General Betting
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Winners are lucky. Losers are unlucky.
Winners are lucky. Losers are unlucky.
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I notice I forgot to explain that 10! is 10 factorial, which is 10x9x8x7x6x5x4x3x2x1.
So instead of 10 we use n. n! (n factorial) increases very, very fast. Faster than exponential  .Here is n! for 0 to 10.
Unfortunately BF doesn't have a spoiler tag but this is 100! I've broken it down in 12 digit chunks so I don't break phones viewing this, but this is all one number! 933262154439 441526816992 388562667004 907159682643 816214685929 638952175999 932299156089 414639761565 182862536979 208272237582 511852109168 640000000000 000000000000 00 Dodging doing anything a factorial number of times is very important in the kind of stuff I do for a living.  | ||||||||||||||||||||||
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So when I ask should you increase your flat bet size ?.
You can't stay forever at your original starting bet size, not if you expect to make reasonably good earnings. ( That is assuming you don't start on day one with a very, very large bank and an accordingly very, very large flat bet size. Also on the gamblers ruin matter. I fail to see that if you establish that a worst case drawdown situation is ( say) 100 units for example, then if your bet size is set at ( say) 5 times this, that is a at a ratio of 1/500 of your bank at its last peak, then unless you experience a drawdown of more than 5 times your forecasted expected worst case scenario ( that is a real black swan scenario), before you get back into profit again, then how can you be wiped out ? | ||||||||||||||||||||||
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Any given length of losses will happen eventually*.
*If we say n is the number of bets made, then the probability of going bust as n tends to infinity equals 1. OK, so it's very very unlikely to actually happen to you, but if you are only betting 1/500th of your bank, then unless you are backing long odds (in which case 500 losses might not be that unlikely) you'll unlikely make better money than you'd make in the bank! There really isn't an "expected worst case". I'm sorry if I find this hard to explain, it's because "expectation" is a mathematical term (although one I do abuse in other threads). Basically you could pick a probability and say "OK I want a system that means I won't lose my bank in 998/1000 cases", and your system would certainly pass that. But that's not the only problem with "increase and never decrease" systems, it means you're always pushing yourself away from your comfort zone and are always maximally discomfort during any losing streak! This will lead to frustration. For instance if you're evens betting, then if you are at a current new maximum bank, then winning 3 then losing 3 will mean you end up down. As I think I said either upthread or on another thread, backing a percentage of your bank also moves a lot of your expected winnings onto fantasy results that are less likely than euromillions! But the addition of not decreasing your bet size just further means you might end up with your current bank in a year's time, but now you're betting larger stakes. Would you be comfortable with that? You should pick a stake size you're comfortable using and then just use that. You still risk being wiped out (by the finite vs infinite bank, you can't avoid this one), but at least you'll be comfortable during the down swings which might make them easier to get out of. Also level staking means it is easier to compare results month to month which is important for checking you're really making money. What would I do? I'd level stake, then every month my bank is up I'd withdraw the money. Now your bank is the right size for your stake again! If you don't withdraw then you're not winning money! This is what people miss when they are running good they just up their bets and get back to average. They might have a buzz and feel good while they're up but if they never withdrew the money they've not won squat! Of course I would also therefore recommend that any month you're down you top up your bank to the right size for your stake. This might feel difficult but the in/out from your bank statement helps you keep yourself honest about if you're a winning or losing gambler! | ||||||||||||||||||||||
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All sports are not just random events. What about the fixed matches which happen every week...how does your maths work those out
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Trevh why do you never post in "how much has everyone won" thread?
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ror : 0.2%? Percentage backing is rubbish! It increases variance,loading all the profit into very unlikely scenarios.
