You took the bonus - now what?

[Nomad]

Based on a 10,000,000 trial simulation, we get an average final balance of $119.65. Ths is a $69.65 profit on something that appears to have no advantage!

Thanks for running the simulation. I agree that, in many cases, the more chance you have of busting out, the higher your EV, even though this is counterintuitive. Would it be possible to re-run the simulation using $300 as the starting point to see what your expectation is if you double on roulette? You would have a $300 starting balance 18/38 times and $0 the rest. Also, what about doubling twice, which gives you $600 on 324/1444 trials and should give you a slightly higher EV also. Not sure how these will work out with the pay table you described.

My personal preference would be to create variance in the doubling phase and then look for the lower variance slots to try to come closer to guaranteeing a profit (for the times I didn't bust when doubling).

 

[chalupa]

I've thought about this some more and I can see some of the points in defense of the slots strategy.

But I think the problem is still that you aren't getting maximum leverage of the casino's money at a reasonable house edge.

When you bet it all on roulette, you are getting ALL of the casino's money on the wheel, all at once, and are paying the house edge only once, at a relatively reasonable 2.70%.

Contrast this with slots, where you are subjecting yourself to a 5% edge repeatedly with smaller amounts. This is a sure-fire recipe for ruin, with the remote exception of hitting a jackpot or a series of smaller wins.

The comparison of 1.2% for slots vs 1.3% for roulette chance of hitting a $10,000 target is interesting if it's correct... I'm not quite sure that the slots have that "good" of a chance given the signficantly higher house edge. But in any case $10,000 is of course a realllly longshot target. Roulette allows you to choose a more realistic target.

By the way... repeatedly doubling your $150 at roulette would be a bad way to shoot for $10,000 because (just as with the slots) you subject yourself to the casino edge repeatedly. A better strategy would be to put your $150 on 20 numbers, then take your $270 win and slap it all on one number for a $9,720 win. This is a higher win than the $9,600 acheived by doubling, and with a better chance of success -- 1.46% instead of 1.33%.

But if you really want the best shot at a huge payoff (greed is good!), I think your best strategy may be video poker. Bet as much as you can on multi-hand Jacks Or Better, and then hammer that double down button until the desired result is achieved. The advantage of this strategy is that the double-down bet has a 0% casino edge.

 

[winbig]

Looks good on "paper", but in any online casino you're not going to be able to cover 20 numbers on $150 ($150/20 = $7.50)...The max numbers you could play to keep the bets the same across each number is 15. That increases your win to $350 instead of the $260 if that number hits, but lowers the odds considerably.


For 20 numbers, the closest you could come is changing the bet size for different numbers; but then you're totally messing with the % depending on which number and what size bet actually hits.

 

[chalupa]

So you put $7 on ten of the numbers and $8 on the other ten, and if you win the subsequent 37:1 shot you are a happy camper either way.

The example was just to show the mathematical advantage of betting it hard and fast.

You could also do it in reverse -- $150 on one number, then $5400 on 20 numbers -- to get around the rounding issue. Same payoff, same chance of success.

A bigger problem in practice is probably whether you can find a casino to allow that much action on a single spin.

I think you are more likely to be able to come close with a strategy where the last bet is a long-shot rather than the repeated doubling strategy. I'm not sure if there are online casinos that allow you to put $4,800 on an even money bet. Maybe they do, I've never tried.

 

[winbig]

So you put $7 on ten of the numbers and $8 on the other ten, and if you win the subsequent 37:1 shot you are a happy camper either way.

The example was just to show the mathematical advantage of betting it hard and fast.

You could also do it in reverse -- $150 on one number, then $5400 on 20 numbers -- to get around the rounding issue. Same payoff, same chance of success.

A bigger problem in practice is probably whether you can find a casino to allow that much action on a single spin.

I think you are more likely to be able to come close with a strategy where the last bet is a long-shot rather than the repeated doubling strategy. I'm not sure if there are online casinos that allow you to put $4,800 on an even money bet. Maybe they do, I've never tried.

True True True....all of it, lol

Just checked solomons, and theirs is $250 max. I'm sure most places are about the same - you'd need VIP status to be able to make it work.

