Tracking my Variance - Is Andy right?

[zenmaster]

This thread is inspired by this comment by Andy

Originally Posted by Andy

In the long run with a decent +EV strategy your bankroll will slowly rise at the rate of the EV. If you charted it with EV on the vertical axis and offers played on the horizontal it would diagonal upwards and if you get above the line you will sooner or later come back down and if you get below it you will eventually be dragged back up. Its like a magnet and nothing can stop you from permanantly going off that line.

So on that note i have decided to do exactly that! one of the main reasons is to convince my OH (and myself although im 99.9% convinced) that casino bagging is worth the risks involved. It also means i get to geek out with stats and numbers. Now this really is also for a bit of fun the sample size is small right now as well but it will be interesting to track this long term and i intend to update this OP with results once a month or maybe more.

Now I'm 5 casino offers in and how many offers I do between now and xmas depends on how well it goes and how much spare cash I have to throw at it. I simply don’t have the bankroll some of you have but from a newbie perspective going softly softly cherry picking the offers as and when I have the money it could be a nice little guide for others reference in the future, and allow them to judge for themselves if it’s worth it.

The table and graph.

So basically what I have done is document the offer the green section contains all the relevant info needed from who the offer is with, the amount deposited to receive the offer, the bonus amount, and the wagering requirement to unlock it.

The red section contains the EV amount as calculated by a variance simulator or an estimated figure this is basically the amount you would expect to withdraw if you did the offer 100000 times. The next column is the real amount I ended up with.

Finally the blue section contains the running totals for the expected EV and for the amount I have actually gained from doing the offers, these are the numbers that are used on the graph and calculate the mythical line Andy talks about. As you can see my £50 loss at 32red on my last offer has set me well below the line if I walked out with the expected total I would be on £102 pretty much right on line so the small sample size is naturally throwing the experiment off at the moment.

Now i have thought about it and decided that it would be a cool idea as Andy suggests to track more data so if anyone wants to add to the data pool you can either post it here or PM it to me. If you provide the following info that would be great.

Casino/offer:
Deposit amount:
Bonus Amount:
Wage Return:
EV Amount:
Result:
Link to offer:
Outline of your Strategy:
Game played:
Bet size:



If anyone has anything to add, suggest or improve then feel free to do so.

[Landprofits]

This is going to be interesting!

[Andy]

Excellent thread I love it. Did you want other people to add their results to it at all so I say the offer, the EV and what I actually got and that is added? If we all did that we would get a decent sample size of a few hundred I expect in time?

Or keep it to just yours will keep it 100% accurate and be an OK guide too.

Its not my theory at all though it is just maths. Over an extended period of time you will never make significantly more or less than the total EV.

[Landprofits]

Was the variance simulator a stand alone application? Any reason why you chose the Simulator over just using the House Edge?

[zenmaster]

Originally Posted by Andy

Excellent thread I love it. Did you want other people to add their results to it at all so I say the offer, the EV and what I actually got and that is added? If we all did that we would get a decent sample size of a few hundred I expect in time?

Or keep it to just yours will keep it 100% accurate and be an OK guide too.

Its not my theory at all though it is just maths. Over an extended period of time you will never make significantly more or less than the total EV.

I could do both with no problem, a graph for me and a graph with as many results as possible would be good and of course would provide some interesting comparison between the two.

I know its not really your idea really but your recent post got me thinking about it again having read about it on more than a few occasions its inspired me to keep track and see, so i went back and plotted the graph.

Originally Posted by Landprofits

Was the variance simulator a stand alone application? Any reason why you chose the Simulator over just using the House Edge?

Im using the beatingbonus and kasinoking websites for my sources of info they have a good simulator which incorporates the house edge of software seems a nice bit of kit so just plugging the info into that or using there casino list with expected EV numbers.

My problem is slots how do you work out expected EV for those offers im not sure but im sure someone can help me figure that out, im just too new at this to know the answer to that right now.

[munk]

Originally Posted by zenmaster

My problem is slots how do you work out expected EV for those offers im not sure but im sure someone can help me figure that out, im just too new at this to know the answer to that right now.

