hands, then that is a single value. On your graph, there would be a single point on the x axis at x= 446,000 * 0.76%, y= 100%. The Y-axis value would be 100% because 446,000 * 0.76% is the only possible value of "ER".
What you are calling "ER" is the `return', not the `expected return'. Creating a graph of the return after 446,000 hands makes sense; a graph of expected return after 446,000 hands does not.
> I further visualize an approximate bell curve sitting on the X axis with Zero ER setting at the negative one std dev of the curve. To the right of this point would be the positive values of ER. The area under the curve to the right of zero ER would be 84% of the total area of the curve. In order to generate a curve of this mean and std dev. would require that 446,000 hands be played perfectly. The mean would be 100.76% and the std dev of the curve would be 0.76. The positive 3 std dev value would then be 100.0% +(4*0.76)% = 103.4%.
>
> If this visulization is correct, then my question is how do I generate the distribution. How do I get the different ERs and I guess if I can get them I can accumulate them on the Y axis.
>
> I do not want to get the numbers using mean and std dev as given for that game but would actually like to generate the curve in histogram form. So again if the visualization is correct how do I make the curve graphically not mathematically?
>If you want to see what the distribution of RETURN looks like after 446,000 hands of FPDW, Dunbar's Risk Analyzer for Video Poker can give you the kind of histogram you describe. Use the "Calc Short-term RoR" button. A good number to use for bankroll for FPDW is 1700 bets, because (1) that's enough so that you won't go broke and (2) it's also ½ of the ER (and therefore ½ of an SD).* (see footnote)
Like NOTI and Harry, I don't know how to generate the graphs mathematically. (I do it by brute force in DRA-VP)
--Dunbar
* The ER after 446,000 hands of FPDW is 0.76% * 446,000 = 3398. The standard deviation after 446,000 hands is the square root of the variance. And the variance after 446,000 hands is 446,000 * 25.8 = 11,523,712. So, the SD is the square root of 11,523,712, which is 3395. Note that ER = SD (or close enough!)
Yes I believe they are a PDF, I believe Jazbo generated them using convolution??. Still, like I said if all I had was as deck of card, how would I simulate that, And how does an 10,000 hand sessin relate to NO of 446,000 hands?
Like I said, explanation in your own words (If you want to take the time) would be appreciated, and not a reference that has a lot if intergral signs.
--- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <nightoftheiguana2000@...> wrote:
--- In vpFREE@yahoogroups.com, "deuceswild1000" <deuceswild1000@> wrote:
> I do not want to get the numbers using mean and std dev as given for that game but would actually like to generate the curve in histogram form. So again if the visualization is correct how do I make the curve graphically not mathematically?Sounds like you're talking about a PDF (Probability Density Function). I don't know of an easy way to generate it. You can goggle it for more information:
http://www.google.com/search?q="Probability+Density+Function"Jazbo's curves are PDF's, I don't know how he generated them:
http://www.jazbo.com/videopoker/
deuceswild1000 wrote:
Harry,
Your step by step instructions is just what I am looking for. Lets
for the sake of discussion pretend that all I have is a regular
deck of cards and lots of time.Run the steps from there or their VPW or Winpoker equivalents. I
do not want to do an analyze bank roll, as that is not telling me
how to get the individual data points on the x axis that I then
accumulate via the y axis and thus make a histogram. The analyze
bank roll is already doing the histogram, but I do not see where it
is getting its data points.Also, your comments on relating 10,000 hands to NO number of hands
would be appreciated also. Instruction wise if it is possible.Further, I will put forth a guess as how to generate a Jazbo
curve/histogram using VPW. Run 10,000 hands, record ending
bankroll in terms of ER. Do this many times ,
Let me try to clarify a couple of things:
The VPW "bankroll analysis" and the Jazbo PDF's are the EXACT AND SAME things. Both are a graphic representation of bankroll distribution. Both represent the outcome of multiple trials, with the frequency of ending bankroll plotted on the y-axis, against the ending bankroll on the x-axis. The ONLY key difference between the two is that VPW plots in $'s, Jazbo plotted in general 5-credit wager units.
Therefore, when you run a VPW analysis for a game for 10,000 hands (using the other input values I offered up, to ensure the ending charts have similar characteristics), you end up with Jazbo's PDF for that game after 10,000 hands of play.
------
There is one modest difference in the charts produced: Jazbo plays all 10,000 hand runs to conclusion whereas VPW terminates early those runs that achieve a specified profit threshold. The difference is that Jazbo's PDF's run smoothly off to the right side of the graph (and continue beyond the edge). VPW represents all sessions that would, at some some, exceed the largest bankroll represented on the graph as a single cumulative distribution spike. For the purposes of illustrating "N0", this difference is of no consequence.
