Casino Question Maths

clickerquicklic

Has bugged me for a while would love to know answer.

I often get bonuses from casinos example 20% or 50% back on my losses up to x amount.

Typical one I get 50% back to 500 , so lose 1k and get 500 back.
My strategy is to bet 100 on 10 numbers on roulette so I am covering 10 out of the 37 numbers , only one number can come up obviously so I have lost 9 bets of 100 already before the ball lands. Question is would I be better off spinning 10 separate spins of 100 on 1 number only ,so 10 spins of covering 1/37 or 1 spin covering 10/37 numbers. If i win on my first spin I obviously stop so don't lose them 9 other spins.

Sorry if i worded this poorly - this real life problem has been bugging me for a while now and would be interested to know if there is a mathematical way to work it out.

Thanks

eoins23456

You would be better not playing roulette , the odds are always against you ..

clickerquicklic

eoins23456 wrote: »

You would be better not playing roulette , the odds are always against you ..

Not sure you read the full question with a 50% refund on losses the odds are very much in your favour.

bnt

I would want to see the fine print on that one, since if there's one rule in gambling it is that the house always wins. You open a casino to make money, not lose it. Why do you think so many are popping up in the UK now, since the regulations were relaxed?

Would they refund you half your losses after every turn of the wheel? Doubtful, but let's see what that means. There are two possible outcomes. Assuming €100 per number, payout of 35:1:
1) one of your numbers comes up, and you make €3500 on that one, minus €900 for the others = €2600 for that turn.
2) None of your numbers comes up, so you lose €1000, and they refund you €500, meaning you lose €500 for that turn.

The odds of scenario (1) are 10/37, and of scenario (2) are 27/37. To simplify the maths, lets assume 37 turns of the wheel. Statistically, then, the expected gain would be 10*2600 - 27*500 = 26000 - 13500 = €12500.

I really don't see any casino allowing that to happen, so I would want to know exactly what conditions are attached to "refunding half your losses". They might do it just once, with the aim of keeping you at the table a bit longer, so you can lose it all over again ... :cool:

PS: if not for a refund, the sums after 37 turns would give you 10*2600 - 27*1000 = 26000 - 27000 = €1000 loss.
If you won the €3500 on the first round - great, you're ahead €3500-900 = €2600.
2nd turn? €1600 up (since you lost €1000 on the first turn)
3rd turn? €600 up.
4th turn? You win €2600 but have already lost €3000, so ... you're down €400.

clickerquicklic

I make a good living from betting on sports and Casino's , don't believe all the hype house always wins , never see a poor bookie etc etc I beat the bookie with maths and some other tricks I've learned over the years.

I may have phrased the question wrong , its a difficult one to work out and I've asked a couple of people with maths degrees and they couldn't give me a definitive answer. For many reasons there are casinos that give away money 50% back on your losses to 500 , this could be as a welcome offer , a one off promotion or various other forms. Its not 50% back on every spin , its a one off welcome to my casino you walk in with a 1k in your hand and if you lose it you get 500 back , you can do what you like with that 1000, i choose to play roulette because it has more value to bet at higher odds when you get a refund on loss type promotion.

My question is what has more value doing consecutive spins or concurrent spins
What has more value , 1 Spin using your full 1000 covering 10/37 equally (100 a number) or 10 spins (100 on one number) covering 1/37 numbers ?
I can work out the value of the first part using this

((10/37) * 2600) - (27/37 * 500) = €337.84 value
But the next formula i struggle with how to work out the value of spinning 10 spins in a row 100 a number instead

bnt

clickerquicklic wrote: »

I may have phrased the question wrong , its a difficult one to work out and I've asked a couple of people with maths degrees and they couldn't give me a definitive answer.

My question is what has more value doing consecutive spins or concurrent spins
...
I can work out the value of the first part using this

((10/37) * 2600) - (27/37 * 500) = €337.84 value
But the next formula i struggle with how to work out the value of spinning 10 spins in a row 100 a number instead

First of it all, it's not such a hard question, and I don't have a maths degree. I didn't do all that well in the Statistics classes I took at university, either. There are folks on this forum with maths degrees, and they're probably too busy laughing at both of us and can't be bothered to reply. :cool:

You quoted a variation of the calculation I did for the "half your losses back on every spin" situation, but you seem to agree with me that that's not going to happen. A once-off with restrictions is more likely, as you said. Maybe you will get some refund, maybe you won't, so let's leave that out of the maths for the moment. You haven't given the exact conditions that would apply, but whatever they are, you can assume that there's a reason for it that benefits the casino. In Las Vegas you can get "comped" (free hotels & meals), but only if you're a "high roller" i.e. the casino expects to make money overall. That's what they do. They do not do charity.

