Kelly Formula

Here's just one that came up in a Google search: http://www.albionresearch.com/kelly/

Assuming this wikipedia page is the correct description of the kelly formula, it does not look overly complicated or difficult to program into Excel. https://en.wikipedia.org/wiki/Kelly_criterion It looks like a relatively simple formula relating the fraction you should bet to the probability of winning and the offered odds. As simple as the formula appears:
Is this the correct formula?
If it is correct, what difficulty do you have programming that formula in Excel?

I am not at all familiar with Kelly's paper or his formula algorithms, so I am dependent on you and any other source I can find to try to understand Kelly's formula(s). If the Wikipedia page is inadequate, then I would need you to help me understand the math formulas/algorithms you are trying to program here before I can help you program those algorithms into Excel.

Is it possible that the "multiple horses" section of the Wikipedia article describes what you are trying to do? This described algorithm requires a few iterations, but the basic equations along that iteration seem simple enough that one should be able to program those equations into Excel and figure out the iterations needed.

If anyone else is more familiar than with these equations/algorithms/strategies, I invite them to contribute. If I am going to help, I need some help from you to understand the math/algorithm you are trying to program into Excel.

I think this can be done in solver, though I don't have any real experience with Solver or the Kelly formula. With the percentages in A2:A4, the odds/returns in B2:B4, and the bankroll in E1, I put the following formula in H1:

=SUMPRODUCT($A$2:$A$4,LOG10(1+$B$2:$B$4*$E$2))

...and used solver on evolutionary method (5 sec. time w/o improvement) to modify E2 to maximize the solution. The return was: 0.894356966441641. Multiply that by the bankroll to get your $ bet.

There's probably a better way, but this seemed to work? You should be able to incorporate more alternatives without difficulty by expanding the A2:B4 range.

If you have an 80% chance of winning $21 on a $1 bet, and 10% of winning $7.50, that's equivalent to having a 90% chance of winning $17.55, which is 18.55:1 expressed in bookie odds. So:

	A	B	C	D	E
1		name	p(win)	win
2			80%	$ 21.00
3			10%	$ 7.50
4	Combined:	p	90%		B4: =B2 + B3
5				$ 17.55	C5: =SUMPRODUCT(C2:C3, B2:B3)
6	Bookie Odds	b		18.55	C6: =C5 + 1
7	Kelly sez bet			89.461%	D7: =(b * p - (1 - p)) / b

You could add any number of other payoffs in like fashion.

Rereading the Wikipedia article, my last post has an error.

The wiki sez ...

b is the net odds received on the wager ("b to 1"); that is, you could win $b (on top of getting back your $1 wagered) for a $1 bet

I read b and thought "bookie", but b as described is decimal odds, not bookie odds, so you don't add one. So,

	B	C	D	E
4		p(win)	win
5		80%	$ 21.00
6		10%	$ 7.50
7	Combined probability (p) & odds (b):	90%	$ 17.55
8	Kelly sez bet this fraction of bankroll:		89.43%	D8: =p - (1 - p) / b

I'm going to feel really bad if you've lost your life savings as a result of this.

Originally Posted by shg

I'm going to feel really bad if you've lost your life savings as a result of this.

Ha! At least this approach should keep him solvent longer than all of the OPs who request help with a Martingale gambling strategy.

Amen .

Well ...

I found Kelly's original paper (newly typeset) at https://www.princeton.edu/~wbialek/r...s/kelly_56.pdf, and it defines (toward the bottom of page 920):

a_s the odds paid on the occurrence of the s'th transmitted symbol, i.e., a_s is the number of dollars returned for a one-dollar bet (including that one dollar)

That "including that one dollar" part makes it bookie odds, which means the 1 should be added.

So ... I dunno.

After rethinking this and looking at some earlier stuff, I realized my definitions of bookie odds and decimal odds are exactly reversed . The bookie odds of drawing a diamond from a standard card deck are 3:1; you get $3 plus your $1 bet back. Expressed in decimal odds, that's 4:1; that's what you get back if you win, and it includes your $1 bet.

Soooo ... the words are misleading in post#9, but the calculation is the correct one.

Not necro-posting (although I had a good chuckle at that term), however it would be considered hijacking, which is a big no-no lol, so thanks for asking 1st (see Rule 2 of our Forum [/I][URL="http://www.excelforum.com/forum-rules/642590-forum-rules.html"]

If you feel an existing thread is particularly relevant to your need, provide a link to the other thread in your new thread.