Simultaneous Event Kelly Calculator--Is there a bug in it?

[Dimwhit]

While messing around with the Kelly Calculator on SBR today, I noticed some odd behavior. While I confess that I don't know the equations for multibet Kelly...the behavior of the calculator seems to go against my intuition. Here are a few examples (all using 110 odds, consecutive series 1, 100% bankroll)

Example 1:
# Independent bets-2
Win prob: 70% on both. Total stake calculated: 46.62%
Win prob: 75% on both. Total stake calculated: 49.8750%
Win prob: 80% on both. Total stake calculated: 48.72%

Seems that the total stake you wager should keep increasing as the win probability goes up, but from 75%-80%, the total stake goes down. If I increase the number of independent bets to 3, then I find a decreasing stake between 70-75%. As the number of indepedent bets increases, the point where the stake begins to decrease gradually drops. Didn't test all the way out to 15.

Example 2:
Fix Win prob at 65%. Start increasing the number of bets gradually from 1 to 15. I find:
# bets @ 65%: 2. Total Stake: 38.955%
# bets @ 65%: 3. Total Stake: 42.9479%
# bets @ 65%: 4. Total Stake: 42.0899%
# bets @ 65%: 5. Total Stake: 38.6692%
Once the total bets exceeds 3 at 65% probability, the total stake suggested keeps decreasing.

So, is that a bug or maybe I'm not using the calculator right. Could be that I don't understand multi-kelly, as well.

[Ganchrow]

The exact Kelly calculator linked to from the SBR Betting Tools & Calculators page yields an unconstrained Kelly solution, meaning that the solution set includes all possible constituent parlays.

So, for example, while 2 independent bets at -110 each with win probability 70% would yield two straight bets at 23.31% of bankroll apiece, the complete solution also requires a parlay of the two at 13.69% of bankroll (click the "Stakes for parlays of size: 2" tab). The total stake for all all bets is actually 60.31% (inclusive of parlays).

If you wish to perform constrained Kelly optimizations that allow the user to limit parlay exposure, then check out my http://forum.sbrforum.com/handicappe...ml#post1215635.