Basically you lose a lot of ev to the results that aren't going to happen. As I don't know the outcome of any results I keep my stake the same on all. Perhaps what I said before came across wrong, in that I don't adjust bet size during the week's betting, and I don't adjust bet size upwards (I used to) after a profitable week because I'm currently happy sustaining this level, but I do reduce stake size to 0.2% of a new lowered bank if it's been a losing week. This works very well for me and it's not something I would change, the stake size never alters very much at all. ror : What would I do? I'd level stake, then every month my bank is up I'd withdraw the money. Now your bank is the right size for your stake again! Of course I would also therefore recommend that any month you're down you top up your bank to the right size for your stake. The first bit is roughly what I do, only I withdraw every week not month so my bank remains pretty constant as does my stake. I never top up funds after a losing week though, I like to build back the loss using a slightly smaller stake (0.2% of lowered bank) as that gives me the mental security of riding out potentially bad runs. Plus the fact that in Aug 09 I said that if I ever had to deposit again I would give up gambling, and meant it. I agree with you Frog that to build a bank up to the size you're happy with to operate level stakes, you obviously need to increase the stake size accordingly thus also decrease accordingly as ror said, although he doesn't like that method. As we're all aware though, there's more to getting it right than best theory dictates, I mean we need to do what we're most comfortable with to create security because we're not robots. Frimpong, if that's the thread on the footy forum, I don't think I'll bother :) I did say once before that I'd post on a general betting thread though. | ||||||||||||||||||||||
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Btw ror, you said "what would I do?" Are you just a theorist then?
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Sorry ror but I'm afraid that I do not find your reasoning convincing.
Btw I'm not talking about consecutive losses or anything like that. I'm talking about extended downturns made up of both many wins and losses. If you can estimate what such downturns are likely to be, obviously not to 100% certainty but to a strong degree of certainty based on extensive testing of back data, then that downturn figure should be the basis for the percentage of your bank you ever put on one bet. It would make no sense then to decrease your bet size if you are experiencing losses which are well within your expected " bad run " parameters. If you don't believe the losses will turn around then you shouldn't be just decreasing your bet sises, you should in fact not be betting any more at all, as you would effectively be just putting in good money after bad. You have to believe that your basic "edge" is still there even when experiencing bad runs. Otherwise what's the point of discovering and trying to exploit any edge ? If you want to use a very simplistic analogy, you could say that those investors who increase their positions in the stock mkt. when a particular share price goes down are exhibiting the same confidemce in their "edge", by increasing rather than decreasing their exposure to that particular share in adverse mkt. conditions. They do not cut and run at the first sign of any losses. | ||||||||||||||||||||||
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Trevh
Our posts sort of crossed. I like the sound of what you do, except for the decreasing of stakes if and when a bad run occurs. I believe that is not correct, for the reasons I have just outlined. Vive la difference. | ||||||||||||||||||||||
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Frog : I fail to see that if you establish that a worst case drawdown situation is ( say) 100 units for example, then if your bet size is set at ( say) 5 times this, that is a at a ratio of 1/500 of your bank at its last peak, then unless you experience a drawdown of more than 5 times your forecasted expected worst case scenario ( that is a real black swan scenario), before you get back into profit again, then how can you be wiped out ?
Misunderstood you above Frog, I know what you mean though, but I had a draw-down earlier in the year which was more than anything I'd previously experienced, and if I'd carried on at the same level of staking it would have come close to wiping the bank, and that's using just 0.2% stakes. As it happens I reduced accordingly and recovered to full bank within 2 weeks - no panic. I wouldn't want to be in that situation using full stakes with no reduction. | ||||||||||||||||||||||
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Clearly the black swan I was talking about.
Without doubt they are swimming around and you have to be constantly on the alert. But overreacting is probably as bad as underreacting, though I would agree that overreaction is less likely to ever result in a total wipe out. But this is a risk game, as there can never really be a no-risk scenario that is highly profitable ( unless you are one of those fortunate few with those fiendishly clever in-running bots). | ||||||||||||||||||||||
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Yep, we all should do what suits us best obviously, and reducing stakes suits me fine. Another part of gambling - learning your strengths and weaknesses. Like I said above, I don't think best theory is always best practice "(unless you are one of those fortunate few with those fiendishly clever in-running bots)". :)
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Ah ok trevh, I think i misunderstood you to be using a strict bank % as many on here do (and recommend) to their peril.