I think it's great what you're doing, very good idea indeed.

Calculating expected value (EV) is just a matter of knowing:

• B=how much the bonus is
• W=how much wagering you have to do
• A=the house advantage of the game you're wagering on

and from those you can calculate the EV (E):

E=B-W*A

All you're doing is subtracting the amount the house will take over the wagering requirement off the amount of the bonus. This is a very rough rule of thumb, there are other factors that affect EV such as the price you put on your time.

So as an example for something like the WH 'no deposit' thing you have:

• Wagering Requirement, W=£3000
• House Advantage, A=0.005 (very roughly assuming 0.5% for Blackjack, ie for every £100 you spend on BJ, on average the house takes 50p)

and from that you can calculate:

Expected Value, E = B - W*A = £30 - £3000*0.005 = £15

Which is very roughly what you have there in your table.

So that's to say that over £3000 of wagering on Blackjack, all things being equal you can expect to lose £3000*0.005 = £15. Therefore after £3000 of wagering you will be left with £30 - £15 = £15. So the EV is £15.

Expected value is the 'long run' average value you can expect from a given bonus - ie if you could play the same wagering requirement on the same game over and over an infinite number of times, the expected value is the average value you can expect to get back over all of those wagering sessions.

You could take your 'experiment' to lots of different places though, although it's probably not feasible for a single person to do, it would need a much larger sample size along the lines of a mass experiment where everyone submitted their data.

For example you could run tests to see what effect increasing the stake size has on EV and variance. Generally the lower the stake size the lower the variance will be, although the EV is diminished because of the increased amount of time it will take to complete the WR which in turn decreases the return per hour.

Anyway... yes great stuff it'd be good if you kept the first post of this thread updated over time just so we can see how you're getting on and how profitable things are over time. The only worry / issue might be if you have a really poor run at the start and that leads you to the impression that it isn't worth doing... which would be unfortunate because over time things do even out and you certainly do profit very well from casinos.

I would also suggest you start up at Ladbrokes very very soon, in fact I would have recommended it as the first one really because they have the best casino out there really in terms of promotions.

Good luck anyway and hope you keep the stats up!

[zenmaster]

Cheers munk that makes a lot of sense, still a lot to learn and i will ask questions and do more research as i go along. I will most likely be doing 1 or 2 of these offers a week as i get the time to do them lets face it they can take awhile!

Now i have thought about it and decided that it would be a cool idea as Andy suggests to track more data so if anyone wants to add to the data pool you can either post it here or PM it to me. If you provide the following info that would be great.

Casino/offer:
Deposit amount:
Bonus Amount:
Wage Return:
EV Amount:
Result:
Link to offer:
Outline of your Strategy:
Game played:
Bet size:

Now the intention will be to have two graphs one for me personally and one for everyone's data combined, to save space i wont display anymore than the last 5 offers done in each screenshot but all the data will be in the graph.

[Andy]

RE The EV it depends on the strategy you use as well. Simply the house edge x wagering will tell you the loss on playing a cashable bonus low stakes from the start, but if you doubled up at the start you will have a higher EV although a much greater chance of hitting a loss.

The EV of an offer is not constant between people it depends how you play it as well. Im not sure you can properly work out the EV of slots offers, I know they are +ve, but im not sure I could prove it to anyone with maths the payouts and variance are too random, they are not like BJ payouts and distributions.

[zenmaster]

bet size and of course how you play the offer will matter maybe a good idea for those posting data for me to add to graph a quick outline on bet size and strategy as well so have added that in.

[advanta]

Originally Posted by Andy

RE The EV it depends on the strategy you use as well. Simply the house edge x wagering will tell you the loss on playing a cashable bonus low stakes from the start, but if you doubled up at the start you will have a higher EV although a much greater chance of hitting a loss.

The EV of an offer is not constant between people it depends how you play it as well. Im not sure you can properly work out the EV of slots offers, I know they are +ve, but im not sure I could prove it to anyone with maths the payouts and variance are too random, they are not like BJ payouts and distributions.

