Kelly Calc

Bet Shooter · 08-02-08, 07:29 PM

Another question while I am here:

It calculates the optimum wager for parleys too. I can't see how ANY parley wager is a good bet with the odds you are giving up. Why does it suggest this type of wager in the calc? I must really be missing something because I know Ganch woudn't put it in there if there wasn't some edge for the player.

Justin7 · 08-03-08, 12:25 AM

2 times parlays are good.

First - correlated parlays. Texas vs. Oklahoma Community Middle School. Play Texas -40 parlayed to over 40.

Second - stale lines. Your internet book asleep? Pound away.

Ganchrow · 08-03-08, 03:32 AM

Originally posted by Bet Shooter

I have a hard time setting the #'s for "number of events" and even harder setting " Consecutive series" in the Kelly Calc. I won't know until each days card comes out how many wagers I want to place, but consistantly harder is how many "consecutive events" when I don't know if I will have 1 or 5 plays a day. Can some one shed some light on how they approach this Calc daily?

The "consecutive events" text box is really only in place to demonstrate the impact of Kelly betting over extended series of bets aned can be safely ignored for bet sizing purposes.

Ganchrow · 08-03-08, 03:33 AM

Originally posted by Bet Shooter

Another question while I am here:

It calculates the optimum wager for parleys too. I can't see how ANY parley wager is a good bet with the odds you are giving up. Why does it suggest this type of wager in the calc? I must really be missing something because I know Ganch woudn't put it in there if there wasn't some edge for the player.

Parlays are an inherent component of the optimal solution when betting Kelly for contemporaneous events.

The rationale is quite straightforward and can most easily be seen via this simple example:

Consider an even odds bet that wins with probability 60%. Given an initial bankroll of $100, this would imply a single bet Kelly stake of $20.

Were you to win this bet your resultant bankroll would stand at $120, and were you lose it would stand at $80.

Now, after the outcome of first bet were decided consider what would happen were you to be faced with a second bet with the same payout odds and win probability. This would result in the following resultant bankrolls under each of the 4 possible outcomes:

Now because these represent proper full Kelly stakes we know that these outcomes are indicative of Expected Growth maximization and so if these bets were instead contemporaneous we'd want outcomes that were identical under each of the four possible outcome.

Well it turns that the only way in which this is possible would be by utilizing parlays. Enter the relevant data into the Kelly calculator, we see that the optimal stakes for two contemporaneous independent bets at even odds and with win probability 60% would be 16% on each of the two singles and 4% of bankroll on the 2-team parlay (at true parlay odds of +300).

Let's see how this stacks up under each of the 4 scenarios:

<table border=0 cellpadding=2 cellspacing=2> <tr> <td align=left class=GANCH> Bet #1 Outcome </td> <td align=left class=GANCH> Bet #2 Outcome </td> <td align=left class=GANCH> Parlay Outcome </td> <td align=left class=GANCH> Bet #1 Result </td> <td align=left class=GANCH> Bet #2 Result </td> <td align=left class=GANCH> Parlay Result </td> <td align=left class=GANCH> Net Result </td> <td align=left class=GANCH> Resultant Bankroll
</td> </tr> <tr> <td align=left class=GANCH colspan=8> </td> </tr> <tr> <td align=left class=GANCH> WIN </td> <td align=left class=GANCH> WIN </td> <td align=left class=GANCH> WIN </td> <td align=left class=GANCH> +$16 </td> <td align=left class=GANCH> +$16 </td> <td align=right class=GANCH> +$12 </td> <td align=right class=GANCH> +$44 </td> <td align=right class=GANCH> $144
</td> </tr> <tr> <td align=left class=GANCH> WIN </td> <td align=left class=GANCH> LOSS </td> <td align=left class=GANCH> LOSS </td> <td align=left class=GANCH> +$16 </td> <td align=left class=GANCH> -$16 </td> <td align=right class=GANCH> -$4 </td> <td align=right class=GANCH> -$4 </td> <td align=right class=GANCH> $96
</td> </tr> <tr> <td align=left class=GANCH> LOSS </td> <td align=left class=GANCH> WIN </td> <td align=left class=GANCH> LOSS </td> <td align=left class=GANCH> -$16 </td> <td align=left class=GANCH> +$16 </td> <td align=right class=GANCH> -$4 </td> <td align=right class=GANCH> -$4 </td> <td align=right class=GANCH> $96
</td> </tr> <tr> <td align=left class=GANCH> LOSS </td> <td align=left class=GANCH> LOSS </td> <td align=left class=GANCH> LOSS </td> <td align=left class=GANCH> -$16 </td> <td align=left class=GANCH> -$16 </td> <td align=right class=GANCH> -$4 </td> <td align=right class=GANCH> -$36 </td> <td align=right class=GANCH> $64 </td> </tr> </table>

Which as you can see mimic the economic outcomes of the non contemporaneous bets exactly and as such represent the expected growth maximizing bet allocations.

