BJ Bonus Clearing - Error in Reasoning?

[HeldDerArbeit]

First of all,

I'm new here and a bloody beginner equipped with some reasonableness and logic and the hope you can help me with the following:

An Online Casino offers a 50 % Pay-in Bonus up to 200 EUR. In order to pay out the bonus you have to bet it 20 times. Meaning 200 EUR x 20 = 4000 EUR must be bet before payout.

If you play the perfect basic Black Jack Game (yes, Black Jack is surprisingly allowed for clearing the bonus) - the house edge of the casino is only around 0.41 %, correct?

As I have to bet all in all 4000 EUR (in order to clear the 200 EUR Bonus) the expected value is around 3984 EUR - meaning I will clear on average (if I played infininitely) 200-(4000-3984)=184 EUR, correct?

As volatiliy is the big enemy and if one is broke you cannot recover I also paid attention to a risk of ruin table:

Let us assume we clear the 4000 EUR with 400 hands, meaning the average bet size is 4000/400=10 EUR per hand.

The number of betting units is in this case 600 (as 400 Payed-in +200 Bonus) / 10 = 60

If we look at the table the value of 60 means the probability to go bankrupt should be somewhere in-between 1-2 %.
source: http://wizardofodds.com/blackjack/appendix12.html

Do you find any problems within this calculation?

What if I play 4-5 hands the same time against the dealer? Does this mean I need to make some changes in my calculation?

Thanks a lot for your help!

 

[UK-21]

You've done your sums. Just bear in mind the more hands you play, the closer to the EV you'll get. So why not play 4000 hands @ EURO 1.00 rather than 400 hands @ EURO 10.00? You can speed things up by playing mult-hands if possible, which won't affect the long term EV.

If you've found an online casino that allows bets on BJ to contribute 100% towards the wagering requirement you've struck gold if online BJ is your thing. The one a friend of mine played not too long ago only allowed 10% - which made it mathematically impossible to get to a point of withdrawing your winnings without having positive variance for 40,000 hands.

Viel Gluck!

 

[Elhombre]

Maloche

Versuchs mal' mit ehrlicher Maloche, looooool

Held der BJ tables

Eh.

 

[HeldDerArbeit]

Thanks UK-21,

Nice if a streak joins you while clearing

But I have to admit - it's hard just to stick to your strategy when you're even 50 % down sometimes - but obviously it pays out - math and probability is on your side...

Does anyone know which other sides offer interesting bonus which can be cleared (100 %) with BJ - with a positive EV and are trustworthy?

 

[UK-21]

Kein positiv EVs mit online Spielen - sie sind alles negativ. Es kommt einfach darauf bei wieviel . . .

"Held" - ein neues wort fuer mich. Aber ich verstehe nicht "Maloch" - es ist in meinem Woerterbuch nicht? Erklaren Sie bitte.

Deutsch nicht zu gut, eh?

 

[Nynefingers]

Just wanted to point out something I learned a few years ago in my bonus-whoring days...This is more interesting from a theoretical perspective than a practical one, but depending on your bankroll/risk tolerance, it can start to matter somewhat.

While volatility is generally considered a bad thing (for good reason), there are some positive aspects of volatility when it comes to clearing online bonuses. Specifically, if you bust out at a particular casino before you clear the bonus, you do not have to continue playing a negative EV game. I know it sounds backwards to be happy to bust out on occasion, but volatility can be good if the total deposit required is small enough relative to your bankroll. That is how you control the "real" volatility of your bankroll.

As an extreme example, imagine if you could play the bonus you mentioned, but you started off with a coin flip for the entire 600 Euros. Half the time you would lose it all and lose your 400. The other half, you win 600 Euros and play out your bonus with an expected loss of 16 for an end result of 1184, or a profit of 784. So your overall EV is 0.5 * -400 + 0.5 * 784 = 192, which is a slight improvement over the 184 profit of doing it the "normal" way. While this example takes it to the extreme, it demonstrates that higher volatility (IE higher bets) will provide a slight improvement to your EV, but the improvement comes specifically *because* you will sometimes bust out and therefore not play as many -EV hands. If the total required deposit is sufficiently small, this is a way to improve your EV and also improve your hourly rate since fewer hands are required.

You might notice that this is similar to the way "sticky bonuses" are played, and it is a less extreme variation of a similar idea.

I also wanted to comment on playing multiple spots. I do not recommend it when playing online because I believe it does not provide an improvement in either playing speed or variance. On all of the software that I used to play, I was always heads up against the dealer, so other players aren't an issue. The software is also much quicker than a live dealer, so the time required to bet through a total of $X isn't significantly shorter either way. You'll get lower variance by playing two rounds of one hand than one round of two hands at the same bet size, and it will take about the same amount of time. If anyone has any counterarguments for playing 2 spots, I'd be curious to hear them, but I can't figure out any way it would help when just trying to clear bonuses at an online casino.