Round Robin parlays vs. Normal parlays

[Ganchrow]

I'll just point out for all those still interested that in the example given by BOT (10 simultaneous events, each with 80% win probability, at odds -300), the solution limited to round-robins by 2 is actually Kelly-preferable to the the solution limited to singles.

Singles:
Stake Per: 9.99997%
Total Stake: 99.99969%
Utility: 5.07742%

By 2s:
Stake Per: 2.11675%
Total Stake: 95.25355%
Utility: 6.89867%


Although the complete Kelly solution, inclusive of all 1,023 singles and parlays, is obviously best:

All:
Total Stake: 26.84355%
Utility: 7.00211%

[tomcowley]

That's largely because you "run out of bankroll" betting singles, and to a lesser extent (which is more important at 4-5 events) because parlays magnify your obscene edge. The stake for one single is 20%, so obviously when you're betting 10 of them simultaneously, you can't even come close to getting enough down as if they were sequential, and the parlays let you effectively bet more. With 2 events, the singles dominate the parlay (by amount to win), and with 3, the singles still have a lead.

If you had the option to bet 10 singles consecutively (EG 7.25%), or 5 sets of 2-team parlays (EG 6.4%) consecutively, the singles win handily (and barely lose to 5 groups of singles + 2-teamers)

[Ganchrow]

That's largely because you "run out of bankroll" betting singles, and to a lesser extent (which is more important at 4-5 events) because parlays magnify your obscene edge. The stake for one single is 20%, so obviously when you're betting 10 of them simultaneously, you can't even come close to getting enough down as if they were sequential, and the parlays let you effectively bet more. With 2 events, the singles dominate the parlay (by amount to win), and with 3, the singles still have a lead.

You got it.

If you had the option to bet 10 singles consecutively (EG 7.25%), or 5 sets of 2-team parlays (EG 6.4%) consecutively, the singles win handily (and barely lose to 5 groups of singles + 2-teamers)

I'll mention that betting 10 singles consecutively is identical utility-wise to the complete Kelly-solution and so can't be improved upon using any set comprised solely of bets on the outcomes of these 10 events.

[Dark Horse]

i dont dont see a round robin BUTTON ON 5 DIMES !!so how do i do it?

Not all books offer round robins. But just as parlays, you can string them together yourself (as long as the games don't overlap). Ways of doing so are explained in detail in 'win more, lose less.'

[Data]

the complete Kelly solution, inclusive of all 1,023 singles and parlays, is obviously best

That is theoretically speaking. The assumptions here are:
1) all the lines are parlayable;
2) the time spent entering 1,023 plays has zero-value.

From a practical standpoint, I would say that since both assumptions above are incorrect, the obviously best solution is playing doubles wherever the best available lines are parlayable. On the other hand, "practical full-Kelly solution" is an oxymoron anyway.

[Ganchrow]

That is theoretically speaking. The assumptions here are:
1) all the lines are parlayable;
2) the time spent entering 1,023 plays has zero-value.

From a practical standpoint, I would say that since both assumptions above are incorrect, the obviously best solution is playing doubles wherever the best available lines are parlayable. On the other hand, "practical full-Kelly solution" is an oxymoron anyway.

Why doubles? Why not trebles? Why not quads? That the best practical solution is always going to be a function of what's available should come as a surprise to no one.

Furthermore, this discussion is taking place in the context of round-robins, so yes, all the lines are parlayable given the terms of the scenario outlined by the poster.

I also think it a safe assumption that someone consistently able to secure 6²/₃% edge on 10 bets a day at -300 already has the technology to submit large numbers of wagers without manually having to enter each one. Of course that doesn't ensure that a book won't move its lines in response to a given bet, but given that this question hinges on simultaneously identifying 10 bets at -300 with 6²/₃% edge this is quite obviously a hypothetical anyway.

Anyway, this is all completely besides the above point, and you know that.

