Accumulators superior to singles

[slapdash]

Re: Accumulators superior to singles

I think I made a fairly detailed post about this some time ago' date=' in response to somebody else's question. I'll try to find it. I doubt it's any simpler than what you've found elsewhere, though.[/quote'] Here you are: http://forum.punterslounge.com/f21/chance-going-broke-level-stakes-betting-43017/#post709531 Don't know if that's any use to you?

[Machine]

Re: Accumulators superior to singles Cheers will read that in depth tomorrow

[Machine]

Re: Accumulators superior to singles Moggis I was once told by a mathematician friend of mine who works for the M.O.D that it is pointless placing a permed bet unless the sum of the multiplied odds of the lowest possible win is equal to or greater than the sum of the whole bet. ie a trixie = 3*doubles & 1* treble = 4 bets So the minimum odds should be 2.00 or evens because the min win is a double and 2*2 = 4 and gets you your money back the rest if any are the bonus His reasoning behind it was that if you are confident enough to place a perm bet then you at least should be confident enough to hit the minimum criteria and get your money back, with any other subsequent winners boosting the pot. And if you weren't confident then singles would be the better option. How true mathematically wise that is I dont know but it sounded logical to me after several pints. Maybe thats how Steele does his permed bets Never read the book so wouldnt know

[moggis]

Re: Accumulators superior to singles ok ,I just want to wrap up the paul steele book business and then leave you to it. I beleive that singles bets came in in 2002,the year his book came out-so obviously it was written when indeed multiples were necessary. At no point does he actually discuss singles v doubles but at one point (on page 18)he does appear to strongly imply that you should do singles- which I would say should trump everything else and it looks like you would all agree. The only thing is,one of the reasons his book was successful,I believe,is because at the end he proofs his bets for 6 months.. And his various multiple bets made a 115% profit!! at the end of the day however,if a man who made 115% profit doing multiples,appears to advocate singles at one point..then it seems to me that singles it is.. sorry therefore to have introduced a degree of noise into the thread.... ironically I have always done far better(on results)with perms than I have with singles..

[moggis]

Re: Accumulators superior to singles only just seen your post monkeys nest.thanks for that. I shall certainly take note of it once I ve had a drink. Paul Steeles book was never enjoyable reading! good luck

[Shy10ck]

Re: Accumulators superior to singles

Blah, pitty to see what this thread has become; it was my favourite reading yesterday evening. ;) Shy10ck, I'm afraid I disagree with you. I said in my first post in this thread that your math looked odd to me, but I couldn't figure it out myself; I just felt it's not possible 12fold to be that more profitable than 12 singles. Monkeys Nest has explained it thoroughly, in both simple words and through math. This is where you are wrong. In fact, the approach is wrong - your statement is correct, but there is no way you can apply it in reality. Let me try to explain: if you place singles, there is indeed no matter in which order you place them, each winning one brings profit. However, with doubles, it very, very matters how winning picks are distributed! Overall, there will be 25% of winning doubles, but problem is that in reality you can choose ONE SINGLE combination of doubles, and there is no guarantee that it will be winning double, it's pure luck. Let's say, you intend to bet on 8 matches this evening, A, B, C, D, E, F, G and H. Nevermind if they start at the same time, or they are consecutive, as you say. How will you combine them in doubles? You can combine this way: AB CD EF GH And you can also combine this way: AC BD EF GH After hour and a half of running up and down the pitch, you find out that winning matches were, let's say, A, B, F and G. If you placed your bets as in line 1, you indeed have 25% strike rate; if you placed line 2, you lost them all, despite strike rate being 50%! Look at post #12 in this thread, that's what Monekys Nest warned you of! Is it possible that you will place line 2, and not line 1 each and every time? Yes, it is - you get correct 50% of matches, yet there is no any guarantee that you will ever place winning combo! If you place consecutive bets, one after another, is there any guarantee that your streak won't look like this: Won - Lost - Won - Lost - Won - Lost - Won - Lost - Won - Lost... and so on, untill infinity? No, there's no guarantee, it's unlikely, but possible! And then again, you hit 50 % of the matches correct, yet you haven't completed any winning double! Of course, there is a way to guarantee some winning doubles: you would have to bet on them all! And that's topic Monkey Nest covered in post #15: Indeed, there is 8 over 2 = 8 * 7 / 2 * 1 = 28 doubles, out of which 4 over 2 = 4 * 3 / 2 * 1 = 6 doubles are winning; you can choose only 4 out of those 6, so your probability of hitting a winning double is ( 4 / 6 ) * ( 6 / 28 ) = 14.28%... again as explained in post #33! And note, it's only in case you back them all, all 28 doubles; in case you continue with random doubles, there is no probability - you may hit winning one each fourth time... but you may pass a thousand doubles without any winning one!

