I'm amazed that no one here has supplied the one and only correct solution.

The Kelly Criterion says Edge/Odds.

If you believe in the long-term consistency of the systems:

System A: Edge=5.6%

Stake = 1.47% (=5.6/3.8%)

System B: Edge=3.2%

Stake = 0.1975%

Hi Duritz,

I'm glad you've raised this type of question as it's something that has bothered me for the last couple of months. In my mind, the first thing you need to do is determine the expected lengths of losing streaks. For this, I've been using a program I found a while ago online called Risk of Ruin. It's pretty simple. You enter your strike rate, length of trials to run it over, and the minimum and maximum number of length of outs to test for, and it estimates for you the probability of the specified number of outs. After looking over the results, you decide on what the best guestimate is for the longest number of outs is.

For instance, in a test over 10,000 trials System A, with a strike rate of 22%, has a 45% probability of having a maximum losing streak of 33 outs. In a test over 10,000 trials System B, with a strike rate of 6%, has a 40% probability of having a maximum losing streak of 114 outs.

To make things difficult though, there's nothing saying that you could have a run of 114 outs, have a small win, followed by another run of say 96 outs! With these lengthy runs of outs possible, it would obviously be foolish to be betting say 5% of the bank as the standard bet size.

As far as staking goes, you obviously need to devise a plan that can sustain these lengthy losing streaks. I like the idea of betting a % of the bank, for instance 1%, so if starting with a bank of $1,000, then you would bet $10 on each qualifying selection. I stick with that $10 bet size for the week (I only bet Saturdays anyway), and revise the bet size based on where my bank stands at the start of the new week. Theoretically, this should help preserve the bank for quite a while in the case of an extended losing streak. For instance, if one had a bank of $1,000, had a 1% bet size, had an average of 10 bets a week and lost 10% of their bank every week during an extended losing streak, here's how the weekly tallies would go:

Starting bank = $1,000
Week 1 = $900 / Week 2 = $810 / Week 3 = $729 / Week 4 = $656 / Week 5 = $590.49 / Week 6 = $535.44 / Week 7 = $478.30 / Week 8 = $430.37 / Week 9 = $387.42 / Week 10 = $348.68 / Week 11 = $313.81 / Week 12 = $282.43 / Week 13 = $254.19 / etc. By this time, the bank has likely endured the longest probable run of outs.

So theoretically, this 1% bet size (amount revised weekly), could sustain System B's initial maximum # of outs, it's just a matter what happens after that. Is it followed by another long run of outs?

Honestly Duritz, as Crash suggests neither System A nor System B seem very strong. System A has a decent stike rate, but it's average return is quite low. Maybe it could be improved by shopping around for better prices, but I suspect it would still be too low. And System B's strike rate is just too low, I would doubt many punters would have the guts to continue betting into a losing streak of over 100 outs. I'm glad you mentioned these systems were just theoretical.

Hopefully, I've been of some help to you. I think you're on the right track in using % of bank to determine betting size. You just need to find a system that has System A's strike rate combined with System B's average dividend (easier said than done).

In case it's of any benefit to you (and honestly to brag a little too), here's how I bet my system:

Strike rate = 23.5%, Average Div. = $7.81
With this strike rate, I can expect my longest losing streak to be roughly 32 in a test over 10,000 races. Decided on a 2% bet size.
My starting bank was $1,000.
Week 1 = Bet size $20, 11 bets for 2 wins returning $37.96 = $539.20 profit, so closing bank = $1,539.20
Week 2 = Bet size $31, 7 bets for 2 wins returning $11.32 = $133.92 profit, so closing bank = $1,673.12
Week 3 = Bet size $33, 17 bets for 5 wins returning $32.93 = $525.69 profit, so closing bank = $2,198.81
Week 4 = Bet size $44, 15 bets for 5 wins returning $48.58 = $1,477.52 profit, so closing bank+ $3,676.33
Week 5 = Bet size $74, 6 bets for 0 wins returning $0.00 = $444 loss, so closing bank = $3,232.33
Week 6 = Bet size $65, 10 bets for 2 wins returning $9.08 = $59.80 loss, so closing bank = $3,172.53
Week 7 = Bet size $63, 13 bets for 5 wins returning $31.20 = $1,146.60 profit, so closing bank = $4,319.13
Week 8 = Bet size $86, 10 bets for 3 wins returning $19.34 = $803.24 profit, so closing bank = $5,122.37
Week 9 = Bet size $102, 12 bets for 2 wins returning $11.91 = $9.18 loss, so closing bank = $5,113.19
Week 10 = Bet size $102, 10 bets for 2 wins returning $26.76 = $1,709.52 profit, so closing bank = $6,822.71
Week 11 = Bet size $136, 16 bets for 3 wins returning $19.78 = $514.08 profit, so closing bank = $7,336.79
Week 12 = Bet size $147, 22 bets for 4 wins returning $24.54 = $373.38 profit, so closing bank = $7,710.17

So after 12 weeks, using a 2% staking plan, my system has experienced an average weekly increase of roughly 18%. The winning horses paid between $4 and $32 for the win. My longest run of outs spread over numerous weeks was 15. I also had 1 run of 10 outs and 2 runs of 8 outs. So far though, these losing streaks haven't seemed to have damaged my bank too much. Fingers crossed my luck continues.

