Math question about Guaranteed streak wins

Hey all,
my first post. been on the wizard site for years, just haven't been a huge forum person.

Can someone check my thinking here to see if, and how far I am off base? Thanks in advance
also... not a martingale question. haha

so.. streaks happen thusly on European..
odds of
a streak of
1, 48.6%
2, 23.7%
3, 11.5%
4, 5.6%
5, 2.73%
6, 1.33%
7, .65%
8, .31%
9, .15%
10, .074%
11+ the rest/etc inconsequentially small.

question 1.. why, when you add up everything above a streak of one, does the math not come out even? IE adding 2-10 is less than 46% and there is no way that when you add the rest (say, up to a streak of 100) it equals another 4% right? What am I missing?

The meat:
if you can guarantee to catch half of the streaks as wins above 1, would that change your odds? I know it doesn't change the house edge that makes your win rate in an even outcome a payout of 48.6 and what have you.. but.. if close to 50% of the outcomes are a streak greater than 1, and you can guarantee you average half of those outcomes as wins, and add that too thae unpredictable "streaks"of every other, ie RBRBRB ie.. a streak of 1.. would that not potentially change the math?

Here is my thinking.. and since my roulette play has given me an inordinate amount of winning sessions.. I ask the question. I get that if you win half of all streaks that is still only 46.8%

Does it change the math question 1)

out of all outcomes.. you have a 46.8 chance of being right vs red or black for a streak of one. what if you add a guarantee of half of all streaks above one making it non random, and still average at least half of the RBRBRB wins as well? Over say.. 1,500 spins.. what would that look like? It seems like it would have to change the math?? I mean.. if you can guarantee 50% of each streak is a W, how can the math stay the same?

I normally see people play for streaks.. or against streaks.. and martingale their bias.. but I figure.. if you never know when a streak is going to start.. or end.. why not bet in a way that guarantees predictability in exchange for catching half of every streak predictably? And yes.. I have done this with a simple switching pattern, not just RBRB but a switching pattern nonetheless. As far as streaks.. I also only hear of people tracking same color streaks.. but there is a third "streak" that needs mentioned obviously. That is a streak of RBRBRBRB.. It seems like there is a greater liklihood of catching RRRR or BBBB for a long series, than there is of RBRBRB for 20 in a row. I don't see anymath that would support that.. but those seem to be the only streaks gamblers talk about. But even on those.. I still average at least half.

(my last conundrum.. Does it change the math question 2) is that I am trying to find a mathematical reason why I am catching more than half of the RBRBRB streaks in a way that doesn't seem like luck or stat variance.. but I cannot seem to come up with anything. It just seems like I broke roulette.. and I honestly hesitate to believe that I could have done so and want to know why I did not. My theory.. is that if 48.6% of outcomes are a single R or B and the rest are streaks.. I seem to be catching the regular variance of 46.8% at about 1/2 but I catch 1/2 of the RBRB singles or streaks coming specifically after a RRRR BBBB streak in a guaranteed manner. 1/2 the time, I am guaranteed 100% to catch whatever RBRB streak comes after a solid color streak. Does that change the math? )

so.. summary.. Catching 1/2 of any streak as guaranteed wins seem to be changing the math in my favor. this means same color streaks of 2 or more.. as well as any RBRB alternating streak after the same color streak.

Anyway. hopefully I am making sense. I've just been puzzling

I know what I wrote may be hard to track... not because the math is hard for you stats wizzes.. just because.. welcome to my brain and the way I say things. hahaha,

happy to clarify anything
thanks again

I'm not a math guy. But I don't see where your streaks account for a green zero (I'm assuming you're playing European single zero wheel). Even though the result (-1) would be the same, and the streak would start over, 0 would lose all R and B, so I think you have to account for it separately. Your example was all about RBRBRB, nothing showed you were factoring in the green as a streak of 0. A second green would be another 0.

I could be wrong.

Quote: Mixxlb07

Hey all,
my first post. been on the wizard site for years, just haven't been a huge forum person.

Can someone check my thinking here to see if, and how far I am off base? Thanks in advance
also... not a martingale question. haha

so.. streaks happen thusly on European..
odds of
a streak of
1, 48.6%
2, 23.7%
3, 11.5%
4, 5.6%
5, 2.73%
6, 1.33%
7, .65%
8, .31%
9, .15%
10, .074%
11+ the rest/etc inconsequentially small.

question 1.. why, when you add up everything above a streak of one, does the math not come out even? IE adding 2-10 is less than 46% and there is no way that when you add the rest (say, up to a streak of 100) it equals another 4% right? What am I missing?

I totally disagree on your table data

European..
Here is mine from a simulation 1 million times (2,000 spins)
and calculated.
yes someone did this before.