 

[sirius]

By the way... repeatedly doubling your $150 at roulette would be a bad way to shoot for $10,000 because (just as with the slots) you subject yourself to the casino edge repeatedly. A better strategy would be to put your $150 on 20 numbers, then take your $270 win and slap it all on one number for a $9,720 win. This is a higher win than the $9,600 acheived by doubling, and with a better chance of success -- 1.46% instead of 1.33%.

It isn't that much of a difference even though when you win, the wagering is approaching 10k for the doubling method but far less in your method (although it's actually the average wagered amount that determines the odds of success). If you aim for a target of x times your starting bankroll, if the game is high variance enough or you can bet high enough, then the chance of reaching x is almost the same whatever the house edge is and this is especially true if you can minimize the average amount wagered to get there. The chance of success in your example is around 10% higher and will affect the average final bankroll by this much too. The effect on EV depends on the ratio between the bonus and deposit. So if you had a high percentage bonus, it will affect EV to a similar degree to the effect on the bankroll.

There is a fundamental difference between the strategies. In Slots only, you cannot aim for a specific win but are playing at a level which minimizes the amount wagered to maximize EV (at the 'expense' of high variance). In the other strategies, you have a specific aim to reach and it's an 'all or nothing' approach. In both, the only thing that really matters is the average wagered amount and this actually determines your EV. In the 'all or nothing' approach you then still have to play the slots wagering in full and this lowers EV further!

[$50 deposit $100 bonus]
Both 'all or nothing' roulette strategies (either you win or you lose it all) :
1: doubling strategy (which is not as good)
0.0133*9600 + 0.9867*0 = $127.68 which is an EV of ~$77.68

A loss of $22.32 which (due to the house edge) means an averaged wagered amount of 37 times that = $826 wagered on average per attempt.

2: strategy you gave to minimize wagered amount:
0.0146*9720 = ~$141.91 which is an EV of ~$91.91 (about 18% more EV due to the 100 bonus on the 50 deposit)

A loss of $8.09 which is an average wagered amount of $299

Without a house edge, you would have a ~1.56% chance of reaching 9600 so the house edge doesn't affect the chance of success too much but the EV can be affected more than this depending on the bonus/deposit ratio. You may think the $14 or so difference ($78 v $92 profit due to the differences in the wagered amounts) is a lot, but the variance will be very high so it actually isn't significant. With the maximum EV I think there is actually more variance due to the reduced number of bets and lower average wagered amount but I'd have to calculate the average bet size to be sure.

Now you will still have to play the slots but the EV of your bonus has now been reduced significantly playing roulette!! If you have boosted your bankroll, you will on average now wager the full amount each time and lose the bonus in the slots wagering. This will bring the average wagered amount up and in turn lower your EV even further but the amount of difference depends on the chance of success of boosting your bankroll in the first place. If w is the slots wagering requirements and s is the chance of success in boosting your bankroll, then s*w will be what is needed to be added to the above average wagering requirements and from there you can easily calculate the final EV of the bonus. The downside of having to play the full wagering requirements in slots whenever you succeed in boosting your bankroll is that you will have to make the chance of success of boosting your bankroll extremely low (such as in the above example when aiming for nearly $10k) to make this effect negligible on the final EV.

If you just played slot in the first place, you can do whatever you want to minimize the wagered amount (i.e. play large coin sizes and more lines) but due to the extreme variance, you will probably usually wager in the hundreds even playing average bets. When you win, you will only be wagering up to the WR but in the other strategies you will always wager even more (the 'boosting' wagers) and the average win in the slots-only strategy, when you don't wipe out, will also likely be in the thousands. This will mean that the average loss (you can calculate this from the average wagered amount) will be similar to the roulette calculations and in effect it is no different than boosting your bankroll using roulette but with the roulette method you have to further erode the EV playing the full WR in slots. That's why the method is flawed. Don't you think it would be best just to play slots?

 

[chalupa]

With the maximum EV I think there is actually more variance due to the reduced number of bets and lower average wagered amount but I'd have to calculate the average bet size to be sure.

Since you are in both cases "going for broke", the result is either $0 or approximately $10K. Therefore the variance will be LESS with the higher EV, since it also has a higher percentage chance of winning.

