LaMunxo Posted October 12, 2006 Share Posted October 12, 2006 I'm sure some of the math guys will know the formula for this, here is the question: When picking odds O (2.0 for example) with H (lets say 60%) hitrate and start bank B. What is the chance C of loosing X% of bank(100% = bankruptcy) over Y bets? Edit: Staking strategy is also important, lets say stakes are flat, 1% of bank. In endless row the chance of loosing is zero and yield is O*H (20% for those values above) but what is it in real life, smaller runs - 50,100,1000 etc bets. Please post if u have the formula which covers this luck factor. Thank You! Quote Link to comment Share on other sites More sharing options...
MetallicIan Posted October 12, 2006 Share Posted October 12, 2006 Re: Luck Factor - Bankrupcy Math Hi LaMunxo! great question. Whenever I have a similar question I find that my maths is not quite up to solving things to a simple formula, I tend to write a program in basic (either qbasic or VB). Nothing is ever idealistic except for "real life" conditions but I find that the following is as near as you get... Set up a parameter for Odds (O), Strike Rate (SR), and others for start bank, number of bets and stake. What I do is use the RND function to generate a random number between 0 and 100. In your case with a 60% SR, anything generated above 60% would be counted as a loss. Run the program for x number of bets. Then loop the program to run say 10,000 times and output the average scenarios. With 10,000 you usually find the most common outcome. You will not only be able to see final profit/loss, but also estimate longest losing/winning streaks etc. Also a simple excel formula I use to estimate longest losing streaks is this one... =ROUND(LN(500)/-LN((1-0.60)),0) where 500 is the total number of bets, and 0.60 is your Strike rate (in this case 60%). In this example the answer is 7. Hope this helps. Ian.:ok Quote Link to comment Share on other sites More sharing options...
LaMunxo Posted October 12, 2006 Author Share Posted October 12, 2006 Re: Luck Factor - Bankrupcy Math Ian, Thanks for answer, yes i was doing some simulations too and am trying to put it into formula. Theres maybe some theory behind all this but i'm not that good at math myself. Heres what i found: odds are 2.0, hitrate 55% (10% expected yield), staking 1% of bank flat, starting bank 1.0 all runs repeated 10000 times to find the bankrupcy percentage First test, maximum possible loss: Bets in Run | Minimum Bank of all runs 10 | 0.90 20 | 0.85 50 | 0.79 100 | 0.722 200 | 0.7 500 | 0.68 1000 | 0.67 Second test, chance of not being in positive balance: Bets | Chance of being in - (bank under 1.0) 10 | 49% 20 | 40% 50 | 28% 100 | 18% 200 | 8% 500 | 1.5% 1000 | 0.05% personally i cant imagine 200 bet run and being in minus, but the numbers give some interesting information. It gives me enough info but still wonder if anyone have this put into formula.gl. Quote Link to comment Share on other sites More sharing options...
slapdash Posted October 13, 2006 Share Posted October 13, 2006 Re: Luck Factor - Bankrupcy Math I'm not quite clear exactly what the problem is. Is it "How likely is it that after exactly Y bets, my bank is at least X% less than it was to begin with?" or is it "How likely is it that by the time I have made Y bets, my bank will at some time have been at least X% less than it was to begin with?" I'll assume the second question, as that seems more relevant to bankruptcy (it's no good being in theoretical profit after 1000 bets if you'd lost all your money after 100 bets and couldn't put any more bets on!) I doubt there is an exact simple formula for a particular value of Y (the number of bets made), but there probably is if you ask "How likely is it that I will ever go bankrupt (or lose 50%, or 25% of my bank)?" I can give you the formula for this if the odds are 2.0, as that makes the problem a lot simpler. If you stake one unit per bet, and your chance of winning each bet is H (expressed as a probability between 0 and 1, so for a 60% strike rate H=0.6), then the probability that you will ever be N units down is ((1-H)/H)^N if H>0.5 and is 1 if H is less than (or equal to) 0.5 (if you're not getting value from your bets, you're bound to go bust eventually!) So for example, if you have a strike rate of 60%, and stake 10% of your original bank on each bet, so you start with 10 units, then H=0.6, so (1-H)/H = 0.4/0.6 = 2/3, and the chance that you will ever go bust is (2/3)^10 = 0.01734..., or about 1.734%. Quote Link to comment Share on other sites More sharing options...
LaMunxo Posted October 14, 2006 Author Share Posted October 14, 2006 Re: Luck Factor - Bankrupcy Math slapdash:thanks for answer. ((1-H)/H)^N yes this is half of what i'm looking for, however can u upgrade that formula with Odds variable ? also, what staking doest the above formula use ? thank you Quote Link to comment Share on other sites More sharing options...
LaMunxo Posted October 18, 2006 Author Share Posted October 18, 2006 Re: Luck Factor - Bankrupcy Math i'm bumping this thread, anyone know above formula including odds parameter ? Quote Link to comment Share on other sites More sharing options...
slapdash Posted October 18, 2006 Share Posted October 18, 2006 Re: Luck Factor - Bankrupcy Math Sorry, forgot about this. I don't have a formula (and actually I doubt there is a simple one), but I have thought more about this. It's a bit complicated, so will take a while to compose my post, but I will when I get some time. Remind me in a few days if I haven't replied. Quote Link to comment Share on other sites More sharing options...
