How to calculate the EV of a sequence of bonuses.

[funeral979]

Sorry if this is a slight derail, but...

Why is it that when blackjack is an allowable game in a bonus, it is normally counted at a reduced rate? For 3Dice I am pretty sure that it counts 5% towards wagering, but it might be 10%.

The reason I am asking is that since blackjack is RTP based and NOT a normal blackjack game(and we shall assume this since no rep disputed this in an earlier thread), and most likely with an RTP similar to slots....why is not counted as 100% towards wagering???

Thanks!

 

[KariRunk]

Sorry if this is a slight derail, but...

Why is it that when blackjack is an allowable game in a bonus, it is normally counted at a reduced rate? For 3Dice I am pretty sure that it counts 5% towards wagering, but it might be 10%.

The reason I am asking is that since blackjack is RTP based and NOT a normal blackjack game(and we shall assume this since no rep disputed this in an earlier thread), and most likely with an RTP similar to slots....why is not counted as 100% towards wagering???

Thanks!

It's simply because with blackjack the house edge is significantly lower than with slots. If Blackjack playing would have the same wagering requirements than slots, the bonuses (with the current terms, average of x30 WR) would be +EV for players and -EV for casinos.

 

[KariRunk]

She stated earlier about low or no WR....thats what i get at 3dice low or no WR so I can totally see the possibility. Thats why I dont think he's suckering anyone.

Overall Im in the hole there, so Im not a 3dice brown noser either. I was just stating my opinion based on the facts as I see them.

I'm sure they give those bonuses to VIP players, also known as losing players. But that doesn't have anything to do with the fact that usually bonuses DO have wagering requirements. And IMHO posting calculations using those rare bonuses with no wagering requirements as example, is pretty misleading.

 

[funeral979]

It's simply because with blackjack the house edge is significantly lower than with slots. If Blackjack playing would have the same wagering requirements than slots, the bonuses (with the current terms, average of x30 WR) would be +EV for players and -EV for casinos.

This would be true if online blackjack was dealt as live blackjack...but its simply a slot game with cards instead of reels. So in my eyes it should be counted the same as slots. Trust me, the house edge on slots is NOT significantly lower than ONLINE blackjack

 

[KariRunk]

This would be true if online blackjack was dealt as live blackjack...but its simply a slot game with cards instead of reels. So in my eyes it should be counted the same as slots. Trust me, the house edge on slots is NOT significantly lower than ONLINE blackjack

Well, then the question here should be, is the online blackjack based on RTP or is it based on random generator. If they're really are RTP, then the casino is cheating, wagering requirements after that fact are pretty irrelevant.

I'm sure Enzo is happy to give you an answer how it is in their casino.

 

[3Dice]

oooh goodie goodie.

Those of you who suggested my first post suffers the Gambler's fallacy, please revisit

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. At no point in my post I attempt to predict the future. The logic I present merely provides in a means to calculate the expected value of the total of bonuses a player has received.

Those of you who disagree with my use of the term EV, please revisit

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. In statistics, EV is but a synonym for mean. At the player's tenth deposit when his total bonus is 500 and his total wagering is 1000, the EV for the total of bonus received is 450. It's not 45. It's not -405. When repeated indefinitly, the player will cashout his deposit and 450 extra on average every 10 deposits. (with the machine being at 95% - so no luck good or bad - just expected value of the game).

Tencard, on the long term, expected wagering and actual wagering are the same thing. I wanted to give the players here a way of calculating that did not involve guesswork.

Those of you whom are questioning my motives for posting this, you have clearly not understood the post to begin with. If players understand and use the information in it - casinos will earn less. not more.

The vast majority of complaints posted on this forum about bonuses concludes wrongfully that they are -EV. Because of this a number of players that are not as much into maths are not claiming bonuses. Hopefully some of them will now realize that it would be better if they did. Better for them. not for me.

I have left WR out of the discussion so far not to complicate things even further, but if you play high variance and try to keep your playthrough low on bonuses, then WR is highly insignificant.

Lets look at my previous sample again and add in a WR of 20x (B+D). Using the (wrong) formula that is still being used here all the time :

50 depo
50 bonus
WR 20x(B+D) = 2000
HE on WR = 100

Then this would typically be followed by the statement that the casino would not only make back the bonus, but also the deposit. And that this bonus is hugely EV-. To the people that still think this is correct .. don't start a casino.

