[the_fredrik]

Hi there, and welcome to my first real post on this forum!

With the following reasoning I have convinced myself that it
will always be better to be doing arbitrage betting, rather
than using a great betting system with a certain large
long-term edge like 15%. I will try to keep it
resonable teoretical even though Ganchrow will probably find me to practical!

We assume we have a bankroll of $1000
We further assume there is a bet with two outcomes, A and B.
We KNOW that each have a 50% probability of happning.

The highest odds for outcome A we can find is 2.300 (+130)
The highest odds for outcome B we can find is 1.826 (-121)

Bet A seems terrific with a nice 15% edge or an expected return of $1.15 for every dollar bet.
Bet B seems horrible with an expected return of only $0.913 for every dollar bet.
(This can be compared with a "random" bet at -110 that returns $0.9545, so bet B is in some sense twice as bad as a random bet.)

I know there is another optimal strategy in this specific case, but let us take a step back and get a bit practical for now.

Let us choose between long-term strategy 'ARBITRAGE', which is to identify cases like above and do arbitrage betting, and long-term strategy 'PRO-BETTOR', which is to build a quantitative model of the real world that is capable of estimating the probablility of outcomes like A and B above very accurately. (easy, right?


STRATEGY PRO-BETTOR
==================

After thousands of hours of work using our super-brain, we use our model to identify cases with a large 15% edge like the one described above.
We do Kelly optimal betting, betting $115.4 on A.
In the long run this will mean an expected increase of the bankroll by $115.4*0.15 = $17.3 for every bet like this.

STRATEGY ARBITRAGE
================

We simply look for arbitrages manually or with a program, and are regularly identifying 1.77% arbs like the one described above. So we use our whole bankroll to bet $442.4 on bet A and $557.6 on bet B. Thereby locking in a profit of $18 each time we find such a bet.

**************************************** **

Which seems more difficult to you, the first strategy or the second? The amazing this is that with ARBITRAGE you are making More money at Much Less Risk!!
Even though we Know we have a Super-System that is able to identify bets with a 15% edge.

If you add practical matters like:
- your system might not be perfect
- you might want to have less risk than Kelly
- I can keep going

then to me, it quickly becomes clear that in order for the PRO-BETTOR strategy to be superior, you need a much higher edge than 15%! Who can honestly say they are confident that they have a 25% edge when betting?

There are a lot of aspects I have left out, like the number of bets available, the amount of dollars you can bet and so on, but the practical point I am trying to make is this:

Finding 1.77% arbs (rather easy) at a certain pace is roughly equivalent to having a reliable model that produces bets with a 15% edge at the same rate (difficult)

This means that most of us will be better of doing arbitrage - right or wrong??

Fredrik

[slash]

Why on earth did you waste your time writing such bs?

Grab a bear instead and get more out.

[ShamsWoof10]

Well there is NO DOUBT arbitrage is by far better overall then any system out there but the one thing about it is the books make life very unconfotable for you... It's not worth it also because Pinny. is no longer around for US players which makes it less efficient... You've got to have a ton of money to make it worth your time and if you play with enough the books will find a way to break one off in your ass.... They don't seem to care about smaller amounts though as much...

[Ganchrow]

Yes. A Kelly bettor, not constrained by betting limits, would indeed prefer a sure payout of 1.803% to a 50% probability of winning an event paying out at +2.3000. (To be indifferent between the two, the Kelly bettor would require odds of about 2.4611.)

However, a Kelly bettor could do even better by risking half his bankroll on A, and half his bankroll on B. In this manner his bankroll would increase by 15% half the time, and would decrease by 8.68% half the time, implying expected profit of ~3.16% and expected bankroll growth of ~2.48% over time.

I'd also add that in general scalpable bets tend to have rather low limits, which will be a problem for bettors with appreciable stakes. As such, out of necessity as their bankrolls increase, most advantage bettors will have to eventually shift their focus away from pure arbs.

