Roulette - interesting question...

[wb]

Ok firstly, I'm not trying to 'beat the wheel' and afer a brief stint of playing, I realised roulette is not for me.

However, I had a conversation in work about odds and chances, which proved interesting - and I want to see what the maths guys here think...

We all know that the chances of landing on red/black have nothing whatsoever to do with the previous spin. But maths can give us a rough idea of our chances of the ball landing on red/black. So presuming there was no zero in the wheel, my chance of hitting black are even money.

Continuing on with this theme, over 100 bets, I can expect to hit black twice in a row 25 times. I can expect to hit black three times in a row 12.5 times (on average of course).

Now, does it matter if I change wheels any time though the sequence of that 100 bets?

If for example, I've 100 spins to take and a choice of two wheels. Let's say I hit two blacks on wheel A, and move on to wheel B for the next spin. Does this change anything? Should I still hit 12.5 blacks in a row on average out of that 100 spins?

[Win2Win]

Maths does not work in the real world of gambling, but the casino's & bookies like to make you think it does. Do you include '0' in your calculations?

[mathare]

I have a few issues with the wording of the question, to be honest.

1) 100 bets isn't a very big sample, but then I'm sure you know that after all I have banged on about in the past :)
2) When you talk of hitting black twice in a row that doesn't mean you'll get just two blacks in a row does it? The only way this can work is if you count longer sequences as many black doubles. For example suppose the first ten spins come out BRBBBBRRBB. Then you have 4 sequences of two blacks in a row (spins 3 & 4, 4 & 5, 5 & 6, 9 & 10) even though once of those sequences actually extended to 4 blacks in a row. Similarly you have two sequences of three blacks in a row.

Now suppose you have spun up two blacks in a row on wheel A and now move to wheel B. Does anything change? Asssuming the two wheels are identical and without bias then the odds of black on wheel B should be the same as on wheel A so regardless of what has gone before on either wheel the chances of extending your run of two to three should be 50/50.

[silax]

its also not uncommon whatever the stats for 1 colour to pop up 8 times in a row. now back to my friend who could beat roulette and have given this some more thought as we were quite drunk when he was chatting with me i think he may have been calculating which number was in a certain spot when the croupier let the ball go and from that he could get the correct place for the ball to finish up within 5 numbers i wonder if this would work with online roulette

[wb]

OK, 100 bets was a bad example, so use 1,000 or 1,000,000 or whatever.

The crux of the argument is...

Does changing the wheel during the overall sequence of bets alter the chances?

If I spun wheel A 1,000 times, then spun wheel B 1,000 times (total of 2,000 spins) - does black have the same chance of coming out in those 2000 spins as it does had I spun wheel A 2,000 times?

[mathare]

OK, 100 bets was a bad example, so use 1,000 or 1,000,000 or whatever. I wasn't picking on your sample size really, just winding you up :)


If I spun wheel A 1,000 times, then spun wheel B 1,000 times (total of 2,000 spins) - does black have the same chance of coming out in those 2000 spins as it does had I spun wheel A 2,000 times?It should make no difference whatsoever. After all, if you spin wheel A 1,000 times it doesn't matter if they are the first 1,000 spins ever on that wheel or not - past history has no effect on the next spin. And because of that fact if the two wheels are identical then changing wheel at any stage should have no effect on the outcome.

If you changed the wheels for coins and red/black for heads/tails the problem is the same. Changing one unbiased coin for another won't affect the outcome of any toss since we are replacing like for like and the coins are identical so the chances of a given result are also identical.

Presumably you brought this up because someone thought that changing wheels would have an effect on the outcome...

[wb]

Well, yeah I brought it up when someone in work told me about a roulette system and I questioned it.

Basically, it's based on the real casino, not online. His point was the following...

Forgetting for a moment that there's a zero - if you were using (wait for it) Martingale and backing black each time, by the time you hit ten reds in a row, you'd be staking 1023 untils to win one.

The chances of that happening per 100 spins are 0.976% (of course, it could happen twice, or not happen at all in 100 spins, but that's the average chance if spinning to infinity).


So then, 10 reds in a row would wipe out most banks. But he wants his bank to last for fourteen reds in a row before it busts. How he thinks this can be done is the following:

Wait until a wheel has spun four reds in a row - THEN start your sequence. So you are effectively starting after the fourth red with 1 unit. By the time ten reds hit, you'd only be on you sixth bet using martingale (32 units).

Now I questioned this strategy and stated the obvious that the previous spins don't affect the next, but he maintains that fourteen reds in a row would be highly unlikely (but he concedes it's possible).

The second problem was adapting it online. That's where the discussion came up. You can play for free online and also with money. So if you spun the free wheel, and it it four reds, what happens if you then move to the pay wheel? Does the sequence continue, or is it a new sequence?

Just your normal coffee break stuff :geek

[mathare]

Wait until a wheel has spun four reds in a row - THEN start your sequence. So you are effectively starting after the fourth red with 1 unit. By the time ten reds hit, you'd only be on you sixth bet using martingale (32 units).So the argument then starts about whether you should be looking at the odds of 14 reds in a row or 18 if you include the previous spins. But when you first get to the wheel do you know the last spin? In most casinos the answer is yes as they maintain a board showing the last 20 or so spins. If it was red do you then wait for 3 more reds before betting or 4 more reds still?


The second problem was adapting it online. That's where the discussion came up. You can play for free online and also with money. So if you spun the free wheel, and it it four reds, what happens if you then move to the pay wheel? Does the sequence continue, or is it a new sequence?The wheels should be identical as they should use the same random number generator (RNG) software but only the software developers (OK, and the auditors I guess if they look at free play software) will really know this for sure. The rest of us have to take it on trust. Assuming the paying wheel is identical to the free play wheel then the sequence should continue as if you hadn't changed wheels. Some online casinos have multiplayer lounges so your friend could always lose his fortune in one of those by just watching others till he gets his 4 reds in a row and then starts his Martingale. He'll run smack into the table limit if he continues though - then what will he do? He'll also be risking a lot to win €1 (or whatever) each sequence but I know you don't need convincing of the madness of his plan

[wb]

Yep, that pretty sums it up Mat. He seems to think that when he hits the house limit, it's a simple matter of moving to a higher stakes/higher house limit table and continuing on his sequence. If only things were that simple!

[mathare]

Yep, that pretty sums it up Mat. He seems to think that when he hits the house limit, it's a simple matter of moving to a higher stakes/higher house limit table and continuing on his sequence. If only things were that simple!:laugh

So he hits the table limit of say £500 and then moves to a table with a higher limit and carries on? Brilliant! I bet the online casinos have never thought of that before.

Suppose he wants to win €1 per winning sequence and you say he wants to withstand a sequence of 14 losers. His bank will need to be huge! On the 14th spin his stake would be up to €8192 having already lost €8191 and all to win €1 :ermmm. OK, even allowing him to come in part way through the sequence and missing out the first four his stake would still be €512 and thus exceeding the limit on most low-stakes tables.

[counterfeit]

If, and it's a bl**dy big if, you want to adopt Martingale on an online roulette table then I would suggest he waits until a run of any even money bet has lost at least 10 in a row. The chances of you then hitting the table limit are slim to say the least but you will only get about 2 bets per day so probably not worth it.