LG John

Quite simply I want to know how to calculate cumulative probability. This relates to the standard European roulette table (i.e one zero) and the odds of an event happening over and over. Firstly does anyone know the exact odds of betting two thirds - from memory you've got a 35% chance of losing and a 65% chance of winning.

More importantly how do you calculate the percentage chance of losing 2,3,9, 100 times in a row?? Again, I seem to recall it being something like .35x.35x.35x100 for 3 times loss in a row which would be 4.28% - This doesn't seem likely though because I've seen a fair few runs bigger than that against me on the thirds.

Reasoning & Logic: As well you know I like a wee gamble but only when its with money I've already won of other people and when the odds are as close to good as I can get so there is no need for the 'saxo you'll empty your life down the drain' posts I have developed a method of playing roulette which combines a number of well known systems and techniques with a mixture of my own ideas and I believe on an online environment it might be possible to win more sessions that not, but I'd like to do mathematical testing - hence the post

P.S. No I won't share my method because at first glace it looks like it 'must' be a winner and I don't want people being silly until I've tested the maths, tested it on play for fun and then tested it for real money. After all that if it works (unlikely) I'll share it happily

P.P.S I also understand that in a pure maths sense with each individual spin of the wheel you have a 35% chance of getting done and that the previous spin or 100 spins makes no difference to that percentage

P.P.P.S I also understand that the percentage chance of a ex-saxo driving, planning officer from edinburgh cracking the roulette wheel when some of the best brains in the world have tried and failed is about 0.00001%

ProperCharlie

just keep multiplying the probabilities.

e.g. to throw a 6 is a probability of 0.16666666 etc
two 6s in a row is 0.16*0.16 = 0.0256 etc

sorry if this doesn't answer your question - i got distracted half way through the title of your post...

milo

morning

remember that losing at least 3 times in a row COULD be losing on the first, second OR third time.

so:
.35 + (.35 x .35) + (.35 x .35 x .35)

in other words.. prob of losing on first spin (and then you stop betting) + prob of losing on second (ditto) + prob of losing on third.

if u only care about the prob. of you losing EXACTLY three times in a row, then your maths is accurate at (.35)^3

milo

p.s. gambling is not the best thing to do if u have a "dont care about anything attitude"

p.p.s. if you put this much thought into your weight lifting, you'd be making ronnie coleman look scrawny by now

OllyK

Think you have just answered your own question. The result of the previous event has no bearing on the subsequent ones. If you were to have remove the number that came up last from the wheel before the next spin, then the probablilities would differ.

ProperCharlie

but that doesn't change the fact that the probability of something happening many times in a row is different (less) than the probability of it happening once.

e.g. heads not tails is 0.5. heads followed by heads is 0.25. heads heads heads is 0.125 etc.

LG John

Cheers for the explanation but I still think I'm going wrong - maths isn't my strong point - nor weightlifting

Lets assume the first spin my odds of losing are 35%, the next (always mutiplying the last no by .35 here) is 12.25%, the next is 4.28%, the next is 1.5%, the next is 0.5%, the next is 0.175%, the next is 0.06% and so on. Am I therefore correct in saying that if you bet on the first 1/3 (no's 1-12 and of course zero) NOT coming up then the odds of having 7 spins in a row against you are only 0.06% (i.e. similar to snowballs chance in hell!). Is this REALLY the acutal odds of this occurance happening?? Does anyone regard 0.06% as the sort of event you'd see in a week, month, year, 10 years. Is that frequent??? Assuming for the MAXIMUM table bet you can possibly place to cover the other two thirds then you could withstand (starting bets of £5 per third) a run of 9 spins against you which I make as 0.00735% which if I'm playing with other peeps money I can live with frankly!!

I must have screwed the maths up

As a note of interest I make the probability of 10 head (on a coin) in a row as 0.04% and I have (when testing probability with a coin) seen runs this long and longer if I recall!! Freak coin or freak occurance?

