Please check my math on this bonus-hustle technique

[EasyRhino]

Wasn't sure where to post this. The question is in the context of online casinos, but it's blackjack-specific, kind of a reverse risk of ruin calculation.

Let's say I'm hustling an online casino bonus. I get a $100 bonus on a $100 deposit, so my starting chipcount is $200.

I like to run up the balance on these on big blackjack bets before grinding out the WR. In this hypothetical case, I would bet $100 per hand.

Now, if I keep my bets at $100 per hand - win or lose- what are my odds of doubling the chipcount to $400 before busting? My assumption is that they are roughly 50%.

Or, if I stayed with $100 per hand, what are my odds of tripling the chipcount to $600 before busting? Again, my assumption is that they are roughly 33%.

In other words, it's a fair tradeoff between the target chipcount and the odds of reaching it.

However, I begin to wonder if the cumulative effect of playing multiple "small" hands to reach that total area hurting my odds worse than I thought.

 

[halcyon1234]

Wasn't sure where to post this. The question is in the context of online casinos, but it's blackjack-specific, kind of a reverse risk of ruin calculation.

Let's say I'm hustling an online casino bonus. I get a $100 bonus on a $100 deposit, so my starting chipcount is $200.

I like to run up the balance on these on big blackjack bets before grinding out the WR. In this hypothetical case, I would bet $100 per hand.

Now, if I keep my bets at $100 per hand - win or lose- what are my odds of doubling the chipcount to $400 before busting? My assumption is that they are roughly 50%.

Or, if I stayed with $100 per hand, what are my odds of tripling the chipcount to $600 before busting? Again, my assumption is that they are roughly 33%.

In other words, it's a fair tradeoff between the target chipcount and the odds of reaching it.

However, I begin to wonder if the cumulative effect of playing multiple "small" hands to reach that total area hurting my odds worse than I thought.

Hrm.. I'm hoping someone will double check my math on this one...

If you were to do this hustle, you're obviously taking on a huge risk of ruin. With 200 units at 1, you should be able to normally get a ~1% (or less) RoR, depending on how many hands you want to play:

http://wizardofodds.com/blackjack/appendix12.html

Of course, if you need play thousands of hands, at ~500 hands per hour, you need a lot of time. I take it you are trying to reduce the amount of time you'll be spending at the online casino?

Your odds look about right, *roughly* 50% (or 33.3% for 3 hands). I'd think that it might be a bit less, since if things start to go south, you won't be able to afford to split or double (which is where some player advantage comes from). That might drop it below 50/50.

If you are going to hedge your whole bankroll against a couple tries, you might want to do Single-Zero Roulette or Mini-Baccarat instead. Both of those have near 50/50 odds, I'd guess closer to 50/50 then a BJ hand you can't double/split.

My guess would be that the EV of this strategy is lower than flat-betting $1, since the risk of busting out completely is significantly higher.

 

[bluewhale]

hey easy, there was a thread about a month ago, http://www.blackjackinfo.com/bb/showthread.php?t=719&page=3, which talked about what you're asking. if you got some time, go through it, it is quite interesting. you can see that i initially didn't believe mick, but he did prove his point.

 

[EasyRhino]

Victory!

Whale, I had remembered that long thread, and I think I was thinking that the "bet big or go home" logic only applied to sticky bonuses, but I had to work out for myself that it also worked better for cashable bonuses. However, I was still thrown if my assumptions over the odds of reaching a certain bankroll target were correct. The link to the Arnold Snyder article said I was pointing in the right direction (doubling ~50%, quadding ~75%).

However, the real kicker was this link:
http://www.qfit.com/blackjack-calculator-c5.htm

While I guess it's meant for card-counting, you can set it up like this:
Starting bankroll = 2 units
Goal = 6 units
Win rate = -1 (losing 1 hand per hour assumption with basic strategy)

... and it gives you about 66% as the result. Sweet.

