singles vs combos

First of all, sorry for my poor English. I am not a native speaker.
I am interested in betting strategy and this forum is the place with by far the best information on this topic.
There is an issue which has been bothering me for a long time now but I couldn't find anybody who could explain the matter to me. The question is: If I have a positive yield on flat betting on singles, why shouldn't I make combos of the value bets I spot? You obviously know that it would dramatically increase my yield( example: you estimate the fair odds for an outcome to be 2. A bookmaker is offering odds of 2.1. You get an edge of 5%. If you combine two bets like this you receive fair odds at 4 and the bookmaker offering 4.41 so your edge is 10,25%, for 3 bets in a combo you have as much as 15,8% and so on...)Where is the catch? It looks like an easy way to pump the yield which is extremely difficult to achieve in any other way. Can anybody point the disadvantages? The few I know are:
1. You are forced to use only one bookmaker so you are not able to choose the best odds.
On the other hand, making combos is the same as betting on the second game the money won on the first one. Therefore the problem is solved unless the games are played simultaneously( what a difficult word you have!).
2. The odds increase so, as Joe once wrote: "the longer the odds you bet, the more bets you should have to smooth out the profit growth, i.e. making it less risky".
Still, is this slight increase in risk not worth the huge( 5% is huge, isn't it?) increase in yield?
3. You make less bets.
It can be solved by putting games in combinations like 2 out of 5 for example, which gives you 10 bets instead of 5.

I may be terribly wrong here but I am only at the begging of my adventure with statistics (as I am in highschool yet) so, please, forgive the naivety. I would be grateful if anybody could prove me wrong and let me sleep calmly.

[Jezza]

If you are 100% SURE you have an edge then you are correct, your advantage is multiplied by the doubles and trebles (I would never go more than trebles). However if you are at a disadvantage, which if you consider most bookies price a football match at an overround of 12% you probably are, then the treble multiplies each disadvantage turning a bad bet into a HORRIBLE one.

I would advise sticking to singles with the best odds available unless you are 100% sure you have the advantage and then go for doubles and trebles

Jez

[Joe]

I'd second all that.

You need to be sure that you have your edge in each selection, otherwise the overround starts to work against you. To reduce the risk to the bank due to the longer odds I'd also suggest a smaller stake size, which of course reduces profit potential, but then everything's a trade-off in betting.

Thank you for the quick reply. Actually I knew that you must be sure to have an edge to bet on doubles or trebles.
The thing I am interested in is what are the results if you don't have the advantage in each game but an average one, which is more like a real life situation. In other words, is it much different if you have an edge of 5% in EACH game than if the AVERAGE advantage is 5%. I know Joe is the person to turn to as I have seen the results of his many simulations including those in which he compared constant edge to an average one. If you find a moment for me I would be grateful and very happy to see the results, Mr Joe.

[Joe]

You'll have to give me a little time to do this. My hunch (and from memory of other stuff) is that provided the average edge for a double is 1.1025 (where you believed the singles to have edges of 1.05) then you'll do OK (but you still need to reduce the stake size as suggested above because of the risks of the longer odds).

Currently I'm sweating about my tax though and I may not be able to get on to this until later tonight or tomorrow.

[Jezza]

Why not just put games you have the advantage in in the trebles? Leave the average or bad ones to the singles.

As for lowering your stake on a treble of advantage games, I would actually INCREASE it. Logically, the bigger the advantage you have the bigger your stake should be and a treble of three advantage matches has an inherently bigger adv than playing the three singles seperately. A good example of this logic would be if you had a time machine and went back to last weekend knowing the results. Ok this is pie in the sky 100% adv stuff, but what would the perfect bet be in this 100% adv situation? As big a multiple as you could put on with the MAXIMUM stake allowed

Jez

Just one more thing that crossed my mind today:
Although the risk of going bankrupt is greater because of the longer odds, the higher yield decreases it at the same time, doesn't it? You proved it yourself, Mr Joe, by presenting some graphs in the topic pointing to the disadvantages of the Martingale system. I wonder if the effect of the yield on the risk is big enough to make up for the increase caused by the longer odds. I guess the only way we can find it out is to wait for Mr Joe to run the simulations...

[Jezza]

there is something called the kelly critereon which calculates the perfect amount to bet for any given advantage and bankroll.