If you're interested in the underlying mathematics, see this post.

Ganchrow · 08-03-08, 03:36 AM

Originally posted by Justin7

2 times parlays are good.

First - correlated parlays. Texas vs. Oklahoma Community Middle School. Play Texas -40 parlayed to over 40.

Second - stale lines. Your internet book asleep? Pound away.

Third - When you're a Kelly bettor.

Bet Shooter · 08-04-08, 09:34 AM

Originally posted by Ganchrow

The "consecutive events" text box is really only in place to demonstrate the impact of Kelly betting over extended series of bets aned can be safely ignored for bet sizing purposes.

I see this now. I thought that the Calc was using the consecutive series to calculate my optimum wager, by stretching these wagers over the entire series length. After changing it to different numbers, I noticed it doesn't have any effect on your optimum wager, just what your expected bankroll should be after the series.

So, I guess it's safe to assume that everyone here keeps consecutive series at 1 as you use this everyday, and just places the correct # of events in the calc each day. Then the proper odds and the win %.

Bet Shooter · 08-04-08, 10:38 AM

Originally posted by Ganchrow

Parlays are an inherent component of the optimal solution when betting Kelly for contemporaneous events.

The rationale is quite straightforward and can most easily be seen via this simple example:

Consider an even odds bet that wins with probability 60%. Given an initial bankroll of $100, this would imply a single bet Kelly stake of $20.

Were you to win this bet your resultant bankroll would stand at $120, and were you lose it would stand at $80.

Now, after the outcome of first bet were decided consider what would happen were you to be faced with a second bet with the same payout odds and win probability. This would result in the following resultant bankrolls under each of the 4 possible outcomes:

-snipped HTML table-

Now because these represent proper full Kelly stakes we know that these outcomes are indicative of Expected Growth maximization and so if these bets were instead contemporaneous we'd want outcomes that were identical under each of the four possible outcome.

Well it turns that the only way in which this is possible would be by utilizing parlays. Enter the relevant data into the Kelly calculator, we see that the optimal stakes for two contemporaneous independent bets at even odds and with win probability 60% would be 16% on each of the two singles and 4% of bankroll on the 2-team parlay (at true parlay odds of +300).

Let's see how this stacks up under each of the 4 scenarios:

-snipped HTML table-

Which as you can see mimic the economic outcomes of the non contemporaneous bets exactly and as such represent the expected growth maximizing bet allocations.

If you're interested in the underlying mathematics, see this post.

OK, I see how these two mimic each other. But I am still holding on to the fact that parleys have a greater vig than a straight wager. I am still a little confused about how Kelly would help overcome this larger vig. Unless you are telling me that the ONLY time you actually wager on these parleys is when you have correlated events. Then that makes sense to me.

Bet Shooter · 08-04-08, 10:42 AM

Originally posted by Justin7

2 times parlays are good.

First - correlated parlays. Texas vs. Oklahoma Community Middle School. Play Texas -40 parlayed to over 40.

Second - stale lines. Your internet book asleep? Pound away.

I understand the reason for the first part of your post. But I don't see how stale lines will overcome the greater vig on a parley vs a straight wager.

Ganchrow · 08-04-08, 11:09 AM

Originally posted by Bet Shooter

But I am still holding on to the fact that parleys have a greater vig than a straight wager. I am still a little confused about how Kelly would help overcome this larger vig. Unless you are telling me that the ONLY time you actually wager on these parleys is when you have correlated events. Then that makes sense to me.

No, that's not what I'm saying.

See http://forum.sbrforum.com/handicappe...1-parlays.html. Please note that this is written purely from the perspective of a sufficiently risk-neutral investor (i.e., not a Kelly bettor). Nevertheless, the point as it relates to EV remains wholly unchanged.

(And for a bit on correlated parlays from a sufficiently risk-neutral perspctive see http://forum.sbrforum.com/handicappe...d-parlays.html.)

tomcowley · 08-04-08, 12:16 PM

Another use is when the limits on what you're trying to bet are really low relative to your kelly stake. You can be better off parlaying 2 of these tiny bets together for your limit rather than betting both individually for the (same) limit.

