How to calculate the EV of a sequence of bonuses.

[KasinoKing]

Enzo,

No one is arguing that as a very basic calculation prior to history the formula is correct the problem is that what I infer from your original post is that the ev on deposit 10 is 405 where as the way I see it, that is the ev over 10 such deposits prior to history and deposit 10 has an ev equal to all the others.
As I pointed out the ev is made up from the accumulation of the expected ev of 10 deposits. The fact that 9 deposits came in well below expected ev does not magically increase the ev 10 fold of the final deposit.

I don't think you read Enzo's last post before commenting, did you?

Again, I'm not predicting the future. I'm not saying he lost 9 times so he will win. I'm describing something completely in the past - or in the future. Take your pick. Its just a game that pays on average 1 in 10 bets. It's a reel of fortune with 10 spots. 9 have no prize, one pays 9.5 times bet.

All I say is that on a machine like that, if you always play with bonus, you will lose 9 times and cashout about $850 1 time ($855 = $500 + 10*$35.5 to be correct). That's an average. The win could be the first session, any session inbetween or the last one. You could have a set of 10 where you don't win and you could have a set of 10 where you win more than once. On average however you will win 1 in 10 sessions on a game like that. On average you will make $350 every 10 sessions if you play a game with that variance following the strategy described.

AVERAGE is the key word; all theoretical EV calculations can only be done with averages... unless you have crystal balls!

KK

[KasinoKing]

OK, I'm going to try to explain what I think Enzo means:

Suppose you took ten bonuses, each 100% on $100 with WR Bx30.
You play high variance games and on 9 of the bonuses you bust out completely having only made it 1/3 the way through WR on AVERAGE. That's $1,000 wagered on each bonus.
On the other bonus you make the WR - so that's $3,000 wagered.

Add up all your wagering; (9x$1,000 + 1x$3,000) = $12,000

Your expected loss on 95% RTP slots = $12,000 x 5% = $600.

You started with $1,000 of your own money & $1,000 in bonuses and have lost $600.
Therefore you are left with your original $1,000 + $400 of the bonus money.
Your EV is +$400

(Figures guesstimated!)
KK

[Wibbler]

OK, I'm going to try to explain what I think Enzo means:

Suppose you took ten bonuses, each 100% on $100 with WR Bx30.
You play high variance games and on 9 of the bonuses you bust out completely having only made it 1/3 the way through WR on AVERAGE. That's $1,000 wagered on each bonus.
On the other bonus you make the WR - so that's $3,000 wagered.

Add up all your wagering; (9x$1,000 + 1x$3,000) = $12,000

Your expected loss on 95% RTP slots = $12,000 x 5% = $600.

You started with $1,000 of your own money & $1,000 in bonuses and have lost $600.
Therefore you are left with your original $1,000 + $400 of the bonus money.
Your EV is +$400

(Figures guesstimated!)
KK

Um no. EV is what you *expect* to get before you start wagering. The $400 you have left here is profit. The calculation of EV is very simple for a post-wager bonus, and is more complex for pre-wager bonuses. To figure out what it is for your example I'd have to know what betsize you were wagering.

[skiny]

Um no. EV is what you *expect* to get before you start wagering. The $400 you have left here is profit. The calculation of EV is very simple for a post-wager bonus, and is more complex for pre-wager bonuses. To figure out what it is for your example I'd have to know what betsize you were wagering.

You would also have to know what the RTP is on every game you played.

The original formula also requires you cash out a thousand dollars on a 50 dollar deposit. If I could do that every 10 deposits I'd quit my job and deposit 10 times a day.

[thelawnet]

The best games are the high variance slot games. Not the low variance blackjack. In fact, blackjack is the single WORST game (it has the lowest variance). Blackjack aligns most closely to that wrong formula.

A high variance slot game gives you the best odds to generate little play, and thus little house-edge. Roulette isn't bad either, a single number bet on roulette has a variance of about 5.8 - our slots go up to well over 10.

Further to my last post, it has occurred to me that your thoughts are probably strongly shaped by your job as a rep for a specific casino with specific bonus rules. For your specific set of bonus rules, with absurd weightings for video poker, slots are an attractive option, but the bonus rules you operate with don't match up with the examples you've been going in this thread.

Bottom line is you can't say 'slots are good, blackjack is bad' or 'blackjack is good, slots are bad' in general terms, because it completely depends on a bonus. Red Dog might be the best game to play at one casino, keno at another, there are no guarantees.