By doing 10 per turn, we get the sums I gave at the end of 37 turns: 10*2600 - 27*1000 = 26000 - 27000 = €1000 loss or €27.02 loss per turn.

Do one bet per turn @ €1000, and a win (paying at 35:1) gets you €35000. The odds per turn are 1/37 to win, 36/37 to lose. So, over 37 turns, you get (1*35000) - (36*1000) = €35000 - €36000 = €1000 loss or an average €27.02 loss per turn. The same, in other words.

These are what are called "expected values" in statistical terms. It does *not* mean that that's where you will be after exactly 37 turns. The more turns, the more things will trend towards these values, in a fair contest. Now, lets say they half your loss, once-off ... you've still lost €500. You can do the maths for different numbers of turns - remember, I'm using 37 turns because it makes the maths clearer. It doesn't change the statistical outcome.

But hey, you might get lucky! And you have a system! The casinos can't see this coming, never employ mathematicians to check the odds they offer, and won't know what hit them. We can see your other posts on boards, and maybe you can score on sports betting by knowing more than other people, for example. Overall, though, I'm still right to say that the house always wins. Look at how much money Paddy Power rakes in per year: €121 million net income in 2012. Poker is another one, where people score by playing the other players, not just the cards.

But the statistics behind roulette are remorselessly logical: it's a game designed to take your brain out of the equation entirely. It is designed so that it can't be "gamed" by you. Many have tried - see http://en.wikipedia.org/wiki/Roulette#Betting_strategies_and_tactics for examples. It includes a link to a page about the "Gambler's Fallacy".

clickerquicklic

bnt wrote: »

But - as I described - that's the calculation for the "half your losses back on every spin" situation, and you seem to agree with me that that's not going to happen. A once-off with restrictions is more likely, as you said. Maybe you will get some refund, maybe you won't, so let's leave that out of the maths for the moment.

By doing 10 per turn, we get the sums I gave at the end of 37 turns: 10*2600 - 27*1000 = 26000 - 27000 = €1000 loss or €27.02 loss per turn.

Do one bet per turn @ €100, and a win (paying at 35:1) gets you €3500. The odds per turn are 1/37 to win, 36/37 to lose. So, over 37 turns, you get (1*3500) - (36*100) = €35000 - €36000 = €1000 loss or an average €27.02 loss per turn.

These are what are called "expected values" in statistical terms. It does *not* mean that that's where you will be after exactly 37 turns. The more turns, the more things will trend towards these values, in a fair contest. Now, lets say they half your loss, once-off ... you've still lost €500. You can do the maths for different numbers of turns - remember, I'm using 37 turns because it makes the maths clearer. It doesn't change the outcome.

[sarcasm]But hey, you might get lucky! And you have a system! The casinos can't see this coming, never employ mathematicians to check the odds they offer, and won't know what hit them ... [/sarcasm]

I do this for a living , i make six figures a year every year from gambling and understand expected values , I could list you 100 casinos that offer cashback on losses . I came here to ask a maths question not sarcasm about gambling and bookies always winning as I say this is what I do and how I make a living, there is marginal difference in the 2 , I've asked a mathematician to work out this problem for me based on % cashback on losses and concurrent v consecutive spins and this is what he came back with


Assume 20% refund on loss,

Compare 2 strategies, (A) 1x £200 spin and (B) 2x £100 spins.

Assume £100 per number in each case.


