Gambling compound interest running balance

[infradigensemble]

I'm not sure how to write this formula in excel. Thanks for taking a look.

Here it is algebraically: C*(A/B) - (A/B) + A = "new" A

With numbers: 1.0125*(.5/2)-(.5/2)+.5=.503

Then I want to insert the "new" A (or .503) into the formula and run the calculation 3000 times so that I can see the answer for each calculation.

For the sports bettors out there the "1.0125" represent -8000 moneyline multiplier. ".5" is a 50 cent sportbook balance which is then divided by two b/c I am wagering half of my sportsbook balance with each wager, or .25. Then the proceeds from a won -8000 moneyline is added to the .5 and the new balance is .503.

So, the hypothetical is if I start with $0.50 and wager half by sportsbook balance on -8000 moneyline. My sportsbook balance is now at $0.503 of which I wager half on a -8000 moneyline...so on and so forth 3000 times.

Thanks for taking a look and let me know any questions!

 

[KRice]

Here is one approach...just select B11:C11 and drag down for the preferred number of trials.

MrExcel20210129.xlsx
	A	B	C
1	C	-8000 moneyline multiplier	1.0125
2	A	50 cent sportsbook balance	0.5
3		fraction sportsbook balance wagered	0.5
4	B	reciprocal of sportsbook bal wagered	2
5
6		C*(A/B) - A/B + A =	new A
7		1	0.5
8		2	0.503125
9		3	0.50627
10		4	0.509434
11		5	0.512618
infradigensemble

Cell Formulas
Range	Formula
C4	C4	=1/C3
C7	C7	=C2
C8:C11	C8	=$C$1*C7/$C$4-(C7/$C$4)+C7

 

[KRice]

As an alternative, you could rearrange your expression (where new A is now called A') to show that A'/A = (C+B-1)/B...which means that each subsequent trial yields a constant ratio. This means that you don't necessarily need to show each trial result since A' = A * ((C+B-1)/B)^(n-1), where n is the number of trials. This is implemented in C5:C7 and is sufficient to return the value of A' for any given number of trials n. Just change the input number of trials (blue cell) to generate the output A (A' in the green cell).

MrExcel20210129.xlsx
	A	B	C
1	C	-8000 moneyline multiplier	1.0125
2	A	50 cent sportsbook balance	0.5
3		fraction sportsbook balance wagered	0.5
4	B	reciprocal of sportsbook bal wagered	2
5		n	3000
6		(C+B-1)/B	1.00625
7		A'	65154473
8
9		C*(A/B) - A/B + A =	new A
10		1	0.5
11		2	0.503125
12		3	0.5062695
13		4	0.5094337
14		5	0.5126177
infradigensemble

Cell Formulas
Range	Formula
C4	C4	=1/C3
C6	C6	=($C$1+$C$4-1)/$C$4
C7	C7	=$C$2*C6^(C5-1)
C10	C10	=$C$2
C11:C14	C11	=$C$1*C10/$C$4-(C10/$C$4)+C10

 

[infradigensemble]

Thank you, Kirk

 

[KRice]

You're welcome...glad to help!

 

[KRice]

I should have asked earlier...did you want the very first value of A to be considered trial 0 or trial 1? I ask because the formula in C7 assumes that the first value of A (0.5) is trial 1 and the "-1" in the exponent (C5-1) ensures the correct number of compounding periods. If instead you prefer to consider that at time 0...or trial 0, the A value is 0.5 and at the end of trial number 1, the value would increase to 0.503, then simply change the exponent from (C5-1) to C5 in the formula shown.