------
The suggestion run do a VPW run of 10,000 hands is just to satisfy yourself that you can reproduce one of Jazbo's 10,000 hand PDF's with VPW (and to give you a stronger idea of what it is that you're viewing in the VPW bankroll analysis distribution).
Of course, in regard to "N0", 10,000 hands isn't of interest. Instead, it's the number of hands determined by "N0" at which point one standard deviation from game ER has breakeven as the lower threshold for play outcome (with a 16%/84% expected loss/profit break).
For a game such as FDPW, that's roughly 460,000 hands, without cashback. If you allow .25% cb, then after 260,000 hands you expect 84% of your results to lie above the bankroll point representing a 99.95% ER. Running analyses of these lengths with VPW should bear these numbers out and illustrate the "N0" concept.
Sorry for jumping in so late on this thread, but my reaction to the deuceswild post is he simply wants to create a line graph based on the numbers in the NO table. If this is not what you want then ignore this post. If it is what you want, I believe Harry has already proposed using VPW to do something similar to my ideas below, but since I don't own VPW I can't be sure.
In any case, assuming I'm correct about your goal, you can create a graph where the Y axis is the Number of Games, and the X axis is ER+CB (ER is the expected return of a game with no CB). The graph would have a separate line for each game. Each line must be labeled to show the game it represents.
This approach would reverse the sequence of games in the current table. The worst game would have a line above all the rest and the best game (FPDW) would, usually, be below all the other lines. Some of the lines would cross one another as CB increases. For example, by the time CB equals 2.00% the 9/6JB line will cross the line graph of 9 other games.
For some games with low CB the Number of Games number is huge (nearly 94M for DDBP at .00% CB). This makes it difficult to create a compact graph. Therefore I would use 4M games as the highest number on the Y axis (0 to 4 million). The result is the line graph for the 10 worst games would show up first at the top of the graph and well to the right of the Y axis. DDBP wouldn't make its appearance on the graph until CB is .30% (3,132,000 games). The line graph for every game would slope downward as the ER+CB increases. The slope of the line for each game would be unique. For FPDW the line would get pretty close to the X axis at 2.00% CB (at 34,000 games fairly close to 0).
The X axis differs from the one in the NO table because it represents EV +CB, not CB alone. This is the tricky part because you no longer have discrete CB increments. You need a new set of values beginning with the lowest ER+CB (BP at .00% CB) and increasing at regular intervals up to highest EV+CB (Loose Deuces at 2.00% CB). Even so, the lines generated would not be very "smooth". For example, Double Bonus drops from 3.806,000 to 2,037,000 games between .10% CB and .20% CB (nearly a 50% drop). To smooth out the line deuceswild would need to compute additional ER+CB values more than the 10 in the current table. Use this formula: NO = Variance/((ER+CB)-1)^2. The Variance and ER of each game is known only the CB changes so it might not take long to compute manually. Not sure if you can use VPW to do the math because I don't own a copy.
--- In vpFREE@yahoogroups.com, "deuceswild1000" <deuceswild1000@...> wrote:
I have the following:
Lots of time
Video Poker for Winners
A pencil
Graph paperTo generate a graphical representation of NO:
What statistic do I generate many many times using VPW to make the graph?
What units is on the x axis?
What units is on the Y axis?
Does anyone know if the Eastside Cannery's Seafood Night Buffet has crab legs? If so, what kind, and are they served hot or cold??
Thanks!
I realize they are the same, but my question is how do I generate the x axis value, if all I had was a deck of card or maybe Winpoker?
--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:
deuceswild1000 wrote:
> Harry,
>
> Your step by step instructions is just what I am looking for. Lets
> for the sake of discussion pretend that all I have is a regular
> deck of cards and lots of time.
>
> Run the steps from there or their VPW or Winpoker equivalents. I
> do not want to do an analyze bank roll, as that is not telling me
> how to get the individual data points on the x axis that I then
> accumulate via the y axis and thus make a histogram. The analyze
> bank roll is already doing the histogram, but I do not see where it
> is getting its data points.
>
> Also, your comments on relating 10,000 hands to NO number of hands
> would be appreciated also. Instruction wise if it is possible.