I dont get why this is so hard to understand. It is simple math, though with a lot of numbers. It doesnt matter if you bet, 2 singles and 1 double, 8 singles and the full permetation of 28 doubles or whatever number of singles and doubles. The math is the same. Lets use the 8 single bets and the 28 doubles as an example. If you bet 8 mathes, you can hit 0,1,2 … or 8. Agree? You can hit/miss in 256 different ways. Hits - Ways 0 – 1 1 - 8 2 – 28 3 – 56 4 – 70 5 – 56 6 – 28 7 – 8 8 – 1 If you hit 0 you, hit 0 singles and 0 doubles, hit 1, you hit 1 single and 0 doubles, 2 = 2 singles and 1 double … 8 hits = 8 singles and 28 doubles. Like this. Hits - Singles - Doubles 0 = 0 - 0 1 = 1 – 0 2 = 2 – 1 3 = 3 – 3 4 = 4 – 6 5 = 5 – 10 6 = 6 – 15 7 = 7 – 21 8 = 8 – 28 You have 8 singles and stake 800/8 = 100 You have 28 doubles and stake 800/28 = 28,57 If you do the calculations Which fx look like, for doubles and 5 hits, 5 hits = 10 doubles x (56/256) x odds 4,84 x 28,57 stake = 302,48 and for singles 5 hits = 5 singles x (56/256) x odds 2,2 x 100 stake = 240,625 If you do these calculations from 0 to 8 hits, You win 880 for 800 on the singles, 880/800 = 1,10 the original value. You win 968,84 for 800 on the doubles, 968,84/800 = 1,21 :-)

[froment]

Re: Accumulators superior to singles

If you do the calculations Which fx look like, for doubles and 5 hits, 5 hits = 10 doubles x (56/256) x odds 4,84 x 28,57 stake = 302,48 and for singles 5 hits = 5 singles x (56/256) x odds 2,2 x 100 stake = 240,625

You lost me here now... :\ Haven't we been talking all the time about strike rate of 50 %, and exactly 4 hits out of 8 matches; where is now 5 hits coming from? :wall In that case, your edge is not 10% anymore, as you stated in your first post, but 17% (probability 5/8 = 62.5%, so true odds 1.60, and you still have 2.20, or 45.5%); I mentioned before that bigger the edge, faster the increase in difference between numerator and denominator with number of bets in a combo, so advantage of combos over singles increases. I'll leave for tomorrow to read it once again, but thank you for efforts to explain anyway! :ok

[doctoritcata]

Re: Accumulators superior to singles Shy10ck is right. The ROI on the accas with value is greater than the ROI on the same bets as singles. The point that Slapdash makes is reasonable,but it all comes down to a personal choice between lower ROI/lower risk and higher ROI/higher risk(of ruin). If one can figure the appropriate MM for he's bets so he's risk of ruin is low enough,he must take the accas and be more profitable than if he was taking singles.That's all. It wonders me how come there is still a discussion going on on here about this stuff when it has to be clear by now that when you're multiplying value bets you are in fact increasing your ROI. P.S. Needless to mention,but we are talking ONLY for bets with edge for the punter (value bets). If the opposite is true,then the more multiples one plays the faster he'll go bankrupt(but he is going to go bankrupt with singles aswell,nomatter how good his MM is it doesnt change the -EV)

[froment]

Re: Accumulators superior to singles Hey, Doctoritcata, :welcome back, nice to see you! I haven't seen you posting on forums ever since that saga with Kma! ;) As for the topic... I usually advocate singles, but never have tried to prove it untill this thread emerged; I see what's your point, but I have given it up for this evening, maybe will try tomorrow... :lol

[doctoritcata]

Re: Accumulators superior to singles Yeah it was quite a saga:lol Hope you're doing well mate!

