DW44 Bankroll Requirements

[farmer1]

FAYGO:THANKS FOR THE LAUGH TONIGHT, I NEEDED IT.FARMER

[Lucky Larry]

Eduardo,
I now remember why I didn't major in math.

PS: Thanks Gordon B. for all the tutoring back in high school calculus/trig. I barely passed only because of you. It paid to have a best friend who WAS a math major because in the late 60's I don't even remember a graphing calculator. Hey, but I'm still pretty good on a slide rule.   

[PeaceFr0g]

Thanks for a very informative post New2vp!  One thing I don't understand...Why are we taking the SqRT of the standard deviation (25.5) AND the # of hands?  In live poker for example, we just take the SqRT of the # of hours x the standard deviation.  Here, we're taking the SqRT of the SD AND the # of hands.  For single play, the way I would think it should be done is:At 700 deals, the SD would be: SqRT(700) x 25.5 = 674.7.  So after 700 deals, you can expect 68% of the population to be within  +/- 674 coins of true expectation (which is -.28).  What's confusing me is the 5x coin that you must play. Does that mean we need to take SqRT(3500) x 25.5 = 1508.6?Sorry...  I'm a bit mathematically challenged.  But your post was very helpful.  It was pretty much what I expected (that bankroll needs to be between $45k - $65k).  I'd just like to understand why we need to take the square root of both the standard deviation AND the # of hands.  Thanks.

[PeaceFr0g]

For example, you get dealt 4 deuces about once in every 55K hands. Since peacefrog is only planning on playing 50K hands that makes it quite possible they would miss getting them. The cost is $4000 vs. being one short on single line cost $1000.This is an excellent point.  Fortunately, I just hit quad deuces the other day, so I'm actually ahead of variance! -lol.  One other important point is that this also assumes 100% perfect play.  I'm not that experienced yet.  So if you make just 3 errors (1 major, 1 moderate, and 1 minor), every 100 hands (which is about where I'm currently at), this will certainly increase bankroll requirements. 
 You guys are great!  Thanks! 

[New2vp]