>
> Further, I will put forth a guess as how to generate a Jazbo
> curve/histogram using VPW. Run 10,000 hands, record ending
> bankroll in terms of ER. Do this many times ,Let me try to clarify a couple of things:
The VPW "bankroll analysis" and the Jazbo PDF's are the EXACT AND SAME things. Both are a graphic representation of bankroll distribution. Both represent the outcome of multiple trials, with the frequency of ending bankroll plotted on the y-axis, against the ending bankroll on the x-axis. The ONLY key difference between the two is that VPW plots in $'s, Jazbo plotted in general 5-credit wager units.
deuceswild1000 wrote:
I realize they are the same, but my question is how do I generate
the x axis value, if all I had was a deck of card or maybe Winpoker?
Run individual simulations (trials) of "n" hands, plotting each result as a histogram. The "x-axis" is your ending bankroll, the "y-axis" is the frequency with which you end at a given ending bankroll. For convenience's sake, you might set up the x-axis as a bar chart, with each bar representing a $1000 bankroll range.
I imagine the curves will start taking shape after 30 or so trials. After 100 trials, the plots will begin to more strongly approximate the Jazbo pdf's. After something like 500, they should be VERY similar.
>
> I have the following:
>
> Lots of time
> Video Poker for Winners
> A pencil
> Graph paper
>
> To generate a graphical representation of NO:
>
> What statistic do I generate many many times using VPW to make the graph?
> What units is on the x axis?
> What units is on the Y axis?
>>>>>>
>>>>>>
Sorry for jumping in so late on this thread, but my reaction to the deuceswild post is he simply wants to create a line graph based on the numbers in the NO table. If this is not what you want then ignore this post. If it is what you want, I believe Harry has already proposed using VPW to do something similar to my ideas below, but since I don't own VPW I can't be sure.
--- In vpFREE@yahoogroups.com, "brumar_lv" <brumar_lv@...> wrote:
--- In vpFREE@yahoogroups.com, "deuceswild1000" <deuceswild1000@> wrote:
----------------------------------------------------------------------
No, I want to create a histogram of the NO distribution.
It seems that everybody is trying to make this too hard. I realize that the bankroll calculator programs are essentially the same as Jazbo's curves. My only question was , given that all I had was a deck of card, how would I create the x axis data. including information relative to number of hands? It is given that the y axis is a frequency of occurrence of the histogram cells.
Here is my take on all of this:
1. If Jazbo would have used 446,000 hands for FPDW instead of 10,000 hands he would have made a NO distribution for FPDW. This is my answer to my question to what is the relation ship to Jaxbo's curves and the NO curve.
2, The 446,000 hand is required to make the std dev be equal to the amoutn of ER exceeds 100% This then would faciltate the positioning of the curve on the x axis so that 84% of all of those 446,000 hand outcomes would equal or exveed breakeven and range upto 4 std dev into the positive return outcomes. This is my answer to my question fo what is the importance of 446,000 hands.
3. If I would play a large number of sessions of 446,000 hands each session, and if I tracked my ending bankroll (return %) of each session of 446,000 hand in a histogram , with return on the x axis and frequency of occurrence of those retuns on the y axis, I wouold have a historgram simulating the NO curve. This is my answer to my question as to how would I generate the x axis data: Deal out and play 446,000 hands play them record the results and then at the end of the session determine the final return. Do this deal and record many many times build the histogram until the histogram starts to smooth out.
One step less work would be to let a VP program play the 446,000 hands and record the ending results as a percent return. Again do this mamy many time and construct the histogram
Lastly, a bankroll type program could do all of the above work if I tell it to play 446,000 hand size sessions and force it to play all 446,000 hands and not quit when the bankroll went broke.
Is this understand basically correct, less all the bankroll suggestion, etc? All are invited to respond.
Yes, I should have said R not ER. Avg R should equal ER as I understand it.
Yes, I saw that std dev had to equal avg R minus 1.0.
So, in essence are you saying that it takes 446,000 hands to make std dev equal to avg R minus one in ths example?
Yes. Let's talk in terms of a 1-unit bet. Then the expected return (ER) is 446,000 * 0.76% * 1 = 3390 units. And the std dev = Sqrt(446,000 * 25.8 * 1) = 3392 units. "25.8" is the variance of one hand of FPDW.
If so, that is pretty simple.
"NO" is pretty simple.
" Creating a graph of the return after 446,000 hands makes sense; a graph of expected return after 446,000 hands does not."
I do not understand the above. Like I asked in another post, lets say I do not have any bank roll prgram, Just a deck of cards or Winpoker how do I create the histogram and do I have to run 446,000 hands TOTAL or 446,000 many many times to get the end point value.