LaMunxo Posted October 18, 2006 Author Share Posted October 18, 2006 Re: Luck Factor - Bankrupcy Math ok thanks. i will look at this aswell. Quote Link to comment Share on other sites More sharing options...
alkarkar Posted October 19, 2006 Share Posted October 19, 2006 Re: Luck Factor - Bankrupcy Math I dont have the formulas but here is a free excel file wich does what you want (I think it's VERY good): http://www.sportpunter.com/Simulation%20Program.xls (0.5 MB) Maybe post should be moved to ''Punters Tools & General Betting Help '' thread? Quote Link to comment Share on other sites More sharing options...
slapdash Posted February 5, 2007 Share Posted February 5, 2007 Chance of going broke with level stakes betting Hodgey asked me roughly the following question recently: If you bet with level stakes, starting with a given bank, what is the probability that you'll go broke at some stage, in terms of the odds you bet at, your strike rate, and the size of your starting bank? I think a similar question has been asked here before, though I can't find the thread, so thought I'd post my answer here in case anybody's interested. Comments/criticisms welcome. I'm afraid this is going to involve a bit of maths, but you're an accountant, right? Let's assume you start with a bank worth N times your unit stake (so N=50 if you are using 2% of your start bank). Suppose all your bets are at the same odds of C in decimal format (so C=2 if your bets are all at odds of evens). Suppose a proportion p of them are successful (so p=0.6 if you have a 60% strike rate). Let's first assume that C is a whole number (I know it's probably not, but this makes things a bit easier to explain). Then, assuming that you have an edge (i.e., Cp>1), then there is a number X (between 0 and 1), depending on C and p, so that your probability of going broke is X^p (by ^ I mean "to the power of"). The hard thing is working out what X is. If C=2, then it's fairly simple: X = (1-p)/p. If C=3, then it's possible to write down an expression for X. It's the solution of a quadratic equation, and involves square roots: I can work out what it is if you're interested. But for other values of C, I doubt there's a simple expression for X. But you can work out numerically what it is. If you look at the equation p.(X^C) - X + (1-p) = 0 then this has one solution between 0 and 1, and that's the X you're looking for. If C is not a whole number then there's probably not an exact formula. This is partly because it's not quite clear exactly what you mean by "going broke": if your bank drops to below one unit stake, does that count as going broke? But I'm pretty sure that exactly the same calculation will work approximately, so long as the starting bank is a reasonably large number of unit bets (50 should be plenty). Of course now you're raising X to a fractional power in the equation, but the equation still has one solution between 0 and 1. If the odds of the bets vary, it gets even more complicated, but if the odds don't vary too wildly, then you'll probably get a reasonable idea by using the average odds and the strike rate that would give your actual yield if all the bets were at those average odds. (Don't use the actual strike rate: that will be different.) By the way, a small change in X can make quite a large change in the probability X^N of going broke if N is quite large, so it would be prudent to be a little pessimistic in your estimate of the strike rate. Hope this helps. Let me know if there's anything that's not clear. I'm afraid it's unavoidably a little complicated. By the way, don't know if you've often had any need to solve equations like this numerically, but there are various free web sites that will do it for you. E.g., http://www.hostsrv.com/webmab/app1/M...lve& s3=basic An example: Suppose your odds are 1.5 and your strike rate is 70% (so you have an edge, as you need a strike rate of 66.67% to break even). Then p=0.7 and C=1.5, so the equation you need to solve is 0.7x^1.5-x+0.3=0 Putting that into the web page above gives you two solutions. One solution is x=1 (this will always be a solution) but the solution you want is the one between 0 and 1, which is 0.815662. So if you start with 50 unit stakes then your chance of going broke is 0.815662^50 which is about 0.0000376, or 0.00376%. But if you start with only 10 unit stakes then the chance is 0.815662^10 which is about 0.13, or 13%. Quote Link to comment Share on other sites More sharing options...
Hodgey Posted February 6, 2007 Share Posted February 6, 2007 Re: Chance of going broke with level stakes betting I think a similar question has been asked here before' date=' though I can't find the thread[/quote'] Was this the one slap? If so: Did you forget about it again or could you not come up with an answer so just banned him?!?! ;) I thought this was excellent...... until it crashed my PC! :lol (Aha - seems to be working again :ok ) Quote Link to comment Share on other sites More sharing options...
Hodgey Posted February 6, 2007 Share Posted February 6, 2007 Re: Chance of going broke with level stakes betting I thought this was excellent...... until it crashed my PC! :lol (Aha - seems to be working again :ok ) Actually this isn't working for me. :( Quote Link to comment Share on other sites More sharing options...
bookie2000 Posted February 9, 2007 Share Posted February 9, 2007 Re: Chance of going broke with level stakes betting Guess it needs more than just mathematics but a lot of reasonings and news reading.. Quote Link to comment Share on other sites More sharing options...
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