What really happens is on average the player loses 9 times and wins once. When he wins, he wins 450 over his total deposit. To clear his WR he'll spend on average 100, and will cashout on average 850 or 350 over his total deposit.

So, the EV of a 100% bonus up to $50 with a WR of 20x(B+D) when played on a 95% game that hits on average 1 in 10 sessions is $35 per bonus.

In this scenario, the WR would have to be 100x(B+D) for the casino to 'earn back the bonus', and 200x(B+D) to also on average earn the customers deposit. Every WR under 100x(B+D) is +EV for the player.

Funeral, all card games at 3Dice are RNG based (and third party verified). The blackjack at 3Dice uses 6 decks that are shuffled in between every game. Weighting of various games towards WR is purely based on the average pay of those games. Roulette has a house-edge on average about half that of a slot - so it counts half, video poker and blackjack have an even lower house-edge and so they count even less.). This is a rule in place to protect the slot players.


Enzo

 

[KariRunk]

Those of you whom are questioning my motives for posting this, you have clearly not understood the post to begin with. If players understand and use the information in it - casinos will earn less. not more.

Sure, they're +EV if you're able to place bets with no limit. But even your casino has betting limits when playing the bonus.

And isn't this kind of "advantage play" just what casinos consider bonus abusing? And you'll get bonus banned because of this.

Cut'n paste from your terms:

Bonuses are issued in good faith by the Casino as an incentive for "real" players, or as a token of appreciation for returning players who have continually shown their patronage and played for entertainment purposes only. They will be denied, declined, or revoked from players who are deemed to abuse the spirit of this offer.

I'm not saying that you have bonus banned players because of this, but I know for fact that there are casinos that have bonus bannned, closed account and even confiscated winnings based on that term.

 

[tencardcharlie]

Tencard, on the long term, expected wagering and actual wagering are the same thing. I wanted to give the players here a way of calculating that did not involve guesswork.

Yes, but... on the other hand, in the long term, actual winnings and expected winnings are the same thing. If I would suggest an algorithm for estimating EV simply by calculating your winnings so far, without any error margins, you would probably think that would be problematic.

I don't disagree with the general idea. I do however think that it is critical to have an idea about at what point the player can draw reasonable conclusions about their expected wagering. Because otherwise she is still just doing guesswork.

And whats worse is that she might not understand that she it's guesswork she is doing. A player that is playing with a negative expectation might be encouraged to play more, because their calculations lead them to believe that they are playing a winning game. And that is a serious issue. Therefore, your method need to take into account the fact that actual wagering might differ from expected wagering. It is better to be doing guesswork and be aware of it than making incorrect conclusions unknowingly IMHO.

 

[skiny]

What really happens is on average the player loses 9 times and wins once. When he wins, he wins 450 over his total deposit. To clear his WR he'll spend on average 100, and will cashout on average 850 or 350 over his total deposit.

How many players here are able to cash out even a hundred bucks on a 50 dollar deposit every ten times much less almost a thousand? By repeatedly saying things like the player will on average make a 450 dollar profit or the player didn't win by luck but because it's just the average RTP or bonuses will have an expected positive value at some point based on the sum of all previous deposits simply gives the impression that if you deposit enough times you will come out ahead and that's not the reality of gambling. We're talking about casinos here. Most players are not coming out ahead. Some of us players are on their 50th deposit without cashing out a dime and 50 more deposits doesn't mean anything will ever average out regardless of what deposit bonuses you are able to find.

So if you want to post formulas that calculate whether or not your deposit bonuses are covering the 5% house edge (assuming the house edge even is 5%) that's fine but I'm going to make sure that nobody is sitting here thinking this means "So, if I make enough deposits I'll eventually come out ahead." You can make a million deposits and even if you do cash out once in a while it doesn't mean you'll ever actually be ahead.

 

[Jufo]

Double post

 

[Jufo]

So, the EV of a 100% bonus up to $50 with a WR of 20x(B+D) when played on a 95% game that hits on average 1 in 10 sessions is $35 per bonus.

Since you are being so player friendly and want to make sure players lose less on average then do you have a suggestion how I should be play the SUB of 3Dice (your casino) to obtain this $35 in expected value? Does you casino have a game, which wins 9.5 units with 10% probability and allows me to make half/full bankroll bets on that game and which also counts 100% towards wagering? If not, then could you give me some other suggestions to use as an optimal strategy to play your SUB, so that me (and other players) are able to extract that $35 in EV, which you want us to have.

Closing thought.

