**Roulette Probability Made Easier**

By Kon-Fu-Sed, 2008, for the VLS forum members

**13. MIXED CHAINS**

Now, with a little bit of logic thinking and a calculator, you can use what you have learned above to make all those calculations for all the roulette-bets there are.

Instead of using the

**18/37** fraction, you change the "

**18**" to the "

**number of covered single numbers**" in your bet.

Each trial can have their own bets:

Trial 1: Bet a

**Dozen** (

**12/37**)

Trial 2: Bet a

**6-Street** (

**6/37**)

Trial 3: Bet

**Low** (

**18/37**)

Trial 4: Bet a

**Split** (

**2/37**)

What's the probability to hit

*ALL* four?

Solution:

**(12/37) x (6/37) x (18/37) x (2/37)** = 2,592 / 1,874,161 (Some 0.14%)

What's the probability to hit

*AT LEAST* once?

First trial:

**12/37** +

Second trial:

**(25/37) x (6/37)** +

Third trial:

**(25/37) x (31/37) x (18/37)** +

Fourth trial:

**(25/37) x (31/37) x (19/37) x (2/37)** =

That is: (12/37) + ((25x6) / 37x37)) + ((25x31x18) / (37x37x37)) + ((25x31x19x2) / (37x37x37x37))

=

**1,358,786 / 1,874,161** to be exact.

Or 72.5% rounded.

- Can you PLEASE explain?Of course...

**The first trial:** The bet is a Dozen so you have a probability of

**12/37** to hit. And a

**25/37** probability to miss. Nothing special.

**The second trial:** First of all you lost the first trial; that's a

**25/37** probability (see above). Then you have a

**6/37** to hit the second trial.

******* The probability to

**hit** at this trial is:

**The probability to MISS the previous trial times the probability to HIT this trial.**So the probability to hit at this trial is

**(25/37) x (6/37)** = 150 / 1369.

******* The probability to

**miss** at this trial is:

**The probability to MISS the previous trial times the probability to MISS this trial.**So the probability to miss at this trial is

**(25/37) x (31/37)***Do you understand the "***25 / 37**" - why is it there?It's because you had lo

**lose** the first trial to come to this,

*the second*, trial. That was a

**25/37** probability and therefore it has to be included.

It's the

**25/37** results in the first trial

*that ***didn't hit**.

A loss here therefore happens in

**(25/37) x (31/37)** as that many results didn't hit here.

The

**25/37** left from the first trial and now

**31/37** left from here.

As they are combined,

*you have to multiply them*.

**REMEMBER:**The probability to

**hit** at this trial is:

**The probability to MISS the previous trial times the probability to HIT this trial.**The probability to

**miss** at this trial is:

**The probability to MISS the previous trial times the probability to MISS this trial.****The third trial:** First of all you lost the second trial and the probability to do that was

**(25/37) x (31/37)**. See above.

Now you bet

**Low**, that has a

**18/37** probability to hit and therefore the calculation is:

**To hit:**

**(25/37) x (31/37) x (18/37)****To miss:** **(25/37) x (31/37) x (19/37)****The fourth trial:** Now you missed at the third trial as well and that was, as we saw above, a probability of

**(25/37) x (31/37) x (19/37)**.

And now you bet a 2-numbers split that has a

**2/37** chance to hit. Calculations:

To hit:

**(25/37) x (31/37) x (19/37) x (2/37)**That is how the probability of

**1,358,786 / 1,874,161** was calculated.

And if we have

**1,358,786** chances to hit, there has to be

**515,375** chances to miss (as 1,874,161 - 1,358,786 = 515,375)

**The quicker (logic) way:**If you quit at

*any time you hit*, you only have to calculate by the probability of a

*miss on ALL the four trials* - if you don't miss all four, you obviously must have hit... right? So, for this four-misses event the calculation is:

**(25/37) x (31/37) x (19/37) x (35/37)** = 515,375 / 1,874,161.

And therefore the chance to hit is (1,874,161 - 515,375 =)

**1,358,786 / 1,874,161**The same exactly.

*Probably correct...*----------------------------------

As a complement to this document I have written a small

**probability calculator** in

*JavaScript*.

It is a

*HTML-page* so it is easy to open it in your web-browser.

Download it from the members download area here:

http://vlsroulette.com/downloads/?sa=view;id=167You can calculate the probabilities to...

*** Hit "this" trial**

* Miss "this" trial

* Hit at least one trial

* Miss all trials

in as long a chain of trials you like with different bets for each.

Bet from one number to all -

**both 0- and 00-wheel**.

Save the output by a simple copy-and-paste.