Value of (A)

((2/37) * £3400) - (35/37 * £160) = £32.40 value per £200 stake


Value of (B)

(1/37 * £3500) + (36/37)((1/37 * £3400) - (36/37 * £160))

£94 - £61.30= £32.53 value per £200 stake

So as you can see there is a difference , he just used an example of 2 spins there is slightly more value spinning consecutive spins. He said he hasn't had time to think of it more yet , but will get back to me when hes not busy , i pose the question here to see if anyone can come up with a definitive answer , it is not the same i'm fairly sure spinning 1 spin or 10 spins from an EV point of view

clickerquicklic

Have you read anything I wrote at all? I don't play roulette for fun or claim to be able to beat the house edge I am speaking specifically about casinos beating casinos when they offer cash back promotions , I only ever play when odds are in my favour, I'm not sure why you are neglecting that point and assuming I'm a roulette or blackjack mug every bet I make is +Ev

bnt

clickerquicklic wrote: »

Have you read anything I wrote at all? I don't play roulette for fun or claim to be able to beat the house edge I am speaking specifically about casinos beating casinos when they offer cash back promotions , I only ever play when odds are in my favour, I'm not sure why you are neglecting that point and assuming I'm a roulette or blackjack mug every bet I make is +Ev

Your numbers are still assuming refunds on every loss, and if that's really the case, then yes, you're going to make money. But I don't believe that is the case. They are more likely to be once-off refunds that do not change the odds of the game. I don't know how to make that point any more clear. That's what I did the calculations without refunds. "Assuming" is fine in theory, but could mean real trouble in practise. You need to be absolutely clear on what they're offering.

So if you only play when the odds are in your favour, but you can't calculate the odds, then I suggest you stay away from roulette entirely, and don't be fooled by "freebies". I don't care what you claim to make already. Skill in one form of gambling doesn't automatically translate to other forms, and the maths behind roulette is clear. You came to the Maths forum, so don't be surprised to get a Maths answer, and Maths is a cold-hearted you-know-what who doesn't care who you are or think you are. If you want to be told how to gamble. head back to the Gambling forum.

clickerquicklic

You have some serious issues in understanding maybe it haven't explained it properly but tried my best , I want a maths answer and you can't give it , forget about the fact of will or won't a bookie give you % losses back I'm asking for the maths answer of which method yields higher expected Value spinning concurrent or consecutive spins when you have a % back on losses . It's pure maths I want the answer too , your the one obsessing over the gambling side of things let me worry about that I can get these promotions everyday why would I list them on a public forum , I asked a pure maths question if you dont know the answer just say so

bnt

I gave you a pure maths answer several posts ago. If you bet £1000 per turn, whether all on one number or on ten (or whatever) separate numbers, you will lose an average of £27.02 per turn. To come out ahead, you would need to be lucky.

clickerquicklic

That's not the answer I was looking for though I was looking for the answer to which strategy gives higher ev out of the 2 I gave you when you have a refund on loss .

Can we agree on one thing to show we are on the same page - with a refund on loss spinning fewer numbers is much better ev than spinning more numbers , so long term you will be up much more spinning less numbers

I don't think we are getting anywhere here 😞 in fairness I probably explained it badly but I tried my best sorry if it was poorly worded.

I can understand your frustration about someone coming on talking about making money from roulette or any casino game the odds are with the house and I (like yourself ) am sick of telling people to stay away from roulette and blackjack and any sports bets that you are randomly putting on , that's why 99% of gamblers are losers overall because long term you will revert to the Ev of your bets and betting -ev over time wil only lead to one thing which is losing. I am not a roulette or blackjack mug believe me I have no interest in playing a game where I am losing ~2% every time the wheel spins .

Anyway cheers for your response it wasn't what I was looking for but I think it's more a mis understanding than anything else

fergalr

Can you be more specific about the precise terms of the refund you get?

Or just precisely define one possible set of refund terms, in order to make it possible for people to get to grips with your question?


Either that, or you just define the particular game that results from playing roulette with a refund, and ask your question in terms of it.

clickerquicklic

I think people are getting too hung up on if a casino offers this promotion or not , lets forget a casino offering it, imagine I have a friend that generously tells me he will refund half of my losses up to 500 and I go into a vegas casino for the night to play.
My thinking is I want to play as few games of anything as possible as everytime I spin the wheel on roulette or play blackjack etc I am losing money to the house edge of the game.

So optimum strategy I know is bet the hole 1k on one number on roulette , thats will result in the highest +EV over time.