It's lady luck that gives out the best bonuses. It's not the best mathematicians that win the most - its the luckiest players.

This way of thinking is wrong and harmful to the players. Usually I have seen these kind of sentences, ie. "Maybe you are the lucky one!" coming as spam e-mail from roguish casinos.
Mathematics clearly shows that even the luckiest of all players will eventually go bankrupt as long as he/she plays long enough. It doesn't matter how much you win, you will lose it back anyway eventually, because the house edge will catch you with 100% certainty. Every casino rep (including Enzo) knows that this is true. So I think a more honest version of that sentence would be:

"When playing without bonuses even the luckiest player loses it all back eventually, but when you play with good bonuses you are likely to win in the end even with slightly below average luck".

 

[thelawnet]

oooh goodie goodie.

Those of you who suggested my first post suffers the Gambler's fallacy, please revisit

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. At no point in my post I attempt to predict the future. The logic I present merely provides in a means to calculate the expected value of the total of bonuses a player has received.

Ok,

'The Gambler's fallacy is the belief that if deviations from expected behaviour are observed in repeated independent trials of some random process then these deviations are likely to be evened out by opposite deviations in the future'

Which is what you're doing. If you lost $450 already and you take a bonus with an EV of $45, you claim the 'total EV' is +$450. This is an 'evening out', an 'opposite deviation', because when you are $450 in the hole and are taking bonus with a $45, the only way you can get to an EV of $450 is by 'evening out' your 9 previous losses. Which is obviously not correct, and is just another form of the gambler's fallacy.

Those of you who disagree with my use of the term EV, please revisit

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. In statistics, EV is but a synonym for mean. At the player's tenth deposit when his total bonus is 500 and his total wagering is 1000, the EV for the total of bonus received is 450. It's not 45. It's not -405. When repeated indefinitly, the player will cashout his deposit and 450 extra on average every 10 deposits. (with the machine being at 95% - so no luck good or bad - just expected value of the game).

This is just obfuscation. Call it mean, call it EV, there is NO difference. The probability of a given event happening or not happening is no longer relevant once it happens. Economists might have said that a financial market meltdown of the kind that happened 2007 to date was 1/100, 1/1000, whatever, but once it happens, it's pointless and ridiculous to say 'over 4 years you can expect your portfolio to increase by 40%', when you know that, to date, it's decreased by 30%. Making the simplistic assumption that the expected increase in any given year is 10%, the expected change in portfolio value over 4 years is most certainly not +40% (ignoring compounding for simplicity's sake), but -30% + 10% (of present value) = -23%.

You've lost the money, it ain't coming back, the expected value of the individual bonus is $45, you've lost $450 already, so the expected value of your 10 bonuses is -$405. It was $450 BEFORE you did any wagering, but it's not any more.

Here's another example - what's the expected number of pips uppermost when rolling six six-sided dice? A given dice has an average pip value of 3.5, so it's 6 * 3.5 = 21. But you wouldn't seriously suggest, that if you knew that five of those six dice were 1s, that the expected value would still be 21. That would be ridiculous.

When you're calculating the EV, mean, call it what you like, you can't say 'I know what several values in the series are, but I'll ignore that fact and pretend I still don't know'.

The vast majority of complaints posted on this forum about bonuses concludes wrongfully that they are -EV. Because of this a number of players that are not as much into maths are not claiming bonuses. Hopefully some of them will now realize that it would be better if they did. Better for them. not for me.

Well no and no and no.

The vast majority of complaints about bonuses are actually due to casinos not wanting to payout for one reason or another. If you don't get paid, it's definitely not +EV.

And the players that are not into maths are not likely to figure out how to play a bonus to be +EV.

And if they don't understand your post, they're unlikely to understand all the rules and hoops you have to jump through to make anything from a bonus, so not necessarily better for them, perhaps actually better for you....

I have left WR out of the discussion so far not to complicate things even further, but if you play high variance and try to keep your playthrough low on bonuses, then WR is highly insignificant.

Lets look at my previous sample again and add in a WR of 20x (B+D). Using the (wrong) formula that is still being used here all the time :

50 depo
50 bonus
WR 20x(B+D) = 2000
HE on WR = 100

This formula is perfectly correct, for those casinos that give the bonus post-wager. Such bonuses can be found at Wagerworks, Chartwell, Playtech (sometimes), and others.

Then this would typically be followed by the statement that the casino would not only make back the bonus, but also the deposit. And that this bonus is hugely EV-. To the people that still think this is correct .. don't start a casino.

