singles vs combos

[Jezza]

lucas

Thanks for the reply, you are exactly right. I am a bit biased towards kelly because In card counting, it is easy to judge your exact advantage over the house for any given set of rules and true count. For sports betting it is of course a lot harder to judge - and it seems to be something I cannot manage to do never mind I enjoy it anyway. I have not completely studied kelly 100% but have read many gambling books explaining it, and advocating its usage.

remember that Kelly staking implies that the stake size is proportional to two things:

1) The edge for that bet
2) The quantity defined by 1/(Odds-1)

Therefore for the treble, a smaller stake would be implied because of the higher odds. e.g for offered odds of 2.0 and an edge of 10%, the edge for the treble would be 33%, but the odds would be 8.0

Therefore the recommended stake size would be 33%/(8.0-1)=33/7=4.9% or so of bank, i.e. less than half of what it would be for the equivalent single.

Remember also that Kelly is based on maximising the expected profit in the long run and doesn't consider the risk incurred along the way.

Also, as I pointed out in a previous thread, True Kelly staing is a little bit more complex than the commonly quoted Edge/(Odds-1)

remember that Kelly staking implies that the stake size is proportional to two things:
...
2) The quantity defined by 1/(Odds-1)

Good point, madmick. I missed that.:o If so then it may really be not such a bad idea to check the results of Kelly criterion on doubles or trebles. I mean Joe rightly advised to lower the stakes and if Kelly does it automatically...
It proved to choose the perfect( in terms of profit not risk) amount to bet and here it lowers the risk, too! If it is still too high, maybe we should try half or quarter Kelly? I feel ashamed to ask Joe to run a simulation. I will register under different username and do it then, so that he doesn't recognize me

I feel ashamed to ask Joe to run a simulation. I will register under different username and do it then, so that he doesn't recognize me

Like your sense of humour my friend but it would be to no avail. Mr. Joe will recognise you alright. Don't get many first time punters with your insight and willingness to do some research before posting.

[Jezza]

yeh you are right mick I forgot all this, it is very hard to calculate true kelly on the spot tho. I just would just bet the % adv I had of my bankroll, which as I am learning would not quite be the correct thing to do with these multiples!!

Would love to see the results of joes simulation using kelly tho

Jez

[Joe]

Well, Jezz, you're gonna have to wait for my book to come out (hopefully some time this year when I've found a publisher).

Mick said..

Remember also that Kelly is based on maximising the expected profit in the long run and doesn't consider the risk incurred along the way.

Actually, you are refuting here what you once said about Kelly, that time correctly, that in fact Kelly aims to maximise the growth rate of bank, not the profits, and does explicitly consider risk in this.

Yes, Kelly is the theoretical best, but remember, the simulations I did earlier used level stakes, not fixed percentage stakes. Thus, as the bank grew (or fell) the stakes stayed at 1 unit (or 0.25 for the third one - this is the factor of 4 I referred to przeszczepan, i.e 4 times smaller since the odds of the treble are 4 times the odds of the single). Kelly, of course is effectively a percentage bank staking plan, so as the bankroll varies, so does the average stake size. Theoretically, it's true you can't go bankrupt, but in the real world you'll soon either quit through demoralisation or reach a bookie's minimum stake limit.

The beauty of Kelly is that it basically combines the 2 important things that the punter should think about - his edge and his odds - so bet more for better edge and less for higher odds. But as for all percentage bank staking, the chief drawback for me is that over x number of bets, you are less likely to be in profit than for equivalent fixed staking plans (because early losses take longer to recover). In summary, when you profit, you profit more, but less frequently over specified betting time frames (if you can follow that), e.g. a season. If your edge is large (say 15% +) or you have the patience to see out longer periods of showing a loss, any percentage bank staking plan is more profitable (in terms of real money, not yield) in the long run. But for many punters whose psychology is influenced so much by the short term ups and downs, this drawback in my opinion is not insignificant and needs to be reflected upon.

[Jezza]

ahhhhhhhhhh of course, the light finally turns on in jez's head (took a while as usual lol). Being a bit risk averse (says me who has a real roullette and blackjack table in the house lol) and with the steepness of the negative swings that happen all too frequently I personally would stick to kelly but I agree with everything you say..... You really have a book coming out joe? Is it on staking, betting systems, sports betting or what?

Jez

Joe wrote:

But as for all percentage bank staking, the chief drawback for me is that over x number of bets, you are less likely to be in profit than for equivalent fixed staking plans (because early losses take longer to recover).

If I am not wrong, they do not take longer to recover for Kelly staking plan using the starting bank method, which is your own invention as far as I know, Joe.

I have got an idea:

Let's consider our trebles. We have got a fantastic edge as well as a huge risk of loosing the bank because of long odds. To lower the risk we use Kelly staking plan which, as madmick proved, advises lower stakes for our long odds and thus decreases the risk of going bankrupt as well as optimizes the profit. If the stakes are still to high we can decide to "reduce the stake size on the trebles by a factor of 4" ( but I guess they would get to low then). To lower the probability of ending in a loss after x number of bets we decide on the version of Kelly which uses percentage of starting bank.