------

I understand (and hadn't considered before some of this thought-provoking debate) what you are saying that if you first go-for-broke with roulette you are always (upon success) subjected to the full slots wagering requirements.

However, as you point out, this is also true for slots (upon success), if you get lucky and win the jackpot.

So if you "need" a $10K slots jackpot to survive, then it seems to me you have to decide if it's more likely that you'll hit that $10K playing out your meager bankroll on slots, or going for broke on a lower house edge game like roulette.

Using the previous assumed numbers for slots and my improved roulette method, the chance of hitting that $10K is 1.2% for slots vs 1.46% for roulette. That is a (relatively) HUGE difference.

So... going for $10K roulette win vs $10K slots jackpot... seems like advantage to roulette.


But I think more importantly, roulette allows you to make money on a more consistent basis. There is no way to do this with the slots-only approach.

Again using the previous numbers, a slots-only approach was estimated to have only a 0.2% chance of not busting out!

With the roulette-first approach, you can adjust your chance of a successful cashout by choosing your initial target, something that slots (with a huge fixed jackpot) does not allow you to do.

Lets say you shoot for a $900 target with roulette first, with a 16.2% chance of hitting it. You then play it out on slots, giving you (I'd guess) something like an overall 15% chance of cashing out with a decent chunk of change.

Yes, you have to suffer the full slots wager requirements, lowering your long-term EV somewhat.

But... making a good (positive expected value) bet with a 15% chance of getting something out, is looking a whole lot better than a somewhat more positive expected value bet with only a 0.2% chance of success.

Sure, I'd take the 0.2% approach if I was convinced (still am not ) it was better... and I could repeat it about 100,000 times.

But since we are talking about bonus hunting, at only 0.2%, you could go a LIFETIME without ever cashing out.

 

[nafanny29]

I think we should rename this thread to "You got the maths degree - now what"

Seriously though very interesting stuff

 

[sirius]

Since you are in both cases "going for broke", the result is either $0 or approximately $10K. Therefore the variance will be LESS with the higher EV, since it also has a higher percentage chance of winning.

You are correct. It is just the success or failure odds in each case (binomial) with no other outcomes considered so the playing method won't affect the variance (the only difference is from the slight difference in the odds). If the probabilites weren't so low, you would be able to approximate the binomial (or any distribution) to a normal distribution after a suitable number of attempts but it's not feasible for such a low chance of success (unless you can play it hundreds of times) so you will have to use the binomial equations and the numbers are not going to be nice at all.

------

I understand (and hadn't considered before some of this thought-provoking debate) what you are saying that if you first go-for-broke with roulette you are always (upon success) subjected to the full slots wagering requirements.

However, as you point out, this is also true for slots (upon success), if you get lucky and win the jackpot.

So if you "need" a $10K slots jackpot to survive, then it seems to me you have to decide if it's more likely that you'll hit that $10K playing out your meager bankroll on slots, or going for broke on a lower house edge game like roulette.

Using the previous assumed numbers for slots and my improved roulette method, the chance of hitting that $10K is 1.2% for slots vs 1.46% for roulette. That is a (relatively) HUGE difference.

So... going for $10K roulette win vs $10K slots jackpot... seems like advantage to roulette.


But I think more importantly, roulette allows you to make money on a more consistent basis. There is no way to do this with the slots-only approach.

Again using the previous numbers, a slots-only approach was estimated to have only a 0.2% chance of not busting out!

I think this was misinterpreted. The chance of going bust was said to be 98.8% I think so success was actually 1.2%. This was actually not the chance of going bust, but the chance of the jackpot! It was said later that it wasn't anywhere near as bad as that because of other wins (even though the example slot only had a few different payoffs).

With the roulette-first approach, you can adjust your chance of a successful cashout by choosing your initial target, something that slots (with a huge fixed jackpot) does not allow you to do.

Lets say you shoot for a $900 target with roulette first, with a 16.2% chance of hitting it. You then play it out on slots, giving you (I'd guess) something like an overall 15% chance of cashing out with a decent chunk of change.

Yes, you have to suffer the full slots wager requirements, lowering your long-term EV somewhat.