Why are we taking the SqRT of the standard deviation (25.5) AND the # of hands?  In live poker for example, we just take the SqRT of the # of hours x the standard deviation.  Here, we're taking the SqRT of the SD AND the # of hands. I can tell from what you have written that you can answer your own question here.  25.5 is not a standard deviation; it is a variance.  To get to a standard deviation, you need to take the square root of a variance, which I think you already know.A minor clarification:  I said SqRT(34.6466), not SqRT(25.5).  Recall, for 4-play, the variance needs to be increased by 3 times the covariance.  If you are now talking about single-line play instead of multi-line play, it would be ok to use SqRT(25.5).Also recall that the variance is 34.6466 bets squared, which makes the standard deviation equal to 5.8861 bets.  The units here are important to answer your next question.
What's confusing me is the 5x coin that you must play.I'll answer your new question in the next section.  In my answer to your original question, you were playing 20 coins per bet ($5/hand x 4 hands).  So, the interim answer that I gave of 3290.45 bets can be converted to dollars by noting that that you are wagering $20 per bet.  There are lots of different ways of doing the calculation, but I generally keep all units in number of bets until the end and then multiply by the cost per bet (as long as all bets are of equal size; if they are not it's a lot more complicated).If you want to change a standard deviation from bets to coins on standard single-line play, you multiply by the 5 coins per bet.  If you want to change a variance from bets squared to coins squared on the same game you have to multiply by 5^2 bets squared or 25 bets squared.There's nothing wrong with initially changing the standard deviation or variance (or EV) to units involving coins instead of bets.  That way you can avoid the transformation at the end, but I find that tougher to understand when you are further complicating the calculation to involve multi-line play as well as multi-coin play per line.For single play, the way I would think it should be done is:At 700 deals, the SD would be: SqRT(700) x 25.5 = 674.7.  So after 700 deals, you can expect 68% of the population to be within  +/- 674 coins of true expectation (which is -.28).  What's confusing me is the 5x coin that you must play. Does that mean we need to take SqRT(3500) x 25.5 = 1508.6?There are 4 problems here.  (#1) I've already addressed that we need to use 5.0496 bets for the game standard deviation, not 25.5.(#2) And then if we want to change that into coins, we would multiply that number by the 5 coins per bet.  So, as it turns out, because of compensating errors (since the standard deviation and bet size both are around 5, using the variance instead of the standard deviation and ignoring the multiplication of 5 coins per bet offset each other), you could get close to the right answer even though 2 different mistakes were made.  My advice is to keep the number of plays separate from the bets for the best understanding and continue to use SqRT(700) in a calculation like this.(#3) For your expectation, which you stated was -.28, you forgot to multiply by the number of coins per bet; I think the true expectation is more like -1.5 coins.(#4) And when you say, "So after 700 deals, you can expect 68% of the population to be within  [1 standard deviation] of true expectation", you are making a fairly large error.  A video poker distribution is significantly different than the normal distribution which has the 68% property that I expect you are using.A normal distribution is symmetric.  A video poker distribution is not.  With a normal distribution you can expect 50% of the time to be over the mean and 50% to be under.  With this game and 700 single-line plays, you will be under the mean 67% of the time.  You often hear experienced vp players say that they lose more than they win even when they are playing with an edge and that's related to this property.With a normal distribution, the mode (or most typical observation) would be the same as the mean:  here 3500 coins rounded to the nearest 5 coins.  With this game, the mode is 3280 or a 220-coin loss.With this game and 700 plays, you will be within =/- 1 standard deviation about 88% of the time, with only 2% worse and 10% of the time better.  It has to be that way so that you can offset the typical 220-coin loss on what is essentially a break-even game.With only 700 plays, you would essentially never be more than 2 standard deviations lower than the expectation (odds of more than 45 million to 1), whereas with a normal distribution, that would occur about once every 44 times.  But you would be more than 2 standard deviations with this game about 4.6% of the time.Unfortunately, you cannot carry those inferences exactly to other games or for other numbers of plays and the calculations are somewhat involved to do this in general.  So, if you want to see what typical deviations from the norm are, you should probably use the autoplay feature on WinPoker and record what happens if you simulate your play a few times.  Another idea would be to purchase VPFW and use their bankroll feature.Best of luck.

[PeaceFr0g]

Thanks again New2vp.  btw- That's a very misleading handle.  You're obviously NOT new to vp! -lol.  Either that, or you're very proficient in math.  I realized my mistake right away when I stated expectation was -.28.  Unfortunately, I couldn't figure out how to edit and correct it.  I think I'm going to drop a couple of hands and just play two.  I'd be pretty sick if I got stuck near $65k trying to achieve the perks for a top tier casino card.  It's definitely not worth anywhere near that.  But I find that I actually enjoy VP.  Mainly, because there is skill involved and a small edge can be realized.  I'm in a casino almost every day of my life and honestly never had a desire to gamble in the traditional sense (i.e., to play craps or any casino game where I know I'm supposed to lose my money with every play).  Anyway, thanks again.  I really like this forum and hope one day I can contribute.  Best of luck to you as well. 

[New2vp]

btw- That's a very misleading handle.  You're obviously NOT new to vp!You're right, I'm not new to video poker anymore, but after all these years, I can't change that name here.But I find that I actually enjoy VP.  Mainly, because there is skill involved and a small edge can be realized.  I think that combination is the draw for a lot of us.

[PeaceFr0g]

Haha.  I thought that was a funny dig when I saw that you edited your post at 5:03pm.  But then I saw this...  I guess you need x number of posts before you're allowed to edit.  You can post new topics in this forumYou can reply to topics in this forumYou cannot delete your posts in this forumYou cannot edit your posts in this forumYou cannot create polls in this forumYou can vote in polls in this forum

[faygo]

PeaceFrOg, at the bottom of your posts there should be  buttons for edit or delete?? 

[Webman]

That's correct. Certain functions require a minimum number of posts because those tools are heavily abused by spammers who only make a few posts before their abuse. You'll be there before you know it.