I hope I made my idea clear to everybody. Can you point out it disadvantages?
I have got a hunch that we are heading for a better staking system then the Martingale. It's only a greenhorn's hunch, though

[Joe]

przeszczepan, you really have been reading those past threads.

Yes to everything you say. For me, A type of Kelly using % of starting bank, not current bank, would improve the chances of profit (although technically increase chances of bankruptcy). But I didn't test this for my book because it's technically not a traditionally Kelly plan and I thought people might get confused. Besides, with the info. I've provided in it, hopefully readers might experiment a bit and look at this particular method themselves, as well as others.

Personally I'd also add that since most of my ratings systems attempts at predicting edge for a bet are pretty useless, and for my more subjective ski jumping analysis I'm really only guessing the strength of a bet, I'd basically use a fixed profits plan and simply assume that my average singles yield (if it existed) was my edge for every bet, thus avoiding an overcomplication. Really there is no right or wrong, best or worst staking plan, it all depends on punter preferences, but the aim should be to think about them a little more and what's most suited to these preferences.

Is it on staking, betting systems, sports betting or what?

Everything relevant to fixed odds, mate. Well, except matched betting, but then all the principles I discuss apply there so I assumed a reader can logically apply them to this area of betting. Here's a summary...

1.&nbsp &nbsp &nbsp &nbsp Sports Betting as a form of Investment
2.&nbsp &nbsp &nbsp &nbsp What is Fixed Odds Betting?
3.&nbsp &nbsp &nbsp &nbsp Beating the Bookmaker
4.&nbsp &nbsp &nbsp &nbsp Rating Systems for Sports Prediction
5.&nbsp &nbsp &nbsp &nbsp Sports Betting & Risk Management
6.&nbsp &nbsp &nbsp &nbsp Risks and Returns for Fixed Odds Betting
7.&nbsp &nbsp &nbsp &nbsp Staking Strategy & Money Management
8.&nbsp &nbsp &nbsp &nbsp A Winning System?

Last chapter is a mish mash of goodies like favourite-longshot bias, statistical significance of your records, reliability of numerical rating systems etc.)

Thanks Joe

Sloppy wording on my part.

Kelly does indeed set out to maximise the growth rate, which in turn over the long term (i.e. as t goes to infinity) will maximise profits - but not necessarily over a shorter term. The risk is considered in the sense of maximising the expected growth rate, but not in terms of minimizing the risk of halving or losing a given percentage of the starting bank at some intermediate time. This is what I was trying, inelegantly, to say above.

A small correction by the way, the odds for the treble are indeed 4 times that for the single, but the profit on a win (Odds-1) is 7 times that for a single. The stake size for fair comparison should therefore be 1/7 and not 1/4 I think?

Lucas, the percentage of starting bank method has been around a long time, its not Joes invention. He just describes the various systems and their associated risk in a more analytical and dispassionate way than his predecessors

Regarding the ideal staking plan, as Joe says, it is in many ways a matter of preference as you balance risk against return.

Percentage of starting bank is a pretty good way to go in my opinion. Exactly what percentage is another point - again from a personal perspective I think going less than your theoretical edge by a factor of 50% or so is no harm.

There is another point I made before which is that I think it is imperative as part of the overall plan that you withdraw money from your bank periodically - otherwise the profit is somewhat notional. That could be after every win (e.g. 5% of winnings), could be after a certain percentage growth in bank, certain amount of time or whatever.

The other factor is that you should 'restart' your bank every so often if you are operating a % starting bank. That could be once a year, or after a set amount of growth (the plateau system), etc

Regarding multiples etc, what I sometimes do, more for fun than anything else is to look at what my expected profit (i.e. edge) on a number of singles is and stake this amount on all the double permutations. That way I expect to 'break even' on my singles stakes (having discounted for the stakes on the multiples) and get occasional boosts from the extra leverage of the multiples. Eg. suppose I am betting 5 singles (5 units each) at odds of 2.0 and expect to make 10% profit. I expect to make 10% of (5x5 units)=2.5 units profit on the singles. There are 10 doubles for those 5 games, so I would stake 0.25 units on each double. If 2 of the 5 come in I have staked 27.5 units and get 21 units back (I lose 6.5 compared to 4 if I had only done the singles). If 3 of the 5 come in I get 33 units bank (profit of 5.5 compared to 2.5 for just the singles). Obviously the real paybacks come if 4 or 5 of the 5 come in (6 and 10 units extra profit respectively over the 15 and 25 units profit for singles).

[Joe]

Or you could pay yourself a wage.

The stake size for fair comparison should therefore be 1/7 and not 1/4 I think?

Yes, indeed. I was being a bit lazy really.