In fact not increasing but sometimes decreasing your bet size may well be a more stable strategy. You would eventually cease betting (if taken literally, that your bet size could only decrease!) but it is clear you increase back to a level stakes cap. I quite like that, it avoids discomfort or loading too much money into the unrealistic dream outcomes. I'm actually going to white a program to show some outcomes under different staking plans. There is a dangerous (very high risk) staking plan that involves actually betting more when your bank is down and less while your bank is up but it has a high bust probability. If you don't go bust you make nice returns though. | ||||||||||||||||||||||
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P.s Yes I think it is fair to say I spend more time on theory than betting. This is mostly because I don't touch horses, so there is very little sport right now! Also I work, so have time to think about this stuff when I can't actually bet.
I tend to minimum bet most the time. While I could stake higher, I get as much pleasure out of making a £2 profit as a £20 one. I'm not here to make money, I'm here to increase my sporting (and xfactor) knowledge and interest. The mathematics of gambling and the psychology of gamblers I find fascinating. I don't work in the city but if it is anything like this place I would hate it. I've made it my mission to tackle some of the myths doing the rounds. | ||||||||||||||||||||||
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Good on you Ror...but you do seem to be making gambling a little more complicated than it actually is
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I gave up on this thread when i read 'all sports are just random events'. Only a number-crunching addled mathematician could come out with that and this forum seems to be full of them. Clearly not got the first clue about sport.
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I reacted to that comment too DI......Typed out a start of a response.....then decided not to bother.
ror has stated that he/she does not bet on HORSE RACING......explains a lot! ror......RETIREMENT STAKING PLAN.....should be one you test...and KELLY. GL | ||||||||||||||||||||||
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Thanks for the suggestion.
Any other staking recommendations? | ||||||||||||||||||||||
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LEVEL STAKING does not exploit any "edge" you might have.........I suspect many who believe they have an edge re FOOTBALL betting use that "method".
So do not recommend that !  | ||||||||||||||||||||||
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DFCIRONMAN: Hopefully this analysis should show some plans which are better than level stakes.
If I do it properly I might even be able to release it as a general tool for others to run their own analysis with. | ||||||||||||||||||||||
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ror, I presume you'll be including some Kelly or Optimal f staking in the simulations?
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I'll try to include any I'm asked to include.
Kelly I can include where I build in an edge, but without an edge Kelly can't really work. If you'd like me to include a staking plan please link to a decent description so I can check we're discussing the same thing! | ||||||||||||||||||||||
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Kelly will do fine. And it should work just fine without an edge, it'll just tell you to bet 0% which will keep your bank at its highest possible level.
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http://www.grandstand.com.au/retirementstakingplan/
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http://www.professional-racing-tips.com/StakingPlanPages/Retirement.aspx
Plenty PLANS there! | ||||||||||||||||||||||
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Thanks guys :)
I've built the results engine, I've not yet worked into it the staking engines. I think that'll be the fun part. But currently you can pick any number of runners and assign a probability to each. It'll then run that race a thousand times, look at what happens to your bank (essentially a random walk), dump those stats out, then repeat that whole process thousands of times. (If anyone is interested, the pseudo-random number generator I'll be using is mersenne twister. It's incredibly good for monte carlo as not only is it unbiased but it's LIGHTNING fast.) | ||||||||||||||||||||||
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How are you initialising your Mersenne twister?
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Initially time(0) but might use /dev/urandom or just "What seed would you like to use?" works well for monte carlo so you can repeat runs to check for interesting stuff after the fact.
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I should add: As long as all the repeated runs etc are processed inside the programme, then having a weak seed isn't a problem at all, and on the same architecture (I think?) letting people input seeds lets you 'share' results easily with others using the same problem. (I could be wrong about this last point?)
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I think that it is possible to choose "poor" seeds for the Mersenne twister, that is ones which will give you autocorrelated variates, but if you try the results with a few different approaches it should be apparent if some of them are odd.
Once you have your engine up and running it would be interesting to build a population of random bettors and see how quickly the wealth moves towards a small subset of the population (which it almost certianly will). The test for a market containing experts would be if the wealth moves to a concentrated few in a faster manner than your simulation. Sadly, only Betfair would have the real-life data but we might be able to get enough info from them to compare to the simulation. | ||||||||||||||||||||||
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Two quants exchanging ideas.
Well there goes the neigbourhood. |