What really happens is on average the player loses 9 times and wins once. When he wins, he wins 450 over his total deposit. To clear his WR he'll spend on average 100, and will cashout on average 850 or 350 over his total deposit.

So, the EV of a 100% bonus up to $50 with a WR of 20x(B+D) when played on a 95% game that hits on average 1 in 10 sessions is $35 per bonus.

Not sure I follow you here.

Let's say the player bets $100. As you say, nine times in ten, he will lose, wagering only $100 of a $2k WR. The tenth time, he will win that bet, winning $950. He can't cashout yet though - he has to complete a $2k WR.

It's possible he'll lose the next 10 bets, wagering $1050, before busting but for simplicity's sake let's say he completes the WR, wagering $2k.

So the amount wagered is $100 * .9 + $2000 * .1 = $290. $290 * 5% = $14.50 lost to wagering.

In fact the amount lost would be a little lower than that, because even if you win the first bet you might still not complete the WR.

Anyway, suffice to say the EV would be a little higher than $35.

In this scenario, the WR would have to be 100x(B+D) for the casino to 'earn back the bonus', and 200x(B+D) to also on average earn the customers deposit. Every WR under 100x(B+D) is +EV for the player.

Actually a little higher than 100BD, because the player will actually complete the $10k of wagering very rarely.

But anyway, I'm sure you're aware the casinos know this, and put numerous restrictions to stop this kind of thing - roulette is nearly always banned, and other games of its ilk, bet limits are set low in software, or by rules.

A casino that actually allowed this kind of thing wouldn't last very long.

More typical would be a high WR, low bet limits, a long list of restricted games, and the best games all being skill-based, where players will in reality make many mistakes..... Not so profitable after all.


From your own terms:

• This bonus sets a wager requirement of thirty (30) times the amount of the deposit added to the amount of the bonus
• The contribution each game has towards the wagering requirements depends on the game and is set to 100% for all Slots and Solitaire; 50% for all Roulettes, Caribbean Stud, Texas Hold\'em and ThreeCard Poker, Sicbo, Red Dog, Keno and Casino War; 25% for Baccarat, Craps and Paigow poker; 10% for Blackjack; 5% for All video and multihand pokers.
• Until the wagering requirement is cleared, table limits are set to $50/25£/35€

It's a 110% bonus, so that's a 573*bonus wagering requirement on blackjack. Typicaly players play at 1.5% HA, so they need to be doing on average around 60X WR. But with a $50 max bet, that won't happen.....

It's not so simple or so easy you imply.

 

[skiny]

Cut'n paste from your terms:

Bonuses are issued in good faith by the Casino as an incentive for "real" players, or as a token of appreciation for returning players who have continually shown their patronage and played for entertainment purposes only. They will be denied, declined, or revoked from players who are deemed to abuse the spirit of this offer.

I thought this weird "Spirit of the bonus offer" went against the rules for accreditation. I don't even know what "the spirit of the offer" means.

 

[3Dice]

Thelawnet,

Ok,
'The Gambler's fallacy is the belief that if deviations from expected behaviour are observed in repeated independent trials of some random process then these deviations are likely to be evened out by opposite deviations in the future'

Which is what you're doing. If you lost $450 already and you take a bonus with an EV of $45, you claim the 'total EV' is +$450. This is an 'evening out', an 'opposite deviation', because when you are $450 in the hole and are taking bonus with a $45, the only way you can get to an EV of $450 is by 'evening out' your 9 previous losses. Which is obviously not correct, and is just another form of the gambler's fallacy.

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.

This is just obfuscation. Call it mean, call it EV, there is NO difference. The probability of a given event happening or not happening is no longer relevant once it happens.
..
When you're calculating the EV, mean, call it what you like, you can't say 'I know what several values in the series are, but I'll ignore that fact and pretend I still don't know'.

Again .. I'm NOT predicting anything here. I'm merely calculating how much of the bonus a player will on average cash out. The only 'predicition' is that for the game described (reel of fortune, 10 spots, 9 lose, 1 spot wins), you will on average win one in 10 games. This is a correct prediction.

Well no and no and no.

The vast majority of complaints about bonuses are actually due to casinos not wanting to payout for one reason or another. If you don't get paid, it's definitely not +EV.

Not getting paid ? Please. I'm talking serious casino's here. Not white labels ran by people who don't understand my first post, but instead think that the 'commonly' used formula is correct, and so obviously hand out bonuses that are so much player EV that they end up without funds.