Not easy but there are various ways to get a good estimation.

I think some, possibly even most, slots, at least those created by reputable software providers, use simulations of physical reel maps. That is the reels behave the same way the old mechanical slots used to-each symbol is as likely to come up as any other. Why they do this is complicated-many of the slot games are versions of real slot machines used in real casinos and there are complex but valid legal reasons to do this in real casinos I won't bore you with.

Assuming this is the case you can record the slots moving in slow motion using some kind of video recording device that you can probably download for free. In theory you could work out the exact EV and variance since once you know the composition of each reel you can calculate the probabilities exactly.

Alternatively you can get a good idea of the EV in a given session by simply running very large numbers of spins on freeplay. This assumes freeplay is the same as real play (a good assumption with reputable operators) and also that you can work around any bonus features (much more of a problem). You won't be able to clock the frequency of rare events (ie jackpots and big payouts) but then these are of only tangential interest to AP's anyway.

Finally, of course, some gambling operators may publish payout statistics, which are somewhat helpful though far from clinically accurate. Wagerworks and maybe other providers publish exact house edges, indeed they will give you even more info if you request it as I understand.

I've always toyed with the idea of running large numbers of simulations and/or attempting to hack the payout % via physical reel analysis, perhaps on a website or something. I'm not sure if there is enough interest in this, though if Ladbrokes keep running slot promos it might be popular enough to try and make it fly.

[munk]

Originally Posted by zenmaster

Cheers munk that makes a lot of sense, still a lot to learn and i will ask questions and do more research as i go along. I will most likely be doing 1 or 2 of these offers a week as i get the time to do them lets face it they can take awhile!

Now i have thought about it and decided that it would be a cool idea as Andy suggests to track more data so if anyone wants to add to the data pool you can either post it here or PM it to me. If you provide the following info that would be great.

Casino/offer:
Deposit amount:
Bonus Amount:
Wage Return:
EV Amount:
Result:
Link to offer:
Outline of your Strategy:
Game played:
Bet size:

Now the intention will be to have two graphs one for me personally and one for everyone's data combined, to save space i wont display anymore than the last 5 offers done in each screenshot but all the data will be in the graph.

That sounds very interesting but a lot of work as well for yourself. JUST an idea, but GoogleDocs spreadsheet application will allow you to create custom forms to allow people to enter data into a spreadsheet on their own without your interaction, that would dramatically cut down on the amount of time you have to spend on processing the data. Just an idea....

Otherwise I'd be up for contributing some data... in fact I could probably give you a lot of data, trouble is I don't have the Ev etc listed at a glance, would have to crunch it first Am quite tempted to do something similar now actually... will see.

[Landprofits]

Munks explanations of EV above a great - but is there a commonly accepted method for working out possible Variance?

[Stevesharpe]

I Like the thread but a couple of points to add.

Looking at your initial table the Will Hill Vegas £25 SUB is only a £400 WR not the £2000 you have noted down so greater EV

When doing a post wager SUB such as this, in order to get true EV you should re-deposit and finish the wagering. This can be scary (I know) but on the 2 occasions I've had to do it the EV has come back and I've finished up both times.

[zenmaster]

Originally Posted by SteveSharpe

I Like the thread but a couple of points to add.

Looking at your initial table the Will Hill Vegas £25 SUB is only a £400 WR not the £2000 you have noted down so greater EV

When doing a post wager SUB such as this, in order to get true EV you should re-deposit and finish the wagering. This can be scary (I know) but on the 2 occasions I've had to do it the EV has come back and I've finished up both times.

I will have to go check that again thanks but i did actually redeposit this is one of those bonuses that unlocks when you finish wagering when i did it so i redeposited £25 and carried on the end result was i was -£19 down when i withdrew.

Just checked and your right must of got my notes mixed up.

--------

I just did the free £25 at ladbrokes now i played 3CP £1 hands after about 40 hands i decided to put 0.5 on the pair plus and up went the balance about 30-50% through the WR i was £70-80 up but around half way i hit a slow decline before bombing in the last 200 of the WR and bust about 6 hands short of completing it. No real surprise to be honest the EV on this was £18.54 but with a 86% bust rate. Bit annoying getting so high then getting so close.