Basically the formula is, determine your %adv and bet that % of your playing bankroll. Obviously, you will never qipe out with this formula and if you are good and your bankroll increases, so will your bet ranges

Jez

That's true. It advises you the optimal stake for a particular value and of course the bigger the value the higher the stake should be. The problem is that if you overdo, for example by overestimating your edge, you will probably go bankrupt very soon. There is a scientific proof for this. I read, or at least tried to, a work by Mr Breiman on the optimal gambling system. It was very challenging for me since it was obviously written in English. I could understand only parts of it and one of the part I did get was about stakes:
"We..noticed the interesting phenomenon that there was a critical fraction such that if one bet a fixed fraction less than this critical value, then Sn aims at the infinity and if one bets a fixed fraction greater than this critical value, then Sn aims at 0." Sn is the fortune after n games. I don't know if I used the words "aims at" properly( There was an arrow in the text but I have no idea how to write it with the keyboard). If I understood it properly then it's always safer to reduce your stakes than to make them higher.
This, however, is not the reason why Mr Joe advised to bet lower stakes on higher odds, I think. The problem is that with longer odds you have obviously lower probability of winning and therefore it's more likely for you to hit a long loosing streak and face bankruptcy as a result. Even if you have a high yield.

PS Could anybody tell me how to quote somebody? Thank you.

[Joe]

Everyone is basically right here, yes the yield should theoretically increase but the increased size of odds will have a bigger influence on bankrupcy risk, so I would not advocate increasing stake size on multiples for this reason. Yes, Kelly is the ultimate answer to determining the stake size. I'll do a quick and simple simulation tomorrow and see what comes up.

By the way, Joe is my Christian (or first) name, so Joe, not Mr. Joe, will suffice.

To do quotes use [ quote ]your text here[ /quote ] (minus the spaces next to the square brackets).

Welcome aboard prezeszczepan

(We'll have to get a nickname so us monoglots can manage to spell )

No need for you to apologise. I think your English is excellent, better than that of many who claim to be native speakers Many other posters might also note that a polite enquiry gets a much more rapid response than the 'I want to get really rich. Please e-mail me and tell me how' types!

I'll make some short comments to add to what has already been posted, most of which is eminently sensible stuff.

1) That arrow can be approximately translated as 'tends to'
2) You are correct in your interpretation of its implications
3) In simple statistical terms think about mean and standard deviation. The edge corresponding to the mean, and the true odds being related to the standard deviation. Higher odds means higher standard deviation in the returns. So even if the mean (edge) is higher, so is the risk.
4) If you want to experiment go to the punterstools section. There is a spreadsheet for download there that I put together to allow you to play around with different edges and stake sizes and look at the risk of bankrupty, or having extended losing runs.

M.

[Joe]

OK, results from a simple simlation...

250 bets (singles vs. trebles), each selection is 1 unit, bank is 20 (so level stake is 5% of starting bank). Edge for each selection is 5% so for a treble is 15.76%.

If you were to have unlimited funds, you'd expect your finishing profit for singles to be 12.5 units and for trebles, 39.4 units (plus of course the 20 starting bank).

Now in 1000 runs, for singles betting, 67 banks were lost at some point, so for these finishing bank = 0. This takes the average profit down a little to 11.1 units, with a yield of 4.44%.

For trebles, 371 banks (over one third) were lost, taking the average profit down to 27.2, and a yield of 10.87%

So OK, profit expectancy is still greater but the risk of bankruptcy is much higher (much too high for me). In the real world it's unlikely you'll have access to 1,000 20 point banks. Blow the first and you might be tempted to start again. Blow the second and you may well jack it in.

So if we reduce the stake size on the trebles by a factor of 4, lost banks are then 8 (less than 1%) and average profit is 9.1, and yield of 14.58% thus confirming the ever-existing trade off a punter must make between risk aversion and profit desire.

I've not tested for variable edge, but basically if your average across singles or trebles is about what you expect it to be (even if it's quite variable and sometimes not real on a bet by bet basis) this won't affect the results much at all.