[Rusty]

Originally Posted by Rusty View Post
Enzo,

No one is arguing that as a very basic calculation prior to history the formula is correct the problem is that what I infer from your original post is that the ev on deposit 10 is 405 where as the way I see it, that is the ev over 10 such deposits prior to history and deposit 10 has an ev equal to all the others.
As I pointed out the ev is made up from the accumulation of the expected ev of 10 deposits. The fact that 9 deposits came in well below expected ev does not magically increase the ev 10 fold of the final deposit.

KK
I don't think you read Enzo's last post before commenting, did you?


Originally Posted by 3Dice View Post
Again, I'm not predicting the future. I'm not saying he lost 9 times so he will win. I'm describing something completely in the past - or in the future. Take your pick. Its just a game that pays on average 1 in 10 bets. It's a reel of fortune with 10 spots. 9 have no prize, one pays 9.5 times bet.

All I say is that on a machine like that, if you always play with bonus, you will lose 9 times and cashout about $850 1 time ($855 = $500 + 10*$35.5 to be correct). That's an average. The win could be the first session, any session inbetween or the last one. You could have a set of 10 where you don't win and you could have a set of 10 where you win more than once. On average however you will win 1 in 10 sessions on a game like that. On average you will make $350 every 10 sessions if you play a game with that variance following the strategy described.
KK
AVERAGE is the key word; all theoretical EV calculations can only be done with averages... unless you have crystal balls!

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Yes I read it but I am saying you can not apply past ev to future ev which is how I read Enzo's original post. There is no such thing as past ev and you make this mistake in your next post.
The ev on even a single deposit does not stay static as you play through it.

If I deposit 50 with 50 bonus with 95% theoretical RTP I have an ev of 45 on 1xwr before I begin to wager. (using Enzo's 10 spins 1 in 10 chance of win 95 at 10 units per spin)
If I wager 90 without a win my ev is not still 45 because that would imply 100% expectation of a win and we know the odds of hitting are only 10%
The actual ev at this point on original deposit is now a negative value.
I would say -40.5 but that calculation is probably too simplistic because I am not sure how to incorporate variance into the equation.

Therefore my argument is that any ev calculation can only be applied to future events and it would be incorrect to include past ev into future ev calculations.
You can not calculate I made 9 deposits at 50 with 50 bonus and lost all but my expected value overall on my next deposit of 50D+50B is 450 (or 405 if you calculate that) unless you are predicting the slot will have exact 95% return over this exact playthrough.

[Rusty]

OK, I'm going to try to explain what I think Enzo means:

Suppose you took ten bonuses, each 100% on $100 with WR Bx30.
You play high variance games and on 9 of the bonuses you bust out completely having only made it 1/3 the way through WR on AVERAGE. That's $1,000 wagered on each bonus.
On the other bonus you make the WR - so that's $3,000 wagered.

Add up all your wagering; (9x$1,000 + 1x$3,000) = $12,000

Your expected loss on 95% RTP slots = $12,000 x 5% = $600.
You started with $1,000 of your own money & $1,000 in bonuses and have lost $600.
Therefore you are left with your original $1000 + $400 of the bonus money.
Your EV is +$400

(Figures guesstimated!)

KK

Right, this is exactly the problem. You are predicting future events you just don't realise you are doing it.

You can make the ev calculation for a series of 10 deposits under such conditions which would be.
$100 bonus*10= $1,000@30*WR= $30,000 @ 95% = 28,500 = -$1,500
$100 deposit *10= $1000 - $1,500 = ev -$500

You can see how this is not such a happy smiley bonus as you suggest.

Why are the figures different?
Because you have predicted the future amount of wagering and RTP on those 10 deposits.

There is no such thing as past expected value - where is the expectation?
As has been said your profit is $400 should that series of events occur.

I can see how busting out quickly on series of bonuses could be seen as possibly beneficial but it is absolutely not a rule because the RTP over that set wager is not a rule.
In your example you got 80% RTP on the first 9 deposits but that does not magically increase the ev on your final deposit from -50 which is the ev each individual D+B (nor is the ev now -950 taking previous losses into account - it works both ways) to +400 unless you predict the RTP on you final deposit+bonus will be 700% ($1,400) to make up for it. (loss -$900+$1,400= $500-$100D=profit $400)

Using Enzos calculations you have a running ev of +$450 after 9 deposits but the reality is you have a negative ev of -50

I like Enzo and he makes some great posts but his Total running EV as named and calculated by him is irrelevant at best and misleading fat worse in my view and I am not sure why it has 4 nominations.
It is encouraging gamblers fallacy in that one can infer that the more you lose the likelier you are to win as total running ev increases when the pertinent calculation is ev for that deposit or the next series of deposits based on theoretical RTP of games played.