The point of the sentence you quoted was to stress that "NO" is a single value. There is no histogram of "NO". "NO" is 446,000 hands for FPDW, that's all there is to it. The units of "NO" is "hands".
If you want a histogram of the possible results after the "NO" number of hands, and you do not want to use the "normal distribution" approximation, then you have to run 446,000 hands many times to get a histogram. Each time you run 446,000 hands, you get a single data point: the "R" (return) for that trial. After many trials you get a histogram. That's what my program does. I assume that's what VPW does, too.
NO implies (to me) that if I played 446,000 hands I would expect to see ending bankroll fall on a curve that has 84% chance of positive or breakeven outcome. If this is correct what are the units on the x axis?
Yes, that's correct. You are graphing the ending bankroll on the X-axis and probability of that bankroll on the Y-axis. The X-axis units will be whatever units you use to define your bankroll. It can be a generic "units", like my example above, or it can be dollars or whatever.
What are the units on the x axis and how do I obtain them manually? I think my question boil down to that. Also how do Jazbo's 10,000 hand curve relate to 446,000 , or was it just an example saying it would look like that, but each sessin would be 446,000 hands. I think that is another way of putting it.
I think Harry answered the 10,000-hand question.
At this point I'm not sure what you mean by "obtain them manually". The extreme interpretation of "manually" would be to deal yourself 446,000 hands of video poker, play them perfectly, then record your final bankroll. Now repeat that process a few thousand more times. Now group your final bankroll results into bins and you will have a pretty good histogram of what things will look like after "NO" hands. Of course, that would be over one billion hands of video poker. I doubt you have THAT MUCH time on your hands!
If you're not going to do that, you may as well let some program like VPW or DRA-VP do the histograms for you.
Here's what I get for FPDW after 446,000 hands, repeated 10,000 times.
Results range Chance StdDevs
-6800 -10200 0.0% -3 SD's
-3400 -6800 1.7% -2 SD's
-1 -3400 15.5% -1 SD
0 3400 35.4%
3400 6800 32.8%
6800 10200 12.4% +1 SD
10200 13600 2.0% +2 SD's
13600 17000 0.22% +3 SD's
The numbers in the first two columns are the range of results. The 3rd column is how often that range of results occured.
Each range is 3400 units wide, very close to 1 std dev. The chance of being ahead is NOT 84% but closer to 83%. Why isn't it 84%? Because the 84% figure belongs to the normal distribution, and even after 446,000 hands, the results curve is not a perfect bell curve. You can see this at the extremes, too. Out of 10,000 trials there were only 4 results that were more than 3 standard deviations on the negative side. But there were 22 results that were 3 standard deviations on the positive side.
Another way you can see that the results are not normally distributed is to note that the expected return (446,000 * 0.76% = 3400) does not split the results in half. In fact, 52.6% of the results lie below the expected return.
--Dunbar
--- In vpFREE@yahoogroups.com, "deuceswild1000" <deuceswild1000@...> wrote:
Thanks. Totally understandable with examples. That was what I wanted. Please read my last post and comment.
--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@...> wrote:
--- In vpFREE@yahoogroups.com, "deuceswild1000" <deuceswild1000@> wrote:
>
>
>
> Yes, I should have said R not ER. Avg R should equal ER as I understand it.
>
> Yes, I saw that std dev had to equal avg R minus 1.0.
>
> So, in essence are you saying that it takes 446,000 hands to make std dev equal to avg R minus one in ths example?Yes. Let's talk in terms of a 1-unit bet. Then the expected return (ER) is 446,000 * 0.76% * 1 = 3390 units. And the std dev = Sqrt(446,000 * 25.8 * 1) = 3392 units. "25.8" is the variance of one hand of FPDW.
>
> If so, that is pretty simple."NO" is pretty simple.
>
>
> " Creating a graph of the return after 446,000 hands makes sense; a graph of expected return after 446,000 hands does not."
>
> I do not understand the above. Like I asked in another post, lets say I do not have any bank roll prgram, Just a deck of cards or Winpoker how do I create the histogram and do I have to run 446,000 hands TOTAL or 446,000 many many times to get the end point value.The point of the sentence you quoted was to stress that "NO" is a single value. There is no histogram of "NO". "NO" is 446,000 hands for FPDW, that's all there is to it. The units of "NO" is "hands".
If you want a histogram of the possible results after the "NO" number of hands, and you do not want to use the "normal distribution" approximation, then you have to run 446,000 hands many times to get a histogram. Each time you run 446,000 hands, you get a single data point: the "R" (return) for that trial. After many trials you get a histogram. That's what my program does. I assume that's what VPW does, too.