I think what justin7 meant by "stale lines" was that you'd bet the game individually for the max, and then parlay it to random things (like both sides of another game) to effectively increase your stake beyond the normal limit (at reduced odds). Some books don't count parlays toward the straight-wager limit (or vice versa).

Bullajami · 08-04-08, 12:45 PM

Where are you getting true parlay odds?

Bet Shooter · 08-04-08, 01:06 PM

Originally posted by Ganchrow

No, that's not what I'm saying.

See http://forum.sbrforum.com/handicappe...1-parlays.html. Please note that this is written purely from the perspective of a sufficiently risk-neutral investor (i.e., not a Kelly bettor). Nevertheless, the point as it relates to EV remains wholly unchanged.

(And for a bit on correlated parlays from a sufficiently risk-neutral perspctive see http://forum.sbrforum.com/handicappe...d-parlays.html.)

I think I am getting my arms around this now. It's the fact that IF you are consistantly picking at a percentage above the 54.????% then this will overcome the large vig AND my age-old perception that Parleys are bad. Also if the calc figues out that the win % and the odds listed don't give you a positive outcome, then it will just fill that field with a zero. Is this correct?

Now, the hardest part for me(and everyone) is to be able to forcast what our win % will be and have actual proof, not just pulling those #'s out of the sky. I guess the calc isn't going to help you at all unless you are truely picking over 55% and over a long enough sample of wagers.

Also, I can see that Kelly is optimum for those picking above 55% but can be drastic for those that aren't or think that they are and aren't. It would be better for them to just wager straight plays with a small size of bankroll until they can be sure that they are above 55% over a long enough sample size and then switch to Kelly once you know you are above 55%. No?

Bet Shooter · 08-04-08, 01:55 PM

Originally posted by Bet Shooter

I think I am getting my arms around this now. It's the fact that IF you are consistantly picking at a percentage above the 54.????% then this will overcome the large vig AND my age-old perception that Parleys are bad. Also if the calc figues out that the win % and the odds listed don't give you a positive outcome, then it will just fill that field with a zero. Is this correct?

Now, the hardest part for me(and everyone) is to be able to forcast what our win % will be and have actual proof, not just pulling those #'s out of the sky. I guess the calc isn't going to help you at all unless you are truely picking over 55% and over a long enough sample of wagers.

Also, I can see that Kelly is optimum for those picking above 55% but can be drastic for those that aren't or think that they are and aren't. It would be better for them to just wager straight plays with a small size of bankroll until they can be sure that they are above 55% over a long enough sample size and then switch to Kelly once you know you are above 55%. No?

On further review, I think the last statement of the above post was incorrect. The best thing for them would be to wager at a smaller % (say .25 or .5) of full Kelly and then increase as the data starts to support that they are consistantly picking above 55%.

One more question: I know almost everyone is hooked on the idea of the greater the win percentage the better. But I have already learned in here that it's better for long-term growth to win 57% of 3000 wagers than pick 60% of 300 wagers. I also see more cleary now about why just a flat win % and even the number of units posted as your record is not a clear picture of someones performance and where that Z rateing (not sure if I have this name correct) is more of a true picture of someones success. No my question.
Is it better for longterm success using Kelly to have a more precise win% or just to have a larger one. Ex:

Your model has shown that you have an edge that equates to a 57% win % and you start wagering and using the 57% in the calc everyday. But after a long # of trails you start to see that your model actually performs higher. How does this effect your performance. I guess what I am asking is: is it MORE important for you to get as close to possible to the % your are using in the calc everyday? Is there any detriment (other than lost opportunities) to having your actual win % not exact to what the reality of the results are? If so at what point + / - would you start to do damage to your overall performance by you being off from the calc # you use and what your actual results end up being. (again assuming that you are still picking above 55% to start with.) If I pick 57% for the Calc but I have a actual result of 60%, am I hurting myself? Or am I just leaving money on the table but no detriment to myself.

Bet Shooter · 08-06-08, 08:04 AM

Just bumpimg this thread to see if anyone can shed some light on my question at the end of my last post above. Thank You in advance.

Another question pointed at the people who wager and use Kelly successfully. Do you adjust your bankroll after each session with the new Roll? I would think that if you started with a 5K roll and you made 300 in your wagering for the first session, then you would use 5300 as your bankroll in the Calc at the start of the second session....yes? Also do you adjust this roll in the calc based on afternoon and night games.

EX:
You have three plays for the day that hit your +EV and one is early in the day and the the other two are late. Would you run Kelly and make your wagers and forget about them for the day? Or would you adjust your night plays based on your new bankroll after an earlier win?