[davidc]

Re: Accumulators superior to singles I am by no means a statistician but it is fairly simple for me: You bet on 8 matches (or 40 or 200 - it doesn't matter how many) as singles with 50% strike rate with odds for each selection being 2.2 and you are guaranteed to be profitable as long as you maintain the strike rate and odds. You bet on the same 8 matches (or 40 or 200 - it doesn't matter how many) as doubles with the same strike rate and odds and you have no guarantee that you will find even 1 winning double because you have no way to guarantee combining 2 winning selections. This means that finding winning doubles is down to pure luck even though you may still maintain a 50% strike rate. Just my tuppence worth. ;)

[froment]

Re: Accumulators superior to singles

In the early days of fixed odds football betting coupons' date=' I believe that it was normal for bookies to take trebles as minimum, and even then only if you included no home wins? I think you normally had to do at least five-folds (or something like that) if you included home wins? I may be misremembering the exact conditions.[/quote'] I remember those days, the same situation was here; minimum bet was 4fold, and treble only if all three bets were draws or away wins, as you said, or if weekend bet was placed in Thursday or earlier; singles were exceptionally allowed only after discrete arrangement with owner / manager in the shop, and usually only with three-digit stakes, not less. And that made me think of this topic in a mathless way: if combos indeed have been more profitable than singles, then why bookies had those restrictions? Why they didn't do the oposite - allow only singles, and prohibit combos? They are not charities, they set the rules in their favour. So they surely must have known something about singles or doubles that was not very advantageous for them, in comparison with combos, eh? It was only rise of competition and online bookies that forced them to allow trebles, doubles and singles without restrictions, and I don't think they were happy with it; "each stake on combos is a small, but irreversible loan to the bookie"...

[froment]

Re: Accumulators superior to singles

Yeah it was quite a saga:lol Hope you're doing well mate!

Yep, thanks! Hope you, too! :ok

[doctoritcata]

Re: Accumulators superior to singles

This means that finding winning doubles is down to pure luck even though you may still maintain a 50% strike rate. Just my tuppence worth. ;)

You are wrong here mate.It's not down to pure luck,but to statistics. As pointed in an earlier post with the same "luck" one can have more winning doubles than expected. Or less. Or exactly as expected. In the long term it will approach to expected value.

[davidc]

Re: Accumulators superior to singles

You are wrong here mate.It's not down to pure luck,but to statistics. As pointed in an earlier post with the same "luck" one can have more winning doubles than expected. Or less. Or exactly as expected. In the long term it will approach to expected value.

Yes...perhaps. But you still have no guarantee and by the time that lady luck catches up you may have done your bank. With the singles you are guaranteed.

[Jase82]

Re: Accumulators superior to singles

Yes...perhaps. But you still have no guarantee and by the time that lady luck catches up you may have done your bank. With the singles you are guaranteed.

Is there ever a guarentee in this game :unsure

[moggis]