[KasinoKing]

In your example you got 80% RTP on the first 9 deposits but that does not magically increase the ev on your final deposit from -50 which is the ev each individual D+B (nor is the ev now -950 taking previous losses into account - it works both ways) to +400 unless you predict the RTP on you final deposit+bonus will be 700% ($1,400) to make up for it. (loss -$900+$1,400= $500-$100D=profit $400)

Sorry, but I think you are totally missing the point.
Neither I nor Enzo are predicting the future, nor have we said at any point that past events will influence the future.

All we have said is on average, given the examples we posted, you will have a +EV.

Again, AVERAGE is the key word.
If I said "If you play roulette, on average the Zero will hit once every 37 spins", no-one could argue with that, but that doesn't mean the Zero will definitely hit once every 37 spins, so put your house on it!

KK

[Rusty]

Sorry, but I think you are totally missing the point.
Neither I nor Enzo are predicting the future, nor have we said at any point that past events will influence the future.

All we have said is on average, given the examples we posted, you will have a +EV.

Again, AVERAGE is the key word.
If I said "If you play roulette, on average the Zero will hit once every 37 spins", no-one could argue with that, but that doesn't mean the Zero will definitely hit once every 37 spins, so put your house on it!

KK

Again I have shown why your example would be -ev not +ev
You can not say it is +ev just because either you happened to defy the odds and win or because you are predicting that is what will happen based on some odd notion of an average.
What is average about receiving 80% RTP 9 times and 1300% another anyway?

Sorry, but I think it is you that is totally missing the point.
I can not explain it any better than I have using your own example.

If you are not predicting the future then the logic is you are basing it on past results such as your examples for instance but I repeat you can not calculate ev (Expected value) based on past results it is simply a mathematical expression of the known probabilities of a random event.

Such as your roulette example has an ev of -0.027. to a $1 stake.
(-$1*36/37) + ($35*1/37) = -0.027.
Or in plain English> You will make a $1 loss every 37 spins on average.
-$1/37= -0.027. cent lost per spin

This ev does not change because of past results it remains the same each time we bet a dollar on a number.
Likewise your example ev which is -0.05c to each $1 wagered (95% RTP) does not change simply because you have made up some results.
In your example if it is was certain or preordained you would wager $12,000 *-0.05ev =-$600 your calculation would be correct but note the ev is still -0.05 to every dollar and the only way we could conclude we would make a profit is by predicting these future results!

How about I change your example since you say it is not a predicted outcome? (what else is an example by the way?)Your ev of $400 can't change since the ev per $ does not change, right?
Lets try we wager 2500 before busting on the first 9 deposits and make playthrough on the last deposit still.
2500*9=22500+3000=$25,500*-0.05ev= -$1,275+$1,000 bonus = -$275ev , Oh dear but I guess it must be right since I am just giving an example and not predicting future results right?




If you told me my ev on 10 deposits of $100 + $100B at 30xWR was positive ev or my average win would be $400 you would be telling me porkies plain and simple.

Enzo is talking about a running ev which he has invented which is simply irrelevant to the ev of any future deposit and bonus as far as I can see and I have explained why many times. How on Earth can your ev based on a known probability improve because of past events? Do more winning numbers get added to the roulette wheel? Do more wilds get added to the slot?
No, and that is why it is misleading whether intentional or not.

[nerv]

Guys..


All of you are right (from your own point of view).


Enzo and Kasinoking are using theoretical approach disregarding how risky it is, thus negating or eliminating "high variance is too risky".
Yes, in theory, it is the best option to play as high variance as you can because you hope that "1 of x hit" (where x is directly proportional to variance) will come a bit sooner than average (this is directly connected to Enzo statement that luck is actually main factor or parameter).
For example if you get good hit early in low variance game you'll get lets say A times bet. But if you get early hit in high variance game you'll get B times bet where B is much larger multiplier than A.
But that's theory is it is applicable in practice (bear in mind that you totally disregarded risk factor), every singe person on this planet would bet all he or she have, just placing one bet, on a game designed to have a variance streaming (is this right word, pardon my ugly English) infinite.
What will happen is that one person (eventually) would win. And the what?
That person would become owner of the everything and others would shoot themselves or starve to death or any other insane reason.
Yes that theory too.

Rusty, Skiny and others focusing on real life limitations more than theory.
But still, yes, in world of probability, it is better to play high variance game. As example above early hit gives you B/A better return, whereas no hit give you zero no mater how high variance is (this is close to derogative simplification but still applicable for the point I wish to make).
But then again High variance is like "Waiting for Godoe". It could become dangerously late.

Point for the rest of players. Play as high variance game (wand as high bets) as you can afford to yourself. Have control over it or you'll become addictive gambler.
And if you prefer more gameplay than lower your variance as low as it possible still not to become boring.