18/37 is the probability of getting a run of black(or red)
of length 2 or more.
and it (prob column) does add up to 1

my 2 programs do not know each other
so I trust the results

run	sim	sim	sim	calc	calc	run
length (X)	freq	prob X	prob X or more	prob X	prob X or more	length (X)
1	256761669	0.513660	1.000000	0.513514	1.000000	1
2	124862921	0.249792	0.486340	0.249817	0.486486	2
3	60711898	0.121456	0.236548	0.121533	0.236669	3
4	29549230	0.059114	0.115092	0.059124	0.115136	4
5	14376170	0.028760	0.055977	0.028763	0.056012	5
6	6990595	0.013985	0.027217	0.013993	0.027249	6
7	3397785	0.006797	0.013233	0.006807	0.013256	7
8	1652044	0.003305	0.006435	0.003312	0.006449	8
9	804287	0.001609	0.003130	0.001611	0.003137	9
10	391082	0.000782	0.001521	0.000784	0.001526	10
11	189742	0.000380	0.000739	0.000381	0.000743	11
12	92445	0.000185	0.000359	0.000185	0.000361	12
13	44536	0.000089	0.000174	0.000090	0.000176	13
14	21960	0.000044	0.000085	0.000044	0.000085	14
15	10674	0.000021	0.000041	0.000021	0.000042	15
16	5067	0.000010	0.000020	0.000010	0.000020	16
17	2508	0.000005	0.000010	0.000005	0.000010	17
18	1195	0.000002	0.000005	0.000002	0.000005	18
19	566	0.000001	0.000002	0.000001	0.000002	19
20	320	0.000001	0.000001	0.000001	0.000001	20
21	150	0.000000	0.000001	0.000001	.	21
22	65	0.000000	0.000000	.	.	22
23	33	0.000000	0.000000	.	.	23
24	12	0.000000	0.000000	.	.	24
25	9	0.000000	0.000000	.	.	25
26	9	0.000000	0.000000	.	.	26
27	0	0.000000	0.000000	.	.	27
28	0	0.000000	0.000000	.	.	28
29	2	0.000000	0.000000	.	.	29
.	499866974	1	.	.	.	.

I read the rest later
and will have fun too

I can easily calculate runs(streaks) of any event
or length
honest (Others did it before me)
Sally

Quote: beachbumbabs

<snip>Your example was all about RBRBRB, nothing showed you were factoring in the green as a streak of 0. A second green would be another 0.

I could be wrong.

I did not yet read all of the OP.

let us take an easy one.

RBR
it IS a possible sequence
as is
BBB or RRR (we also call these runs (or streaks))

the wait time for each is not the same
I get (calculated)
BBB or RRR = 14.966221 spins
(I show the calculation later)
but for
RBR or BRB = 10.740912 spins

yes, interesting I too think so
Sally

Hey! Thanks for the responses!

I factored in the green 0 in the figures right?

I like your table better, don't get me wrong.. because .5136 sounds way better than 48.6. haha. I was just using 18/37 for my table. 18/37 = 48.6, 18/37^2 rounded to 24, 11.5 etc. Did I do that wrong?


and thanks for being willing to help me with my thinking. I swear that Table games.. daytrading.. and my daughter's math, are the only times I've used any substantial math since college. ha!



I have my 2 main math questions in the op, but maybe it would help to hear the thought that started me looking at the game differently. You can't change the house edge, I get it, but why can't you play into the probabilities inherent in the game? There are different ways I was thinking to do this.. here's one example..

Why can't you always be wrong on a streak of 4 in order to always be right on a streak of 3 and (almost always) 1? So guarantee that you are wrong 5.6% of the time, over time, to guarantee that you are always right that extra 11.5% of the time. any time there is a streak of 2, bet on the third, this would negate the occasional streak of 1, but you would make up for it by always betting opposite on a streak of 4 making it impossible to be right for a streak of 4 but possible to be right on a streak of 5. Now.. I'm thinking like 1,500 outcomes here. does that shift a percentage in some way or am I missing something?

so.. like..
r B B B B B r
r B r B r B r
WWLWLWW

or

r B B B r B r r B B
B B r B r B r B r r
LWLWWWWLLL

when there is an opportunity to bet for a streak of 3, bet for, when there is opportunity to bet for streak of 4 bet against, making sure to always capitalize on a streak of 1.

You could set yourself up to catch all 3's and 5's and still catch streaks of 2 and 3. Unless there is math to show that the streaks of 1 are decreased by the same amount, then I would be correct about a predictable advantage/disadvantage right?

When we play the games.. why don't we work in the streak probability expectations and work WITH the expected variance instead of fighting it all of the time?
I mean.. in Games like Blackjack it becomes a little more difficult, but why not use expected loss to your advantage, you know?

That's just one idea for roulette. maybe it will help you see where I am coming from with my first 2 questions.

Would you be available to meet in Vegas, .... Jan 20th or 21st?

guaranteed streak wins???
What exactly is guaranteed at a roulette table? Even a 1.35 edge is a guaranteed negative number for the player.
A streak is guaranteed to last only until fleastiff shows up, then it reverses itself.

Quote: Mixxlb07

Hey all,
so.. streaks happen thusly on European..
odds of
a streak of
1, 48.6%
2, 23.7%
3, 11.5%
4, 5.6%
5, 2.73%
6, 1.33%
7, .65%
8, .31%
9, .15%
10, .074%
11+ the rest/etc inconsequentially small.

question 1.. why, when you add up everything above a streak of one, does the math not come out even? IE adding 2-10 is less than 46% and there is no way that when you add the rest (say, up to a streak of 100) it equals another 4% right? What am I missing?

Because what you are claiming to be probabilities of "a streak of N" are actually the probabilities that the next N spins will win on a particular even-number bet.
The probability of winning N bets in a row on a single-zero wheel is (19/39)^N.
The sum of your numbers is 19/39 + (19/39)² + (19/39)³ + (19/39)⁴ + ...
= (19/39) / (1 - 19/39) = 19/20.

As for your second question, your numbers are misleading. Remember, your 48.6% chance of a "strreak of 1" is actually a "streak of 1 or longer"; you cannot add, say, the 23.7% for a "streak of 2" to it as the 23.7% is already included in the 48.6% number.