Re: Accumulators superior to singles Okie Dokie,this time I really,really believe I have the definitive answer. I knew one of my books must have it! this is from "fixed odds sports betting-statistical forecasting and risk management"byjoseph buchdahl page 90: .."the performance of a punter with an edge over the bookmaker will be superior for doubles than for singles... for singles profit is proportional to the margin of success and increases linearly as the prediction rate improves. for doubles,however,profit is proportional to the square of prediction success and consequently increases faster.... where a punter has considerable confidence that he has achieved an edge over the odds doubles are theoretically preferable to singles.By the same token,trebles will perform better still with profit proportional to the cube of prediction success... as a general rule,the size of expected betting return will be proportional to the nth power of the betting edge where n is the no. of selections in an acca.,assuming that each selection has the same edge." WELL,I make that a TKO in the 10th for Shy10ck. I think I should be careful about too many more quotes as I am not sure how copyright works.....so as you can guess it goes on to caution against putting too many things in 1 acca,talks about increased risks of bankrupty,points out that 1 way to limit risk is to reduce stake size...and ends the chapter with this passage......... "There always exists a trade-off between the impulse to achieve higher profits and the need to control risk. HEREIN LIES THE ESSENCE OF GAMBLING. The most important decision a successful punter will make concerns the positioning of his betting strategy on the risk-reward scale. blah,blah,blah...............THERE IS REALLY NO RIGHT OR WRONG WAY TO BET" amen goodnight all

[doctoritcata]

Re: Accumulators superior to singles

Yes...perhaps. But you still have no guarantee and by the time that lady luck catches up you may have done your bank.

Yes it might happen.Thats why MM is of big importance.And experience.

With singles you may experence a long losing streak aswell no mater the chans of winning is greater than the odds suggested. There is no guarantee,but yes the variance is lower with singles. The MM is the key. P.S. Damn,how do I qoute in the middle of post,so it's done right and not like I just did?

[Shy10ck]

Re: Accumulators superior to singles

Let's try to keep this civil, guys. Let's take the example you gave in the first post. Two betting opportunities, each with a 50% chance and odds of 2.2. You looked at two strategies: (A) Two 100 unit singles. This gives an expected profit of 20 units. (B) One 200 unit double. This gives an expected profit of 42 units. Certainly (B) gives a higher expected profit than (A), which is good. But equally certainly it has a higher risk/variance, which is bad. At this point you could just say that one strategy has better profit, and the other has better (i.e., lower) risk, so it's just a matter of individual preference, and how risk-averse you are, which is better. But let's look at a third strategy: © Two 210 unit singles. This gives an expected profit of 42 units. So (B) and © have exactly the same expected profit. But, even though your total outlay is higher with ©, it's actually less risky in the medium or long term, for any reasonable measure of risk. Let's look at three different measures. (i) Risk of ruin. Suppose the same scenario occurs repeatedly, and each time you choose the same strategy, either (B) or ©. And let's suppose you start with a bank of 4200 units (the exact size doesn't matter much, but I've chosen a figure which is an exact multiple of the stake for both strategies, just for simplicity). With strategy (B), you have about an 11.1% chance of going broke, but with © only about a 3.6% chance. (ii) Variance. Both strategies have an expected profit of 42 units per go. But the profit from (B) has a standard deviation of about 419 units, whereas the profit from © has a standard deviation of only about 297 units. (iii) Kelly staking. Rather than fixing the stake, let's look at what the Kelly criterion would suggest, given that you've already decided whether you're going to do two singles or one double. The Kelly stake for singles with these odds and probabilities is about 8.33% of your bank (this should be reduced very slightly if you're placing the bets simultaneously), and then your expected profit would be about 1.67% of your bank for the two singles together. The Kelly stake for the double is about 5.47% of your bank, and then your expected profit would be about 1.15% of your bank for the double. So © is less risky than (B), but gives the same expected profit, so is "better" in any reasonable sense.

Thanks for a good reply. But there is something I dont get, so to get things straight. You would rather bet 50 singles at 2,20, 50% winning chance, at stake 210 than 100 doubles at 4,84, 25% winning chance, at stake 200

[froment]

Re: Accumulators superior to singles

You would rather bet 50 singles at 2,20, 50% winning chance, at stake 210 than 100 doubles at 4,84, 25% winning chance, at stake 200

Well, I think he already provided a valuable reply in another thread:

