Friday, 23 March 2012

Conditional Probability

Referencing my earlier example of Roulette, BigAl suggests that I
“Cross the floor from your roulette table and take a seat at the blackjack table.

How do you think the professionals win? They plug away all day taking hundreds of negative EV bets before pouncing when the deck is favourable with large bets.

"If a system cannot show profits at level stakes over an extended period of time, then no alternate staking plan in the long term can produce a profit."

If they play level stakes all the time, they lose in the long-term. Their alternate staking plan produces a profit.

Any arguments? Presumably you'll attempt to come up with some sort of different interpretation of your statement."
I think the different interpretation comes from BigAl here, since he is quite possibly the only reader to take this discussion away from the world of sports betting, or at least on bets where the probabilities are independent.

This clearly doesn't apply to a game such as Blackjack, where the probability of winning is conditional on the outcome of previous events, a whole new ball game you might say.

Yes, in a game such as Blackjack, the edge can vary, and an expert player will know when there is an edge in his favour. If you play to level stakes you will lose at Blackjack, but if you are fortunate enough to be able to find a venue that will let you vary your stakes, and not decline your business, there are times when you can have a positive edge, and know that you have an edge. The edge is dependent on previous events, but this line of thought has nothing to do with sports betting.

With sports, the edge on each bet is independent.

Tony commented:
a) "someone with an edge misjudging the size of their edge" - if they have an edge, Cassini has already said that to level stakes they sbould be in profit, so a system that is in profit to level stakes is correct from what I can see? Just because the person with the edge misjudges that they can make profit to level stakes by playing a system of some kind of "revolutionary" staking system is not Cassini's fault.

b) Why use a staking plan if your edge is profitable to level stakes?

c) The fact the edge or perceived edge will vary depending on the odds available.

Available prices determine the edge, so if the prices are not there, the edge is not there, so the bet is therefore not there.

To summarise I think you are picking arguments with Cassini for the sake of arguing.

On to your second statment regarding blackjack. Blackjack is a game of skill, not chance, so i personally dont see how an edge is sports betting is comparable? Predicting the outcome of a set deck of cards based on what cards you have previosly seen dealt is different to predicting the winner/loser of a particular sporting event based on the previous number of minutes/plays viewed in the game? E.g., the dealer rarely fumbles a King making the play void after 10 consecutive low cards compared to a quarterback throwing an interception for a returned touchdown after an 11 play 90 yard drive.
BigAl picking an argument for the sake of it? Who ever heard of such a thing!

Of course comparing Blackjack to sports betting is false. Confusing the debate on sports betting (independent) with a game featuring conditional probabilities (e.g. Blackjack) might give me a post to write about, but it's of academic interest only to most readers.

Regarding Tony's mention of using a staking plan once you are confident that you have an edge, use of Kelly has been mathematically proven to maximise the growth of your bank over time, although a fractional version is more practical.

BigAl is misleading when he suggests:
That said, almost every successful sports bettor will misjudge their edge. Basically this is because there is almost always someone who knows more, or is simply superior at estimating prices every time you have a bet (not the same person every time of course).

So, to make it simple, let's assume his edge is always 3% lower than he thinks.

His bets at what he perceives to be 1% value are actually -2%. His bets at 5% are actually +2% etc. etc.
With historical data, it is a simple process mathematically to calculate your edge. How someone's edge could possibly "always be 3% lower than he thinks" is, again, a statement that defies mathematical principles. If his value is 1%, it is 1%, not -2%! 2 plus 2 always equals 4, even in Blackjack.

Example, the XX Draws hit at 33% over three years plus. I need a price above 3.0 to have an edge. Not all matches are the same of course, and the beauty of sports is that two teams can play each other on consecutive days and the result may well be different, but if I know that 'on average' the probability of a game resulting in a draw is 0.33, (3.0), then if I can back above this price, then all things being equal, I have value. I work with the knowledge that pre-game, there are lots of people who know more than me, and if the weight of all that money from gamblers in the know pushes the price below my value threshold, then there is no bet. Knowing when not to bet is as important as knowing when to bet.

As for the statement that
Basically this is because there is almost always someone who knows more, or is simply superior at estimating prices every time you have a bet (not the same person every time of course)
this statement should probably be qualified to specify pre-game on the more popular sports, but if you specialise on in-play trading on some of the less popular sports, you can learn to estimate the 'true' price as well as anyone else out there.


jokerjoe said...

Being off a maths bent, Kelly all the way for me. As you say, never full Kelly unless you can explicitly calculate the probabilities (as in casino games). Using a statistical model optimal kelly fraction is roughly the actual winnings over expected winnings when betting kelly stakes, and probably safest doing a fraction of that. Patience is the key.

BigAl said...

Cassini, you write very well and your blog is an interesting read but so many of your posts are full of gross inaccuracies.

Firstly, the blackjack example was used to show the principle behind your statement being false. i.e. that a system can have many negative value bets but using a correct staking plan can produce a profit.

The same principle can clearly be applied to sports betting, the difference being that you won't purposely have negative ev bets. But if you do - and almost everyone will - then a decent staking plan can still produce a profit.

If you honestly think that each individual xx draw bet of yours is value then you're living in a different world. Stick all the bets together and maybe you have found enough total value to make it profitable. Your results haven't hit the long run yet - time will tell.

You say "How someone's edge could possibly "always be 3% lower than he thinks" is, again, a statement that defies mathematical principles. If his value is 1%, it is 1%, not -2%! 2 plus 2 always equals 4, even in Blackjack."

Christ, you so don't get it. Read things properly man! "LOWER THAN HE THINKS" What part of that is difficult to understand.

By the way, nobody knows their precise edge in sports betting - FACT.

I might think a one-off two way sporting event is 50-50 but the price is 11-10. I think I have a 5% edge. The reality is that I will very often have over-estimated my edge. Unless you are betting on shit like roulette you don't know your edge. A professional gambler is really attempting to quantify the unquantifiable given that no two sporting events are the same.

Instead of sticking to your guns in your normal pompous way, you really should occasionally take a step back sometimes and think things through properly. Your logic and reasoning is often way off and your overall understanding of what you talk about is limited to say the least. But fair play, you have a great knack for wrapping up untruths in such a way as to convince the average reader you're correct.

BigAl said...

Three questions for you Cassini (I don't expect a reply to the above post).

When you started selling your xx draw picks how big did you think your edge was?

At this moment in time how big do you think your edge is?

Do you believe you under-estimated your edge, over-estimated your edge, or correctly stated your edge?

Make it 4 actually. How have the picks done since you first advertised your service?