This formula is perfectly correct, for those casinos that give the bonus post-wager. Such bonuses can be found at Wagerworks, Chartwell, Playtech (sometimes), and others.

That formula calculates the EV only for one machine. A machine without variance. One that pays back 95c for each 1$ bet. For all other machines its a complete bs formula. This post is all about demonstrating that.

You seriously believe that a 100% match up to $50 with WR20 is -EV ? You honestly think a casino will make money on it if players play the way I describe ? If you do - let me know - I'll give you the opportunity to run a bonus like that and 'make some money'

But anyway, I'm sure you're aware the casinos know this, and put numerous restrictions to stop this kind of thing - roulette is nearly always banned, and other games of its ilk, bet limits are set low in software, or by rules.

Roulette is allowed at 3Dice and it is in fact incredibly easy to think of a strategy that very closely aligns to my sample here.

A casino that actually allowed this kind of thing wouldn't last very long.

More typical would be a high WR, low bet limits, a long list of restricted games, and the best games all being skill-based, where players will in reality make many mistakes..... Not so profitable after all.

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.

It's a 110% bonus, so that's a 573*bonus wagering requirement on blackjack. Typicaly players play at 1.5% HA, so they need to be doing on average around 60X WR. But with a $50 max bet, that won't happen.....

It's not so simple or so easy you imply.

Again a low variance game like blackjack is the least smart thing to do. This post is about how variance influences bonuses. With a variance of 1.1418, you could not pick a worse game than blackjack.

Are you saying the 3Dice SUB is EV- ?

Kindest regards,

Enzo

 

[hitobito2005]

That formula calculates the EV only for one machine. A machine without variance. One that pays back 95c for each 1$ bet. For all other machines its a complete bs formula. This post is all about demonstrating that.

You seriously believe that a 100% match up to $50 with WR20 is -EV ? You honestly think a casino will make money on it if players play the way I describe ? If you do - let me know - I'll give you the opportunity to run a bonus like that and 'make some money'

What he's saying is that the "BS" formula is perfectly correct for bonuses which are credited after the wagering is completed, such bonuses can be found at many online casinos. This is because you are forced to complete the WR to get the bonus.

 

[Rusty]

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.

To simplify and make it a real world example, because I am not sure we are talking the same language here, we can make 1 deposit of 500+500 bonus with the same calculations and in essence what you are saying is that the first 900 yielded 0% return therefore the last 100 is expected to return 950% to make up our ev.
Your example game pays 95 to 10 with a 1 in 10 hits and the rest busts and we play 10 games at 10 units per 100 wager.
This means that you would have to hit 10 from 10 with final 100 which would have odds of 10,000,000,000/1, this makes no sense.

So as I see it your example would only be proper in a zero variance game with a guaranteed real return of 95% over the total wagered and as we know this is not reality so I am still scratching my head.

I think this is the reason Lawnet is saying this is gamblers fallacy because using your example we are predicting the future because we say 9 deposits pay 0% RTP and therefore the predicted return of deposit 10 is 950%RTP.

The ev on a single deposit of 50+50 at 95% RTP is always 45 and your formula is only applicable to any future series of deposits unless the game has memory and must return 95% over a preset amount of games.

I think this is the source of confusion (for me at least) because you appear to be applying past history and ev to future ev rather than just calculating future ev.

 

[Jufo]

So as I see it your example would only be proper in a zero variance game with a guaranteed real return of 95% over the total wagered and as we know this is not reality so I am still scratching my head.

The way I understood this is that Enzo describes a 95% return game from casino's point of view, which means that in the long term, after thousands of players have played the game, it returns a value close to 95% and its expectation is always 95%. From player's point of view there can very well be 10 consecutive losses trying for that 1 in 10 shot to win.

I guess what Enzo is trying to say is that from casino's point of view the casino is losing money by offering such a bonus with $35 EV per bonus but this $35 EV per bonus will be distributed among players unevenly and there will be some losing players as well as winning ones.

 

[skiny]

I think the idea isn't to use the formula to see what the EV will be on your current or next deposit+bonus. I think you're supposed to use it after you've either lost your deposit or cashed out to see if you're + or - EV on all your previous bonuses.

It could be interesting to see but for most people not really worth the work keeping track of your deposits and bonuses and not worth the work to figure it out. I think most people only really care if they were able to cash out this deposit. In fact I think a lot of people don't even care if they're up a little bit or down a little bit over all. It's the seemingly endless losing deposits that get to people after a while.