[Data]

I am trying to bring in some reality into this discussion. I am not attacking the beauty of your theoretical constructions, which I truly admire. I am just trying to talk about what I am interested in hoping that this interests the other posters, and hopefully you, too.

Recently, I found myself frequently thinking about what utility function I should chose considering my personal preferences and market's realities. So, I have been thinking about Kelly's aplicability in real-life sportsbetting, hence my off-topic arguments. Feel free to divert this.

On a side note, here is an idea for your multiple-Kelly calculator. Say,

o - is the best available line
x - a parameter, 0<x<1
x*o - the best parlayable line

If you could include the ability to replace o with x*o in all the parlays while looking for geometric mean that would be a very nice step towards the reality.

I am sorry if I upset you, I did not mean to.

[chemist]

Whether or not it's worked well for a given a individual (or 10) in the past is largely irrelevant.

For an advantage bettor the strategy you're espousing generally corresponds to a high-risk, suboptimal money management framework and as such is likely antithetical to optimal bankroll growth.

No matter how much it might "seem" otherwise, advantage bettors unconcerned with "having fun" when betting should for the most part completely avoid uncorrelated parlays unless doing so as part of a sound and disciplined money management strategy (or in order to circumvent limits/discourage line movements).

What about books that offer promotional parlay odds? eg 6.5/1 for a three team ATS parlay. If you have three uncorrelated plays that you believe are +Ev, wouldn't it be better to take the parlay rather than three bets SU at -110?

My approach to solving this would be to compare the expected rate of bankroll growth of the two options, but I have to go shopping so I'll ask you instead.

[tomcowley]

For 3 bets at 53% and -110, it's better to take the 6.5:1 parlay.

[durito]

Are you telling me you couldnt hit 80% with a -300 home fave consistently? Are you nuts?

I will pay you $100,000 a year to come work for me if you can demonstrate this ability.

[gridiron guru]

Pardon me for being naive but can someone please explain exactly how round robins works, i been playing on intertops and i noticed it there but never played....

[Dark Horse]

Pardon me for being naive but can someone please explain exactly how round robins works, i been playing on intertops and i noticed it there but never played....

Four four bets (A, B, C, D), a two-team round robin is AxB, AxC, AxD, BxC, BxD, CxD; each paying out as a separate parlay.

[Ganchrow]

I am trying to bring in some reality into this discussion. I am not attacking the beauty of your theoretical constructions, which I truly admire. I am just trying to talk about what I am interested in hoping that this interests the other posters, and hopefully you, too.

Recently, I found myself frequently thinking about what utility function I should chose considering my personal preferences and market's realities. So, I have been thinking about Kelly's aplicability in real-life sportsbetting, hence my off-topic arguments. Feel free to divert this.

No worries.

The general methodology for addressing problems of financial economics is to initially consider the simplest case and then increase the degrees of freedom as necessary in order to elucidate the specific issue at hand. Enumerating each nonconvexity at every turn can quickly becomes tiresome, especially when the direction of the gradient is already well understood (and also an exercise in futility without specification of the model parameters -- that's why we use optimization engines, after all).

On a side note, here is an idea for your multiple-Kelly calculator. Say,

o - is the best available line
x - a parameter, 0<x<1
x*o - the best parlayable line

If you could include the ability to replace o with x*o in all the parlays while looking for geometric mean that would be a very nice step towards the reality.

The JavaScript Kelly calculator doesn't perform any optimization but rather determines an exact algebraic solution only to the general Kelly problem that assumes no constraints on event exposure (at single odds) other than a general budget and non-negativity. Your best bet with a problem specification such as this is probably just to find a solution computationally.

[Ganchrow]

What about books that offer promotional parlay odds? eg 6.5/1 for a three team ATS parlay. If you have three uncorrelated plays that you believe are +Ev, wouldn't it be better to take the parlay rather than three bets SU at -110?

Yes. I was specifically referring to parlays at true odds. Increase the odds beyond true and there will be Kelly value to the parlay in excess of that which could be obtained from simply taking the bets sequentially.