Kelly Calculator

[PerpetualCzech]

Many of you will already have something like this but for those who don't, you can download a simple Excel program I made which will calculate full Kelly betsize here (http://www.mediafire.com/?2z2u0j0gilx).

It's very simple to use. Any cell coloured purple is a cell used for input. Enter as many legs of a parlay as you care to fit in any one of the 3 formats, American Odds, Percentage or Decimal Odds. Leave the rest blank. For a straight bet, just enter one cell in any format and leave the rest blank.

The block on the left represents the odds you get on your bet. The block on the right represents what you think are fair or breakeven odds. If you have a flat tax as a percentage of risk, you can enter that in cell A18. If you have a Betfair or Matchbook style commission attached to the bet you can enter that in cell C18. Otherwise leave these blank.

Output should be self-explanatory. Cell H20 tells you the percentage of your BR you should bet if you want full Kelly. H22 is your expected return. The example that comes with the download is for a bet at -110 that you believe is 55% to hit.

A quick note: cell H24 is an underrated measure and for my money the most important output of all. When measuring results all everyone usually talks about is ROI. What's really important is the equity you pick up on your bets, not the ROI. That's what the "Expected BR Growth" figure represents. It's simply the betsize multiplied by the Expected Return. Something like a 0.2% BR growth for a bet might not sound like a lot, but if you do the math you'll quickly see that all you need is just one of these bets a day and you'll double your BR in less than a year.

[kimlee]

I'm not sure the full spreadsheet is necessary. The Certainty Equivalent is almost always close to half the EV of an optimal bet. The important exception is if you bet less than optimal. For example, suppose you have a 10% edge on an even-money bet, p = .55. Then the Kelly bet is 10% of bankroll. Your EV is 1% of bankroll. Your expected growth is .55*ln(1.1) + .45*ln(.9) = .50%. If you can only bet 5% of bankroll then your EV is .5% of bankroll and your expected growth is .55*ln(1.05) + .45*ln(.95) = .375%. Thus the Certainty Equivalent of a half-Kelly bet is 75% of the EV of that bet.

[PerpetualCzech]

I'm not sure the full spreadsheet is necessary. The Certainty Equivalent is almost always close to half the EV of an optimal bet. The important exception is if you bet less than optimal. For example, suppose you have a 10% edge on an even-money bet, p = .55. Then the Kelly bet is 10% of bankroll. Your EV is 1% of bankroll. Your expected growth is .55*ln(1.1) + .45*ln(.9) = .50%.

I don't know what Certainty Equivalent is. But why isn't your BR Expected Growth 1% in this case?

E.g. you have a BR of $100. That means your betsize is $10 and you have an ROI of 10%. The equity you pick up is $10 * 0.1 = $1, or 1% of your original BR.

[Username]

Certainty Equivalent Analysis (http://www.bj21.com/bj_reference/pages/certaintyequivalentanalysis.shtml)

The return that would be accepted for the chance at a higher, but uncertain, amount.

[The Chaperone]

I don't know what Certainty Equivalent is. But why isn't your BR Expected Growth 1% in this case?

E.g. you have a BR of $100. That means your betsize is $10 and you have an ROI of 10%. The equity you pick up is $10 * 0.1 = $1, or 1% of your original BR.

You should definitely know what CE is by now imo.

[kimlee]

Why isn't your BR Expected Growth 1% in this case?


Initial bankroll = $100, betting 10% with proportional resizing and hitting 55-45. Your bankroll will grow to $100*1.1^55*.9^45 = $165.

Suppose instead you earn 5% risk-free on each bet. Your bankroll will grow to $100*1.005^100 = $165.

Within rounding error, you get the same growth from 10% EV or 5% risk-free bets.

EV is not growth. If you maximized EV then you would bet everything with any edge.

[BONAVENTURA]

shutup and pick a winner

[DavidM]

Isn't picking 55% winners at -1.10 equal to about 5% EV ?

Edit: It looks like you were assuming zero vig.