But... making a good (positive expected value) bet with a 15% chance of getting something out, is looking a whole lot better than a somewhat more positive expected value bet with only a 0.2% chance of success.

Sure, I'd take the 0.2% approach if I was convinced (still am not ) it was better... and I could repeat it about 100,000 times.

But since we are talking about bonus hunting, at only 0.2%, you could go a LIFETIME without ever cashing out.

The 0.2% chance is wrong. You could easily make it 20% or more chance of not busting or anything you like with slots too by adjusting betting levels. Having a high chance of success defeats the purpose of this method which is to maximize EV. You should try to bust as often as reasonably possible, otherwise the method obviously won't work as well!

If you increase the odds of hitting the target in roulette (by lowering the target), you will reduce the overall EV in the opposite way to before. With this roulette method, not only will you be reducing the EV playing the roulette but you will then reduce the EV further when you win because the full wagering requirements need to be played through on slots. Usually, if playing to maximize EV, the main loss in EV is in the 'booster' wagering requirements but if you lower the target, the most EV is taken from the increased wagering in Slots. For a 16.2% chance of success, for the $3k wagering on a 5% slot edge means you will lose a further .162 * 3000 *0.05 =$24.3 of EV on top of the EV loss going for the roulette target. The slot method will have exactly the same EV loss for successes (assuming the playing method will create the same 16.2% chance of wiping out) and no further wagering is required.

The further wagering in roulette will lead to a further EV loss. 0.16216*900= 145.944 so your 16.216% chance of reaching $900 will mean an extra $4.05 lost in EV for the roulette method ($28.35 altogether). This means $150 (37*4.05) on average wagered on each roulette attempt (there are other ways to get there too but it would mean more wagers and slightly different odds). We can ignore the wagered amounts on slots for the successes because it is the same for both methods ($3000 is wagered 16.2% of the time on both the slots-only and the roulette methods) and adds the same $24.3 loss to the slot-only method EV.

This just leaves the average wagered amount in the slots method excluding the times when you win. Due to the higher house edge it would actually have to be around $96.66 wagers (on non-successes) on average to have the equivalent EV as the roulette method ($4.05/[0.838*0.05]). Obviously this isn't possible but it doesn't mean playing slots is a bad idea with a 16.2% chance. As long as you can keep it down (remember this is the average wagers for the times when you don't succeed in completing them), you will keep most of the bonus. A quarter of the bonus is gone anyway due to the chance of success being set quite high (this is nothing to do with which method you choose).

To play it properly to maximize EV would be to minimize the chance of success even more (higher target) and both methods would then approach a similar EV because more roulette wagering will be needed in that method to reach the target (low table limits will increase the amount needed to wager) so more can be wagered in the slots to have the same EV result and the EV difference between the methods should reduce.

The chance of success is really dependent on the variance of the slot which can also be manipulated with changing bet sizes. It's hard to say what a 16.2% chance of not busting in slots will mean in terms of average total amount wagered but it shouldn't be too many times the bankroll.

 

[chalupa]

Having a high chance of success defeats the purpose of this method which is to maximize EV. You should try and bust as often as reasonably possible, otherwise the method obviously won't work as well!

In the theoretical math world, yes you would always maximize EV. In the real world I'd prefer to cash out now and then.

Which would you rather bet $100 on if you could do it once per day?

A. Coin flip for $250 if it comes up heads (EV=$25)
B. Million-to-one shot to win $126 million (EV=$26)

If you choose "B" with a superior EV, let me ask you again in five years... after you've refinanced your home a couple times. I'll drive over in my new Mercedes (vanity plate CNFLIP) and we'll do lunch.

(Yes, in 0.18% of parallel universes* you can come see me in your Learjet. In which case YOU are buying lunch, you lucky bastard! )

The 0.2% chance is wrong. You could easily make it 20% or more chance of not busting or anything you like with slots too by adjusting betting levels.

Ok, it's 1.2% not 0.2%, my mistake.

But how in the (real) world can you obtain a 20% chance of success with slots in this example?


* 0.18% = 1 - (1 - 1/1,000,000 odds) ^ (365 days * 5 years)