[magnavox]

Originally Posted by slash

Why on earth did you waste your time writing such bs?

Grab a bear instead and get more out.

[slash]

Is that you in that picture magna?

Exactly the thing I was talking about. Get out, take a breath of fresh air and have fun.

[magnavox]

Yep, I can assure you, this bear was quite tasty.

[slash]

Originally Posted by magnavox

Yep, I can assure you, this bear was quite tasty.

LOL!!! It took me 2 posts but now I know what you mean

I should probably edit my post to get that spelling error out

[magnavox]

[ShamsWoof10]

Originally Posted by Ganchrow

I'd also add that in general scalpable bets tend to have rather low limits, which will be a problem for bettors with appreciable stakes. As such, out of necessity as their bankrolls increase, most advantage bettors will have to eventually shift their focus away from pure arbs.

I totally agree that is maybe the biggest factor...

[wack]

Originally Posted by Ganchrow

Yes. A Kelly bettor, not constrained by betting limits, would indeed prefer a sure payout of 1.803% to a 50% probability of winning an event paying out at +2.3000. (To be indifferent between the two, the Kelly bettor would require odds of about 2.4611.)

However, a Kelly bettor could do even better by risking half his bankroll on A, and half his bankroll on B. In this manner his bankroll would increase by 15% half the time, and would decrease by 8.68% half the time, implying expected profit of ~3.16% and expected bankroll growth of ~2.48%.

I'd also add that in general scalpable bets tend to have rather low limits, which will be a problem for bettors with appreciable stakes. As such, out of necessity as their bankrolls increase, most advantage bettors will have to eventually shift their focus away from pure arbs.

Quick question for the master. Is 50/50 the best bet because the p is 0.5 of each event occurring? Or is it not as simple as that?

[vanman]

arbitrage every time,no risk to money.

[Ganchrow]

Originally Posted by wack

Quick question for the master. Is 50/50 the best bet because the p is 0.5 of each event occurring? Or is it not as simple as that?

Actually, it is. It's not at all obvious but the math works out such that in a case of a pure arb within a market, the Kelly optimal weights, assuming no other constraints would be the same as the outcome probabilities.

So for example, given three outcomes with odds of:
o₁=3.9600
o₂=1.6333
o₃=8.0000

and win probabilities of:
p₁=25%
p₂=60%
p₃=15%

we see that a pure arb exists (1/3.9600+1/1.6333+1/8.0000 ≈ 0.98977 < 1) and hence the Kelly optimal weights are (k₁, k₂, k₃) = (25%, 60%, 15%).

Note that if o₁ were twice as high, let's say, at a line of 7.92, the Kelly optimal weights would not change as the arb would still exist.

However, if o₁ were only slightly lower, at let's say 3.800, then no arb would exist and the above equivalence will not hold. The Kelly-optimal weights in this case would be (k₁, k₂, k₃) = (0%, 1.7476%, 3.1068%).

[wack]

Thanks Ganch, that's what I thought

[wack]

Originally Posted by Ganchrow

Yes. A Kelly bettor, not constrained by betting limits, would indeed prefer a sure payout of 1.803% to a 50% probability of winning an event paying out at +2.3000. (To be indifferent between the two, the Kelly bettor would require odds of about 2.4611.)

However, a Kelly bettor could do even better by risking half his bankroll on A, and half his bankroll on B. In this manner his bankroll would increase by 15% half the time, and would decrease by 8.68% half the time, implying expected profit of ~3.16% and expected bankroll growth of ~2.48% over time.

I'd also add that in general scalpable bets tend to have rather low limits, which will be a problem for bettors with appreciable stakes. As such, out of necessity as their bankrolls increase, most advantage bettors will have to eventually shift their focus away from pure arbs.

Another question - this is an interesting topic. If the odds in the example were +150 and - 121, and the p of both was 0.5, are you saying the optimal strategy is now to just bet the value side of the line in the top paragraph?