Any probability experts or users of markov chains

[vampsthevampyre]

Afternoon All,

Just been watching a video regarding probability of coin flips. The initial set up I can understand, how to create a state chart (see attached spreadsheet) of the chances of 7 heads in a row. But after this the video stated that to simulate the flipping a coin 200 times. the video states that if you raise the initial state matrix to the power of 200 you will then get the second matrix which shows the probability of getting 7 heads in a row raises to 0.54 or 54%.

I've tried searching for how to recreate this in excel but the maths goes way beyond my knowledge and the solutions also show markov chains and that really makes my head hurt. Is this possible to do in excel? and if so how.

Also how easy is it to change the number of flips and introduce a biased coin (i.e. 67% tails, 23% heads)

Any help would be appreciated

Regards

Ian

roulette.xlsx
	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V
3																	After 200 flips
4						Next State											Next State
5			0	1	2	3	4	5	6	7				0	1	2	3	4	5	6	7
6		0	0.5	0.5	0	0	0	0	0	0			0	0.23	0.11	0.06	0.03	0.01	0.01	0.004	0.54
7		1	0.5	0	0.5	0	0	0	0	0			1	0.23	0.11	0.06	0.03	0.01	0.01	0.004	0.55
8		2	0.5	0	0	0.5	0	0	0	0			2	0.22	0.11	0.06	0.03	0.01	0.01	0.004	0.55
9	Current	3	0.5	0	0	0	0.5	0	0	0		Current	3	0.22	0.11	0.05	0.03	0.01	0.01	0.003	0.57
10	State	4	0.5	0	0	0	0	0.5	0	0		State	4	0.2	0.1	0.05	0.03	0.01	0.01	0.003	0.6
11		5	0.5	0	0	0	0	0	0.5	0			5	0.17	0.09	0.04	0.02	0.01	0.01	0.003	0.66
12		6	0.5	0	0	0	0	0	0	0.5			6	0.11	0.06	0.03	0.02	0.01	0.003	0.002	0.77
13		7	0.5	0	0	0	0	0	0	1			7	0	0	0	0	0	0	0	1
Sheet10

 

[StephenCrump]

@shg, it's good to see you back on the forum!

In the link @Eric W posted, the "1" value in the k-step Fibonacci is regarded as the zero-th term. I'm following that counting method.

If you use the OEIS versions, with the initial zero values, you'll need to shift to the right, e.g. by 7 in the case of heptanacci.

 

[shg]

@StephenCrump, thank you.

 

[shg]

Very descriptive write-up in a master's thesis here.