ProperCharlie

i think your calculator is fooked

mine says that 10 heads in a row (0.5*0.5*0.5 etc to 10) is 0.0009765.

milo

essentially your maths is correct (although for your coins example you've done a run of 11, not 10)

the odds of 0.06 is right for a run of 7 35% chances. this is the actual probability given a large sample - in other words, given a large enough sample you would expect 1 run of 7 losses in every 1667 spins.

given that:
* your scheme probably makes a small average win per spin so you need a LOT of spins to make a lot of money
* you don't have access to unlimited money, so the 7 in a row will bugger you
* you will end up spinning considerably more than 1667 times

so you WILL lose

you can see why the bookies really do love people who try the "law of averages" schemes. a lot of people think bookies will ban people trying these schemes.. in fact they love them.

law of averages schemes are saying "eventually i will have a win - the law of averages says so". unfortunately the law of averages also says "eventually you will have a run of 7, 10, 10000 losses against you".

milo

further to this:

the prob of heads/tails is 50/50.

what you have to remember is that although 10 heads in a row is small... IT IS THE SAME PROBABILITY OF ANY OTHER RUN OF 10 since it's 50/50.

so:

h,h,h,h,h,h,h,h,h,h is just as likely as

h,t,h,t,t,h,h,t,h,h

ProperCharlie

milo, i agree with what you are saying except: - how is a run of ten heads 0.04?

1h = 0.5
2h = 0.25
3h = 0.125
4h = 0.0625
5h = 0.03125
6h = 0.015625
7h = 0.0078125
8h = 0.0039062
9h = 0.0019531
10h = 0.0009765

where am i going wrong ?

LG John

I was using the poxy windows calculator which sometimes misses a mouse click Milo, how do you relate 0.06 to a loss once in every 1667 spins? I'm aware of the 'eventually' it'll happen thing but I also have a method to hopefully offset that. In 1667 spins there will also be a lot of runs (and longer ones) that will be in your favour and you can take advatange of those by doubling your winnings up Another element is sessions play where you'd probably cut your losses for the day well before such a nasty run against you. As I said, rest assured I will NEVER do this with my own money earned from 9-5 working - only what I made playing the system last night and my poker winnings (i.e other peeps money). Still playing with maths for now though

milo

it isnt

like i said to saxo "essentially your maths is correct (although for your coins example you've done a run of 11, not 10)"

so...

10h = 0.0009765
11h = 0.00048825 = 0.0488..%

in other words, saxo was trigger-happy and did one too many reps (theres a first )

ProperCharlie

ahh, i see. i had forgotten that sb was talking %ages and i was talking fractions...

milo

sorry - that should be 1667 RUNS of 7, not spins, my typo.

the maths:
100/.06 = 1667 (or in prob terms 1/0.0006).

in other words it takes 1667 runs of 7 to get a prob. of 1 back (1667 x 0.0006 = 1)


yes - but whats your average win per spin? usually there's a payback of VERY little per spin... like 1.0001 of your money.

your doublings usually have come at the expense of a lot of losses initially.

and because there are lots of runs in your favor.. there will also be lots against u.

you hope depends on odds, but if they're 50/50 (say a coin toss), it's just as likely that you'll get 10 in a row against you as any other combination of 10.

the fact that you have monetary limits as to what you can spend means that doubling up WILL cause you to lose eventually.

LG John

You double your money for a win so if you have nos 1-24 covered with £5 on each of those two thirds and hit an 11 you get £10 back. Most systems then advocate sticking £5 back on each of those chosen thirds and continuing as such. The problem here is you make a maximum of £5 profit per win but a big run against you will wipe out by a massive amount of money. Based on the wheel I was studying i found a way to cover 2/3 of the table with £7500 and this is the absolute maximum bet. Starting at a £5 if you lose you then have to pay £10 to cover the loss, then, £20, 40, 80, 160, 320, 640, 1280, 2560 at which if you lose you've now lost over £5k worse yet you need to hit on the next bet or you are in real trouble from the limit. That said, you can theoretically withstand a run of 10-11 against you with a big enough bankroll and such a run is pretty unlikely. Nevertheless such a run would wipe you out by over £10k so you'd want to have made at least that by the time such a run comes along. Gaining £5 per winning spin its not likely you will - for a start you need 2000 winning spins to make £10k.