Best of luck to ya Duritz. Hope you find a winner or two.

__________________
...time held me green and dying, though I sang in my chains like the sea. - Dylan Thomas

This has nothing to do with staking but a simple method I sometimes use to control a string of outs. It is used with an automated program when betting on every race.

The idea is to keep betting when you are winning and stop betting as soon as you come up with a loss until such time as another win is detected.

Here is an example:

Win keep betting
Win keep betting
Lose Lost bet (stop betting)
Lose no bet
Lose no bet
Lose no bet
Lose no bet
Win no bet (resume betting next race.)
Win keep betting
etc etc.

It can turn a losing day into a winning day, but it can also be disastrous when there is alternate wins and losses.

I should mention that the program continues making selections and calculating bets even though it may not be making bets

First of all you have to have total confidence that your system is profitable and will hold up in the long term, only you can determine that. Research, a database and filters are all needed to be kept.

If your system is profitable any sensible staking plan will suffice.

Personally though, I am a big advocate of silver and sands system too, 1% of the back then recalculating it each week or month, not after each bet. The account grows as the winners come in, but is also protected as the losing streak kicks in. Hypothetically using this simple staking plan, you can NEVER do the lot.

I am amazed how people sometimes well and truly complicate simple things.

BTW, silver and sand. After 52 weeks, you'll have $5,800,000. Let me know in about 10-20 weeks when you are banned from betting, or if your bets are capped. Personally interested as I am not far away if my systems hold up over the next few months...

Was it BECAREFUL who used to use the KELLY criteria?

Cheers.
darky.

Hi JFC, long time no see[?]

Oh boy. not the Kelly again. Edge = overlay. Must know what the [true]overlay is to use this very aggressive staking plan, True overlay in sports betting? How long is a piece of string?

Rather than anyone suffering this Kelly nonsense championed by someone who never uses it by his own omission [JFC], here is a forum thread on this rubbish before you get sucked in:-)

http://forums.ozmium.com.au/showthr...highlight=kelly

This seems to be the trouble with all the statistics based answers I've ever seen to this question. I know enough basic statistics myself to be able to work out the theoretical maximum number of outs (as per above) but as you point out that figure isn't a great deal of use. Possibly a deeper knowledge of stats would give a value to the worse loosing streak which is the important thing here. The worst loosing streak (as I see it) is the greatest amount of money lost from your bank at any time. So if you start with $1000, build to $1200, then at some point get down to $800 before rising again to $1300 your worst losing streak is $400 (1200 - 800). If you are betting a percentage of bank you must assume this worst run could happen at the start of betting and not after you have some winnings to cushion the fall. Anyway, to stop rambling and ask the question I wanted to ask at the start, does anyone know enough stats to work out this theoretical likely loosing streak? I think that is the answer Duritz' question really seeks.

KV

Kenny,

I agree with you on what is important:

Quote:
"The worst loosing streak (as I see it) is the greatest amount of money lost from your bank at any time. So if you start with $1000, build to $1200, then at some point get down to $800 before rising again to $1300 your worst losing streak is $400 (1200 - 800)." End quote.

Call the $400 'Max. draw-down'. Something real we can work with.

I have already supplied the maths formula in this thread to work out the odds of any run of outs for any winning % [odds]. A formula is what was asked for.

Expected run of outs for 10% = 65
'''''''''''''''''''''''''''''''''''''''''''''''''' '''' 20% = 31

Betting level stakes , bank should be at least 3.5 times the run of outs.
E.g. 10% SR for a run of outs of 65 X 3.5 = 228
Bet $1.00 for a bank of $228

20% run of outs 31 X 3.50 = 109
Bet $1.00 for a bank of $109

Cheers.

__________________
Cheers.

Expected run of outs for 10% = 65
'''''''''''''''''''''''''''''''''''''''''''''''''' '''' 20% = 31

Bagman, how did you arrive at the above [what formula] ?

'Expected' [it will probably happen] just doesn't make sense. Have you worked out the odds of either of the above happening ? So why are they expected and why did you settle on 65 and 31 ? Why not more [or less]?

I think it would be a very long wait indeed for either of the above outs to ever happen. They might happen, yet so might 200 runs of outs for either 10% or even 20%. It's seems like nonsense to me to say this is the [definitive?] run of outs you can expect. Please explain, I'm mystified. Thanks.