Tracking my Variance - Is Andy right?

[zenmaster]

This thread is inspired by this comment 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]

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.

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]

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]

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.