This is where I suggest that you don't try for £5 win but rather try and catch runs in your favour which by virtue of the 65% win odds mean they are likely to be more frequent and also longer runs. If you keep reinvesting your winnings say to catch a run of 6 before banking you will win £160. With bigger ***** you could try for bigger runs in your favour and they do come along. Last night I had at least 2 instances of 10 wins in a row but didn't have sacks to keep doubling up that long!!! Another element you could add is session play (i.e. race the wheel first to 100 up/down) i.e if you go 100 down you stop for that session no matter how tempting it is to cover you loss with a £200 bet. The REAL problem is self control. Last night I decided to play with £110 and said I would NOT go below £70. At one point a run came against me and to cover the bet I had to put all but £60 on the table thus £10 into my WILL NOT GO BELOW limit. The bet came in and I went on to turn that £110 into £200 before calling it a night. In reality I had a 35% chance of blowing it and going BELOW my cut off limit. Clearly this was just childs play though because limiting myself to only going £40 down means that even a half assed 4 runs against me would have ended my session.

milo

i take it you're saying double up on a win only... and keep at (or drop down to) £5 in the event of a loss.

so you're hoping that you'll get a run of 6 wins (around 6.3% chance) and will then stop. not getting this results in a loss?

LG John

****, was just sitting thinking about my last post and I made a mistake. You don't double up with every bet. For £5 on each of 2/3rds you win £15. So its double minus half the stake I was thinking about red/black, doh! If you don't take advantage of winning runs then the profits you make aren't going to build up enough to resist the house going on one of its winning runs. This is why I suggest you reinvest your winnings. Catching one run of 6 wins IMHO in a night will be better than sitting around trying to make the same amount £5 at a time (note: all to be tested and tweaked).

milo

no, u were right the first time... i think

for £5 you win back double your money which is £10. your initial stake of £5 is cancelled out by the £5 loss. so in other words, you spend £10 total and you get back £20 total for a win. so your winnings are indeed £10.

you do realise that you're just on the other end of the "doubling up a loss" scheme? in other words, the bookie is doubling up the bet with you every time it loses!

so the bookie gets the benefit of the "double up a loss" scheme as well as the limitless (compared to your) resources needed to win at that scheme.

your only saving grace is that you'll be stopping after 6 wins... which mathematically i dont think will result in favorable payoff based on the odds for you.

Old_Fart

I presume you can't cover the green's either..so those losses have to be factored in? The win odds seem to be very similar to red vs black and doubling up when you lose? Roulette is not a game of skill..the house owns the greens and in the long run you lose. If a 'system' was available to beat the casino then the Investment Banks, with all their funding and PhD's would have cleaned up already..we'd hire guys off the street and train them to go in to cover the tables.
Poker is a game you can make a living in in Casino's, roullete is not.
Rgds
Chucky

LG John

Come to think of it I probably was right the first time I'm nowhere near a table just now so can't remember the pay out but I'd expect 1:3 which would retain the only advantage that the casino has - the one zero (european table).

They method of playing (I don't like the use of the word 'system') is based on choice. The house has no choice, only a slight mathematical advantage that remains 100% fixed with every individual spin of the wheel. If you go on a winning run against the house it can't choose not to accept your bet unless you hit the table limit which lets face it would be one monster run!! You can however nullify a large percentage of the houses winning runs by doubling up to recover. For the freak runs which don't come up too often you can cut your losses by setting a 'session' limit that will get you out of that game before a bad run to start to multiply into big numbers. Playing the thirds has the advantage that with each spin you are actually statistically likely to win.

I'll try this on play for fun and then when I've accumulated enough money off the poker 'suckers' I'll consider sticking £1275 onto a roulette table. This would allow me to withstand a run of 8 against me which (again assuming 35% chance of losing (is this correct for European table?)) has a 0.021% chance of occuring (relatively remote I feel). I will then 'race' the table to it either wiping me out or me doubling my money to £2550. At this point I take my initial money back and repeat the process thus playing exclusively with 'house' money and I keep trying over and over to profit in the same manner. I can treat each £1275 won as a new game which will give pryamid effect stemming from the first investment. If I can cross the finishing line before the house more times than not then each new 'game' will create more 'game' money to play with. Even if some of them go bust if the method works over all the other 'games' will continue to grow (hope that makes sense).