>
> NO implies (to me) that if I played 446,000 hands I would expect to see ending bankroll fall on a curve that has 84% chance of positive or breakeven outcome. If this is correct what are the units on the x axis?Yes, that's correct. You are graphing the ending bankroll on the X-axis and probability of that bankroll on the Y-axis. The X-axis units will be whatever units you use to define your bankroll. It can be a generic "units", like my example above, or it can be dollars or whatever.
>
> What are the units on the x axis and how do I obtain them manually? I think my question boil down to that. Also how do Jazbo's 10,000 hand curve relate to 446,000 , or was it just an example saying it would look like that, but each sessin would be 446,000 hands. I think that is another way of putting it.
>I think Harry answered the 10,000-hand question.
At this point I'm not sure what you mean by "obtain them manually". The extreme interpretation of "manually" would be to deal yourself 446,000 hands of video poker, play them perfectly, then record your final bankroll. Now repeat that process a few thousand more times. Now group your final bankroll results into bins and you will have a pretty good histogram of what things will look like after "NO" hands. Of course, that would be over one billion hands of video poker. I doubt you have THAT MUCH time on your hands!
If you're not going to do that, you may as well let some program like VPW or DRA-VP do the histograms for you.
Here's what I get for FPDW after 446,000 hands, repeated 10,000 times.
Results range Chance StdDevs
-6800 -10200 0.0% -3 SD's
-3400 -6800 1.7% -2 SD's
-1 -3400 15.5% -1 SD
0 3400 35.4%
3400 6800 32.8%
6800 10200 12.4% +1 SD
10200 13600 2.0% +2 SD's
13600 17000 0.22% +3 SD'sThe numbers in the first two columns are the range of results. The 3rd column is how often that range of results occured.
Each range is 3400 units wide, very close to 1 std dev. The chance of being ahead is NOT 84% but closer to 83%. Why isn't it 84%? Because the 84% figure belongs to the normal distribution, and even after 446,000 hands, the results curve is not a perfect bell curve. You can see this at the extremes, too. Out of 10,000 trials there were only 4 results that were more than 3 standard deviations on the negative side. But there were 22 results that were 3 standard deviations on the positive side.
Another way you can see that the results are not normally distributed is to note that the expected return (446,000 * 0.76% = 3400) does not split the results in half. In fact, 52.6% of the results lie below the expected return.
--Dunbar
I may not ask the question technically enough, but I know the answer I want when I get it. Thanks.
--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:
deuceswild1000 wrote:
> I realize they are the same, but my question is how do I generate
> the x axis value, if all I had was a deck of card or maybe Winpoker?Run individual simulations (trials) of "n" hands, plotting each result as a histogram. The "x-axis" is your ending bankroll, the "y-axis" is the frequency with which you end at a given ending bankroll. For convenience's sake, you might set up the x-axis as a bar chart, with each bar representing a $1000 bankroll range.
I imagine the curves will start taking shape after 30 or so trials. After 100 trials, the plots will begin to more strongly approximate the Jazbo pdf's. After something like 500, they should be VERY similar.
To answer your crab leg question, my husband and I had dinner Wednesday night at the Eastside Cannery for the first time. They had sent me a 2 for 1 buffet coupon last month, which I did not take them up on. This month, they sent me 2X 2 free buffets, and a small amount of free play.
If it's for free, it's for me, so we checked out the ECan buffet.
They had both hot and cold queen crab. We both agreed that the quality was not terrible, but not the best we have had at a Vegas buffet. I had the cold legs. The texture was a bit mushy, and there was a bit too much saltiness for me. He had the legs hot, and commented that they did not taste sweet. That sounds strange, but if you've had good crab legs, you'll know what he was talking about.
I enjoyed many other items. I think this buffet will be fine after they figure out the timing. Some dishes were left out a bit too long, and others were slow to be replaced after they were depleted.
I don't anticipate playing at the ECan much, though. The machines that have .25 FPDW are even more frustratingly slow than Sam's Town. I used to play a little at the original Cannery in North LV, and I don't recall anything like this.
Also not so great is the fact that these machines are near a bar offering live music, and like most casinos, they do not turn off the prerecorded Musak when there is live music. The Eastside Cannery is not the only offender.
It was really painful tonight, so we left.
--- In vpFREE@yahoogroups.com, "Nathan O. Roemer" <public@...> wrote:
Does anyone know if the Eastside Cannery's Seafood Night Buffet has
crab legs? If so, what kind, and are they served hot or cold??Thanks!