I think punters should concentrate on demonstrating to themselves that they can find a viable edge over the bookie using singles. Once they have proved this to themselves on a long term basis, they might wish to think about multiples, but at reduced stakes. Given the risks of bankrupcy involved in securing higher actual profit, I'd say that it's probably not worth the effort. However, if you do reduce stake size, you may not make any more in real terms, but your bank is much safer since the yield is higher than for singles. But there is much to prove on the part of the punter before he gets to this stage I feel. Also, I'd keep my multiples to quite short odds thus making the most of the favourite longshot bias.

To do quotes use [ quote ]your text here[ /quote ] (minus the spaces next to the square brackets).

Thank you.

By the way, Joe is my Christian (or first) name, so Joe, not Mr. Joe, will suffice.

No problem, Mr. Joe.

Welcome aboard prezeszczepan
(We'll have to get a nickname so us monoglots can manage to spell )

Sorry for that. If there's a way I can change my username, please, show it to me and I will gladly follow your advice. If not, than you can call me "rszczszczszrz" or simply "hjflgvvjkll" ( I hope these usernames are not taken yet) . My name in English is Lucas. I will sign my posts at the bottom so that if somebody is so kind to answer them, he doesn't spend half of a day spelling my name.

3) In simple statistical terms think about mean and standard deviation. The edge corresponding to the mean

Could you, please, explain the term "mean" to me? I think it would be enough if you wrote an equation by which it is expressed in the theory of probability.
Btw, I found your comments very useful. Still, they were not half as useful as the spreadsheet you put together, which is really top class.

Lucas

Make sure you select the ezCodes radio button. You must have had HTML or plain text selected when you posted the above.

You can't change your username, sorry. You need to take out a new one if you don't like it.

This is not a comment on the subject you're discussing, just wanted to praise you, Lucas, for the way you introduced yourself and made your first posts to the Punters Lounge. Serves as a great example to everyone, new and old.

The mean is the average.

Average(a,b,c,d)=[a+b+c+d]/4

[Jezza]

Thanks for the simulations joe, I was wondering what would happen if you set the stake in your simulations to be calculated by the kelly criterion? I dont think 1/3 of the trebles would go bust then?

Cheers,

Jez

Unfortunately, I am afraid it would, Jezza. Kelly criterion advises higher stakes for higher advantage and for trebles your theoretical edge would be much greater than for singles, thus so would be your stake, thus so would be the risk of loosing everything.

I am really grateful to you, Joe, for doing the simulation just for a common Mug punter. I don't want to behave like a stubborn donkey( do you have this saying in English?) and persist that combinations are better, because from what you have written they simply are not. I have got one more question, though:

Now in 1000 runs, for singles betting, 67 banks were lost at some point, so for these finishing bank = 0. This takes the average profit down a little to 11.1 units, with a yield of 4.44%

So if we reduce the stake size on the trebles by a factor of 4, lost banks are then 8 (less than 1%) and average profit is 9.1, and yield of 14.58%

Which one is better? The profit in the second case is not much less then in the first one, whereas the risk is significantly lower( 1% chance of loosing the bank compared to 6,7% for singles). Maybe it would be possible to find the size of stake which would provide better profit as well as lower risk? By the way, what does "by a factor of 4" mean? Could you explain it to me, please?

Thank you for the explanations, madmick and OddsAgainst, and to you Lardonio for your kind words.

Lucas

[Jezza]

Lucas - You can never go bust using kelly, the stake is always a % of your bank (the same as your advantage %) therefore if you lose a couple of bets, your stakes are automatically reduced. It is the perfect staking system, provided you can calculate your advantage exactly.

Jez

You are right, Jezza. As far as you are using Kelly criterion with fixed stakes as a percentage of current bank. However, Joe did a great job to point the disadvantages of any staking plan based on current bank percentage in comparison to those using fixed stakes as a percentage of starting bank. Therefore he suggested using Kelly criterion with the starting bank method which proved to be saver as you were more likely to end the season in profit then using current bank. On the other hand, you CAN obviously go bankrupt in this way that's why I wrote what I wrote...
I see you are very interested in Kelly therefore I would strongly recommend you reading the topic "Kelly Criterion Staking Plan" by Joe. Some fantastic research is made there. Actually, this post was one of the reasons I joined this forum and also one why I felt it would be appropriate to call Joe- Mr. Joe( from what he knows and what skills he has I simply assessed that he must be more or less 1000 years old. My Mom taught me to show respect to the elder people).