Stake and strategy management
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So I finally decided to create a blog. The stuff I’ve been working on recently is quite statistical in nature and probably not of interest to a lot of people and therefore probably wouldn’t fit in any of the existing forums. It’s very interesting to me however and hopefully there’s a few others who feel the same and we can connect here. So, have you ever asked yourself this question:
At what point can I be confident that a strategy is profitable and safely increase the stake?
Most likely you have. I’ve asked myself this question hundreds of times, but never really had a good answer. I recently started creating and testing strategies using the horse racing software. My plan was to start with a very small bank and stake 1% of the bank on each bet. For strategies that proved themselves to be profitable, I’d raise the stakes, get rich and retire on an island somewhere sipping cocktails.
My stake management for back strategies is mostly as follows. I start with a bank of $100 (an amount I’m quite comfortable losing if the strategy turns out to be unprofitable). I stake 1% of this bank for each bet and that stake increases and decreases with the bank. This method means that profitable strategies will slowly increase the stake and therefore the profit indefinitely, whereas unprofitable strategies will eventually fade out with a minimal $100 loss . But being the impatient bastard I am, I don’t want to be stuffing around with $2/$3 bets with a strategy that has already proved itself profitable. So I made a rule that if the bank of a strategy doubled, I’d consider it profitable and increase the stakes faster.
Now this has already happened with one of my strategies. After 1000 or so bets the bank hit $200. Great time to up the stakes right? Not so fast. Something didn’t sit right with me. Sure this strategy had doubled it’s bank, but before that it had a bad run and reached half the initial value. If it had halved before it could halve again, leaving my bank back where it started. Or worse, if I increased the stakes a lot, it could leave me well and truly in the negative. I decided not to raise the stakes and sure enough, the bank has gone back almost to where it started.
This left me feeling a little uncomfortable. I was now pretty sure I was wrong about assuming that doubling the bank made for a profitable strategy. But when could I assume a strategy was profitable? My intuitive understanding of variance (and I believe most people are the same) wasn’t good enough in this situation.
I decided I wanted to have a more scientific approach to this, so I decided to get my hands dirty and code some simulations. I set up a simulation where I could run strategies indefinitely until one of the following occurred:
• The bank reached zero
• The bank reached double it’s starting valueThe simulation had the following properties:
• Prices for each bet are selected randomly but in a way that matches the price distribution of my actual strategies (if anyone is interested I can give details on how I did this)
• The probability of the bet winning is completely fair – ie the win probability exactly matched the odds
• A 5% commission is applied to all winning bets (matching my commission rate at betfair)I set up a program that would run this strategy 10,000 times starting from a bank of $100 with a 1% staking strategy. I wanted to see how often a random strategy with no edge would double it’s bank. My expectations were that given my 5% commission rate, the vast majority of the time the bank would dwindle to zero before doubling. I was wrong. As it turns out an incredible 3107 times the strategy doubled it’s bank. Wow. 30% of strategies with this price distribution double their bank even when they are not inherently profitable!
I’m now convinced that doubling my bank with this strategy is absolutely not proof of a profitable strategy. So what is? The above simulation tested whether my starting bank of $100 would reach $200. What if I changed that target to $300, $400 etc? The results are below:
Target Bank Number of simulations that reached target Average number of bets before reaching target or zero 200 3107 2007 300 1743 2491 400 1133 2696 800 395 3007 1600 150 3115 3200 41 3168 I find these results most interesting. When we set the target to 4x the original bank we still get over 10% success rate. Even at 16x the bank we get a success rate slightly over 1%. Remember, these are strategies with no edge whatsoever – that is they are not intrinsically profitable. It’s not until we reach around 32x the original stake that I’d start to feel very confident that I was on a winning strategy – because the likelihood of an unprofitable strategy reaching that point becomes extremely low (about 0.4%). By that time my stakes would be getting to a pretty decent amount anyway.
As a conclusion to all this, I’ve decided that there is not much advantage to artificially increasing the stakes beyond the natural increase that occurs with a percentage based staking strategy. So I’m just going to leave my strategies running with their current parameters. If they are indeed profitable as the horse racing software suggests, eventually they will keep doubling until they are making me good money. If not, I will lose my $100 bank. No big deal.
I guess all this really does is reiterate the old maxim that experienced gamblers keep repeating – start with small stakes and don’t be in a hurry to increase them. But for me it provides some solid scientific evidence to take that advice seriously. As I once heard Peter Webb say, “A bad gambler wants to get rich quickly. A good gambler wants to get rich slowly”.
Afterthought: There are some caveats to this experiment. The price distribution used has quite a big effect on the results of an experiment like this. The strategy I was testing works on odds of 10 – 100. Strategies where you are betting on odds around 2.0 will yield very different results. I played around with different parameters such as different odds distribution as well as what happens when your strategy has a 1% edge. If anyone is interested in the results of these experiments I’d be happy to share and chat.
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I'd be interested in this for a strategy I'm working on right now. I've back tested over 4000 data points and now refined that to about 2200 data points with some filters.
I similarly was looking at a bank % staking plan rather than a flat stake and would be interested to see how your simulation tests my strategy.
I've done some excel testing with different formulas but would be great to have another rigorous test if you would be up for it?
Taff
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@ian-parry I think organically growing the bank is the best way and you are on the right track. I know it's tempting to up stakes quickly but in my experience that rarely ends well for people, maybe due to the lack of discipline in upping stakes too early.
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@martin said in Stake and strategy management:
Great stuff! Pleased you have started this blog, I will be following with interest.
Firstly please get yourself on the 2% commission tier! You are giving 3% extra to Betfair and the ‘rewards’ for that are not going to be worth it long term.
Secondly how long have you been forward testing your strategies?
Thirdly, I’m not sure where the misconception comes from that we aren’t that interested in stats, heard this a couple of time lately. It’s pretty much all we talk about and myself, @ryan and @adam are pretty much full time statistical analysts at this point!
Thanks Martin for the kind words. It's good to see the blog post on bank management for set and forget.
Unfortunately with Betfair Australia it is very difficult to get a commission discount. We used to be able to get the discount, although the bar to achieving this was much higher than in the UK. But I believe they took that away and now we are just stuck with the 5%. There is no other exchange over here so they can do pretty much what they want.
As far as forward testing goes, I am still doing it. I prefer to do testing with very small stakes rather than paper trading, and I'm willing to lose a small bank to do that. Some of my strategies are at over 1000 bets but none of them I would say have had enough forward testing to use larger stakes.
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Great stuff! Pleased you have started this blog, I will be following with interest.
Firstly please get yourself on the 2% commission tier! You are giving 3% extra to Betfair and the ‘rewards’ for that are not going to be worth it long term.
Secondly how long have you been forward testing your strategies?
Thirdly, I’m not sure where the misconception comes from that we aren’t that interested in stats, heard this a couple of time lately. It’s pretty much all we talk about and myself, @ryan and @adam are pretty much full time statistical analysts at this point!