Suppose I can find even money bets with a 55% strike rate and I can either back them in singles or 4-fold accumulators. It's true that a one unit accumulator will, on average, make me more profit (0.4641 units) than four one unit singles (0.4 units). Does that mean I should bet accumulators? No. Another way to increase my profit is to increase my stake on the singles. If I increase my stake to 1.5 units, say, then my average profit on the four singles increases to 0.6 units, easily more than the accumulator. This seems rather facile, as obviously I can increase my expected profit by increasing my stake indefinitely, and if I go up to betting my entire worldly wealth, then that's obviously a good idea! However, although betting four 1.5 singles involves staking a lot more than just one 1 unit accumulator, it turns out that, by any reasonable definition of "risk", it's a lot less risky (as well as making more money). For example, suppose I start with a bank of 50 units, and measure "risk" by the chance I'll go broke if I keep placing these bets. With the one unit accumulators, I have over a 6% chance of going broke. But placing four times as many 1.5 unit singles, I have well under a 0.2% chance. So the higher-stake singles are not only more profitable, they're also "safer".

[Machine]

Re: Accumulators superior to singles Fromet I wouldnt even bother replying to him anymore,your just wasting your time

[froment]

Re: Accumulators superior to singles

Fromet I wouldnt even bother replying to him anymore,your just wasting your time

Nevermind... But I don't try to convince him, or anyone else, who is wrong or right - I don't think there is necessarilly wrong or right way to bet, some prefer singles, some other combos, and that's it. Obviously, both fans of singles and combos stand firmly on their positions, so this has been interesting discussion!

[moggis]

Re: Accumulators superior to singles

Well' date=' I think he already provided a valuable reply in another thread:[/quote'] Everyone is discussing theory,but there is a practical aspect of increasing singles stakes that needs to be mentioned. I assume you are all successful punters.And that means that getting bookmakers to take the stake that you require on a bet already poses most of you problems. Its all very well to talk about betting a significantly higher stake on a single but anyone who is easily able to increase the stake by 50%(or even double it,in one example)either: a)has a small bank,in which case the increased risk of going broke is simply not as important or b)cant be that successful Now,of course this point depends on whether a successful punter is able to get multiples taken by the bookies. And the point is,if the successful punter has been doing them for a long time,then yes,since the bookie always believes that it is much less likely that all parts of a multiple have value in favour of the punter.

[moggis]

Re: Accumulators superior to singles As far as point a) is concerned,let me add that ANYONE smart enough to make money from gambling,can always start again with a new bank- if they are unlucky-if the original bank was not really big.

[slapdash]

Re: Accumulators superior to singles

Thanks for a good reply. But there is something I dont get, so to get things straight. You would rather bet 50 singles at 2,20, 50% winning chance, at stake 210 than 100 doubles at 4,84, 25% winning chance, at stake 200

There would be more singles than doubles. Assuming you have the 50 and 100 the wrong way round, then yes, I'd rather bet the 100 singles.

[Machine]

Re: Accumulators superior to singles Slapdash Read the link you gave me It was the same(similar) formula as I was using I think the way im implementing it in the code that may be the problem :$ Wil have to get my thinking cap on. cheers :ok

[Shy10ck]

Re: Accumulators superior to singles

There would be more singles than doubles. Assuming you have the 50 and 100 the wrong way round' date=' then yes, I'd rather bet the 100 singles.[/quote'] Sorry, it should have been 100 singles instead of 50 singles. You would rather bet 100 singles at 2,20, 50% winning chance, at stake 210 than 100 doubles at 4,84, 25% winning chance, at stake 200

[slapdash]

Re: Accumulators superior to singles

Sorry, it should have been 100 singles instead of 50 singles. You would rather bet 100 singles at 2,20, 50% winning chance, at stake 210 than 100 doubles at 4,84, 25% winning chance, at stake 200

No, but I'd rather bet 100 singles at 2,20, 50% winning chance, at stake 210 than 50 doubles at 4,84, 25% winning chance, at stake 200. The scenario I was looking at was repeatedly (say 50 times) coming up with two bets and deciding whether to back them as two singles or one double. So the number of potential singles would be twice the number of potential doubles.

[v-zero]

Re: Accumulators superior to singles The Kelly Criterion essentially puts paid to this question. When many bets are placed at once, the ideal staking plan for maximal growth is given by a combination of multiples and singles. This, however, assumes that the multiples get the same prices as the singles, which is not always the case.