[M1ghtyDuck]

Originally Posted by Andy

In the long run with a decent +EV strategy your bankroll will slowly rise at the rate of the EV. If you charted it with EV on the vertical axis and offers played on the horizontal it would diagonal upwards and if you get above the line you will sooner or later come back down and if you get below it you will eventually be dragged back up. Its like a magnet and nothing can stop you from permanantly going off that line.

I'd actually disagree with this. We all know that previous play has no effect on future play. Big losses are not "balanced out" by big wins, it just sometimes feels it does because we usually and statistically get a roughly equal amount of each.

As such, if you dropped below the EV line, or climbed above the EV line, you wouldn't be expected to gravitate back towards it, you'd be expected to follow a new line parallel to the original EV line, starting from your current point. (For the maths heads, the equation of your EV line would just have a +n number at the end, a different y intercept.)



In zenmasters case, his new line is starting from £40 rather than £155 or so, and his EV line from now on would be £115 lower than the orignal EV line, (until he drew a new EV line, based on where he currently was). Of course, he could climb back up to the orignal EV line, but there's just as much chance of going even lower. So actually, it's not like a magnet at all.

[Fella]

Hurry up & do some more casinos, this is my favourite thread right now!

[zenmaster]

Been a little while since my last post dont worry im working hard in the background added some more offers to the first post a few days ago currently working on a number of promo offers and hope to be cashed out this time next week. Dont really want to document them at this moment in public since i have a sizeable amount invested.

32red i did on monday that was a nice boost for the blue line!

[Super_Dash]

Originally Posted by M1ghtyDuck

I'd actually disagree with this. We all know that previous play has no effect on future play. Big losses are not "balanced out" by big wins, it just sometimes feels it does because we usually and statistically get a roughly equal amount of each.

As such, if you dropped below the EV line, or climbed above the EV line, you wouldn't be expected to gravitate back towards it, you'd be expected to follow a new line parallel to the original EV line, starting from your current point. (For the maths heads, the equation of your EV line would just have a +n number at the end, a different y intercept.)

Yea thats the conditional expected value, conditioning on what we have where do we expect to be?

But based simply long run stats, we can still expect to be close to the true expected value after a large amount of offers. The more expected value we are up, the smaller individual deviations become relatively.

Thats how I see it anyways.

[DireEmblem]

Are you still looking to compare various results to check the EV on bets, if they consist to the norm?

I'm just starting out at the casinos, decided this week since i've had a good run of bonuses, and looking to delve into other areas, so I consider using my profit from this week to start the casino's as non-risk.

Interesting thread anyway, hope you keep it up!

[Digi]

Well I just made a graph of the last 50 casino offers/reloads I did.

Not running very good atm... oh well

Numbers are units (€,£,$)

[zenmaster]

Cheers Digi very interesting graph you seem to have done some good offers between 15-25 very sharp increase in the line. Offers 25-30 seemed to set you back a bit and you have been holding fairly steady since then. Do remember one thing though you have made £3600 from those 50 offers and that i think is the key thing to remember.

I should be posting more results of my own by the end of the week, i am due to make a sizable withdraw.

[My_User_Name]

Digi, could you please post which offers did you do? (just name the casinos, please)

[Andy]

From the results so far it appears to be slightly under the EV but you can see it basically trends the same way, that was more the point. I can see what the earlier post means about past results not effecting the future and I agree, I just meant more that as the "expected value" of each offer is just that, the "expected" amount, if you ever get more than that is was goodluck and if you ever get less it was badluck and over time and enough offers these will cancel each other out and you will, more or less, just stick to the EV line.

I still think you will do in the long run.

[jopre]

The law of averages only works with an infinite number.

[zenmaster]

A few issues at the moment which might delay i am trying to find as accurate data as possible on payouts for certain slots, if anyone knows where microgaming post data on payouts id love to see it. Not yet been able to find it otherwise i will just wing it and run my slots data with a 5% house edge until such a time i can find something more accurate.