Expected Value covering 1 number is

((1/37) * 35000) - (36/37 * 500) = 459euro EV

Expected Value covering a red/black

((18/37) * 1000) - (19/37 * 500) = 229euro EV

So as you can see it has a much higher EV if you cover fewer numbers but the variance is really high. As a nice balance I bet on 10 numbers , I understand long term i am losing EV over the 1 number strategy but I can't handle the variance of betting the whole 1k on one number

((10/37) * 2600) - (27/37 * 500) = 337euro EV

Every time I fill the 10 numbers on the roulette wheel with 100 euro chips I always think even if i win i am losing 9 x 100 on the other numbers , would i be better off doing 10 spins of 1 number (100 a time) or 1 spin of 10 numbers (1000 covering 10) that was my original question.

fergalr

(I share the other posters' concerns that in a real situation you generally will be losing in some way you don't realise; but lets leave that aside and focus on the abstract problem.)

Ok, so if you lose all your money at any time, you can stop playing, even if you just spun the wheel once, and get 500euro back.


What's the object of this exercise?
Its not to get highest expected value (as you've said). Otherwise you'd just make one bet.

So what do you want?

Do you want to reach a certain amount of money and then quit? If so, how much?

Or maybe you just want to get 1 win before you quit?

Or maybe you want to play for as long as possible without being 'ruined'?

clickerquicklic

fergalr wrote: »

(I share the other posters' concerns that in a real situation you generally will be losing in some way you don't realise; but lets leave that aside and focus on the abstract problem.)

Ok, so if you lose all your money at any time, you can stop playing, even if you just spun the wheel once, and get 500euro back.


What's the object of this exercise?
Its not to get highest expected value (as you've said). Otherwise you'd just make one bet.

So what do you want?

Do you want to reach a certain amount of money and then quit? If so, how much?

Or maybe you just want to get 1 win before you quit?

Or maybe you want to play for as long as possible without being 'ruined'?

Honestly I really appreciate you guys taking the time to answer, its a bit pointless though because we seem to be going around in circles , I wanted to know which holds more value spinning 1000 on 10 numbers (evenly spread) or 100 on one number of 10 spins , when you have rebate on loss to x%

I probably should have posted the question on wizardofodds or other gambling forums where I don't have to explain each detail.

I know alot of people think bookies only win but with low house edge games even 10% rebate on losses can be very valuable played the right way , the variance is the killer but there is a +EV in every bet I make with casinos.

Some stats since 2008 from casino rebates
Year - Number of casinos played - EV - Actual result (50% up only)
2008 -42-6550- 4830
2009 -60- 8160 - 5440
2010 - 51- 6840 - 7170
2011 - 114 - 9560 - 8890 (started doing 25% offers also)
2012 - 132 - 10,150- 12445 (included 20% offers)
2013- 145- 12340 - 21269 (done some 15% offers)


Anyway thanks guys for taking the time to reply , power of maths is amazing will beat any tipsters or gambler over time.

fergalr

clickerquicklic wrote: »

Honestly I really appreciate you guys taking the time to answer, its a bit pointless though because we seem to be going around in circles , I wanted to know which holds more value spinning 1000 on 10 numbers (evenly spread) or 100 on one number of 10 spins , when you have rebate on loss to x%

If you follow the strategy of "100 on one number of for 10 spins" what happens if your number comes up on the 2nd spin? Do you continue playing, or do you quit?

That is a decision you have to make, as you play the game. What you decide in that situation is going to affect how profitable the game is.

More specifically, what you would decide in that circumstance depends on what your objective is.

We can't specify the result of every set of decisions you could possibly make.
So, if you want an answer to your question, you have to tell us a little bit more about what you are trying to do.

Because, you have clearly said you are not trying to achieve the highest expected value, so we can't just assume that.

clickerquicklic wrote: »

I probably should have posted the question on wizardofodds or other gambling forums where I don't have to explain each detail.

Unless they have psychic powers, and can magically deduce what you are going for, you are going to have to answer the same question on that forum.


Edit: I appreciate you don't want to get into a frustrating conversation about whether you really can get a 50% payback if you lose - fine, understood. But you still need to tell us something about what you want to optimise for, in order to constrain the question so that its simple enough to give you an actual answer.

clickerquicklic

Sorry sir , you see I made the assumption that you's would know I'm going to stop after a win

The most +ev way is one number but the % chance of bust is very high I could go long periods without hitting my 1 number that's why I choose 10 numbers a balance between decent EV and lower % bust rate , I'm spinning 1k or 100 a time until a win - why I started this question is imagine I spin 100 and win on first spin then I walk away with 3500 win on second spin 3400 third 3300 and so on , doing 10 numbers on one spin only one can hit so I am losing 900 if I win so +2600 is max I can win