It shouldn't take too long to get to £1275 up on the basis I went £90 up last night playing very conservatively and not trying for big winning runs.

milo

this is true for a one-off spin... NOT for a run however. for you, a single win doesnt matter. its only the run of 6 (or whatever) that matters.

almost correct... given 36 numbers and one zero thats 35.12% chance of losing (i.e 13/37).

thats what u need to compare in that case - the statistical probability of it wiping u out vs. u doubling your money.

LG John

Great suggestion Any idea how

LG John

I figured you'd do 100/0.02 (for 8 losses) which would be once in every 5000 spins? Is this correct? By the way I checked and for every £10 staked (£5 over two thirds) you get £15 if you win so you don't double up. The 5000 spins thing must be wrong because of those 5000 spins 3250 (65%) would be winners so even assuming for just taking your £5 profit per win you'd make £8750 from £1000 risked JUST before you're £1000 would get wiped out. Therefore my maths MUST be way off Where did I go wrong?

milo

a couple of places

* it's not 65%.. its just under that for a win (remember the 0)
* a single win does not matter for you, as if the proceeding spin is a loss, you lose all your money as you've placed all you won in the next spin

milo

heres the maths...

a single win is 24/37 = 0.6486...

you only make money with 6 in a row in your favour = 0.074... chance

anything else is a loss = 0.926 chance

you're screwed if you get 8 consecutive 'losses' = 0.54 chance... you're NOT looking for 8 spins AGAINST you.... 5 in your favor and 1 against you would STILL be an overall loss.

unless you're only re-investing SOME of the winnings (so in other words a single win at 0.6486 does net you SOME money), you're royally screwed.

i understand it that you re-invest everything you've won so far... though im sure thats not the case.

LG John

I know but I was sticking with the old figure at the moment just for number crunching

I played around last night again and managed to with a bankroll of £170 turn that into £230 (very risky I know). At one point there was a run of 4 IIRC against me which put me all in (scary moment!).

Was my method of relating % odds of an event occuring to no. of spins of a roulette wheel required before the event would occur correct. Can we say that if something has a 0.02% chance of happening that it will occur 1 in every 5000 thus. For every 5000 spins of the wheel there will be one occurance of a run of 8 against you (again sticking with slightly inaccurate numbers as they give nice rounded figures). If so, with £1250 to play with (to resist 8 losses) and a 5000 spin 'window' to capatalise on wins I think there is a reasonable chance of me beating the table to double or bust. This would not however involve always reinvesting or doubling up to a positive run of 6 but rather a more instinctual decision taking on when to bank and when to double up/tripple up and so on.

Btw, at this point I'd like to thank you Milo for your invaluable contribution to this thread - I've greatly enjoyed the discussion

milo

ALMOST... it would be for every 5000 "runs" you'd get exactly 8 against you. but you could be wiped out long before that with the loss that will almost always happen before you get to your run of 6 wins.

when you put instinct into the equation, you lose the ability to do any maths on it. if you're not able to mathematically model your instinct... then there's no way you can work out likelihoods of losing all your money.

remember.. no instincts are needed here. this is not poker.. this is 100% luck.


likewise

LG John

LOL, there was never any doubt in my mind you'd come back with that

If 1 in every 5000 'runs' would produce a run of 8 against then its fair to assume the amount of spins required to produce all those 5000 runs would be far greater

In some respects you can maybe liken this to poker. The aim of poker is to carefully defend your stack when you don't have the cards/hand and to exploit others when you do. Professionals will typically look to win ONE big hand an hour!! On this 'game' of roulette your aim is to beat the house to £1250 up for you or £1250 up for it. You have covered all but 0.02% of the weakness in your 'game' What you must do now is exploit the weakness in its game and see if you can take £1250 from it before it plays its killer hand.

ProperCharlie

i can't see how it's anything like poker, tbh. maybe it's like playing poker where you can't see any of the cards or the faces of the other players. there is no "weakness" in the roulette wheel's "game". it is statistically likely to beat you. You can get lucky and win one time, but you can get unlucky even more.