Nice to know it's that my gameplan wasn't off, even if I had hit a stretch of bad luck lately :cry:

 

[aka23]

I didn't read through the full thread, so my questions may be answered there. I see the default SD per 100 hands is ~28 in the calc. That's much higher than I expected. The Standard Deviation per hand of BJ is about 1.1 to 1.2 with most online rules. Wizard of odds lists 1.2, I believe. This makes the Standard Deviation per 100 hands 11 to 12 (multiply by sqrt of num hands). How is the SD of ~28 num calculated?

=========================================================

Answering the original question, a near coin-flip game with large bets, you can roughly approximate the chance of reaching the goal as init bankroll/goal. To get a more precise answer, you need to include the house edge of the game. Note that the house edge may not be standard BJ house edge. The house edge would increase by ~2% for a full-bankroll bet (no double or split option), and may increase by up to 0.2% for a half-bankroll bet (no double after split or resplit option). If large bets are not used, the house edge loss increases from the long wagering .

=========================================================

The big bet strategy is beneficial for any cashable bonus in which a large portion of the bonus is lost during wagering. As you increase the risk of busting, the average wagering and HE loss through wagering decreases. The change in EV from a no-HE coin flip double can be estimated as Increased EV = (Standard EV + Bonus)/2. For a triple rather than a double. you'd change the multipliers/dividers as appropriate.

 

[dacium]

You are correct about the accumulating factor.

The house edge applies to each bet made, not your total money. So if you bet $100 and the house edge is 0.5% you loose 0.5% on average.
But if you make 10 bets of $100 you now expect to loose a total of 5% of your $100.

 

[EasyRhino]

Yep, the accumulating factor killing me is what I was worried about. However, I'f i'm using the "odds of reaching goal" calculator correctly, it's not a big deal. Although, I guess if I was likely to be churning through blackjet bets a ton (like, playing through my initial chipcount 5x+), I might be better off with a spin on a single zero roulette wheel with a bet customized for the desired payout (barring that roulette is often forbidden from bonuses).

 

[aka23]

For the triple bankroll example, my simulator gives the following estimates:

No House Edge -- 33.3% chance of reaching goal
Bet size = Bankroll/5 -- 32.5%
Bet size = Bankroll/10 -- 31.5%
Bet size = Bankroll/20 -- 29.3%
Bet size = Bankroll/50 -- 24%
Bet size = Banrkoll/100 -- 14%

So once you have bets smaller than bankroll/10, the house egde loss from the wagering starts becoming a good-sized influence. Results of bankroll/2 or less vary with specific rules.

 

[EasyRhino]

aka, that simulator did not have the bet being resized after wins, did it? Just want to make sure.

 

[aka23]

The initial bet size is constant. Some more information is listed below, to confirm reasonable values.

Bankroll/5 -- Average number of hands = 41, HE lost to 41 hands = (41/5)*0.4%=~3%, Expected decrease from 33.3% = 3/3 =~1%, Actual decrease = 0.8%

Bankroll/10 -- Average number of hands = 156, HE lost to 156 hands = ~6%, Expected decrease from 33.3% = ~2%, Actual decrease = 1.8%

Bankroll/20 -- Average number of hands = 600, HE lost to 600 hands = ~12%, Expected decrease from 33.3% = ~4%, Actual decrease = 4.0%

Bankroll/50 -- Average number of hands = 3600, HE lost to 3600 hands = ~29%, Expected decrease from 33.3% = ~9.7%, Actual decrease = 9.3%

 

[EasyRhino]

After getting through an initial stretch of sucky variance, I've converted and realize that balls-out wagering is the way to go (well, 3x or 4x target is "balls-out") to me.

When computing the EV of a bonus, I generally compute it per bonus. However, there's a lot of RTG's out there that offer multiple stacks of bonii. These are friggin sweet, as you can generally keep trying until you hit one, and... something I didn't really realize, but the EV's of the bonuses tend to add to each other.

In other words, if you have four bonuses, with an EV of $100, and you play four of them (bust first 3, cash out on 4), you're probably going to end up with a profit of around $400, not $100. I guess it's a "duh" moment, but I didn't notice until there seemed to be too much money in my neteller account.