For some people it's a half dozen deposits, others can go dozens but there is a point for every gambler when they have lost too many in a row and say "Ok, this is getting bad now." I don't think knowing if you're + or - EV on your bonuses will change that perception.

 

[DiamondGeezer]

Enzo, a couple of points:

1) If you play on without bonus on a 95 RTP game the HE will rapidly gobble up your EV. HE is an EV gobbler.

2) It ignores the very obvious fact you could use the money on another bonus at a different casino. Your workings are reduced to rubble by the economic theory of opportunity cost.

3) There is no mention of bankroll, which is critical when EV/variance calculations are concerned.


Look I have no problem over depositing without a bonus and gambling/having fun etc. But it won't boost your EV. All it can do is affect your bankroll.

You are normally very good on this stuff but it does sound dangerously like a charter for chasing losses.

 

[thelawnet]

Thelawnet,

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.

Yes that's true for a set of future 10 sessions, but you were describing a scenario where you had played and lost 9 sessions already, and claiming that didn't affect the average for all 10.

Not getting paid ? Please. I'm talking serious casino's here. Not white labels ran by people who don't understand my first post, but instead think that the 'commonly' used formula is correct, and so obviously hand out bonuses that are so much player EV that they end up without funds.

You specifically referred to casino complaints. Clearly these will disproportionately come from casinos with bad management.

This formula is perfectly correct, for those casinos that give the bonus post-wager. Such bonuses can be found at Wagerworks, Chartwell, Playtech (sometimes), and others.

That formula calculates the EV only for one machine. A machine without variance. One that pays back 95c for each 1$ bet. For all other machines its a complete bs formula. This post is all about demonstrating that.

You seriously believe that a 100% match up to $50 with WR20 is -EV ? You honestly think a casino will make money on it if players play the way I describe ? If you do - let me know - I'll give you the opportunity to run a bonus like that and 'make some money'

Pardon me, but I thought you'd been around the block a few times, and knew that many casinos only credit the bonus AFTER you've done the wagering.

If this is the case, the variance of your game choice doesn't affect the EV at all, it merely affects the amount you could stand to win or lose. If you are bonus hunting, you will most likely want to minimise this, i.e. select the game with the lowest variance.

Roulette is allowed at 3Dice and it is in fact incredibly easy to think of a strategy that very closely aligns to my sample here.

Most casinos don't allow it. Nonethless, it's not as if you allow players free reign - you restrict bet sizes and you increase the wagering for roulette players.

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.

Not true at all. Why would you play slots at up to 10% HA, when you could play video poker games that have similar variance and a HA of <0.5%?

As for blackjack, some online casinos offer the game with a HA of <0.2% but slots with a HA of as high as 10%. Even playing through your bonus + deposit once is going to have a significant expected loss with slots, but near-zero with a good blackjack game.

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.

Well that depends. At many casinos you can play $100 or more on blackjack, or perhaps $5 on slots. High stakes table games will drastically reduce the amount you play, and because the HA is so low, it doesn't cost much to do so.

And there are less liquidity issues with blackjack. If you play $100 blackjack, you might win a few thousand. But high stakes slots could see you winning tens of thousands, and at many online casinos, that's a risky proposition in terms of getting paid.

Again a low variance game like blackjack is the least smart thing to do. This post is about how variance influences bonuses. With a variance of 1.1418, you could not pick a worse game than blackjack.

That's the standard deviation not the variance, and of a specific blackjack variant - so the last 2 decimal places can be dropped, because you can't be more specific than that for 'blackjack' (nor do you need to be).

If someone's offering a 40xbonus wagering bonus, on 1/4% HA blackjack, then flat betting 1 cent (as an example - assume you complete the wagering) will mean you retain 90% of the bonus. In what sense is that 'least smart'?

And you underestimate the effect of that variance when coupled with a high bet size. $100 hands on blackjack, 100 hands, you could win/lose $3000 or more.

And of course whereas blackjack is a known, well-documented quantity, most slots are not. Sites could be operating 10%+ HA slots and you'd never know. And of course you won't know the variance of the slots either, so you've actually got no idea whether a given strategy is a winning one with a given bonus or not, much less whether it is 'better' than say high stakes blackjack.

Are you saying the 3Dice SUB is EV- ?

It depends how you play. For many people it will not be.

 

[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.