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Mr. Blonde
01-15-2003, 10:40 PM
There has been some discussion in other threads regarding win%, bet size, expected consecutive losses, and avoiding "gamblers ruin"


Is there a formula where you can plug in your win% and figure out the longest losing streak you would have in, say, 1000 plays, and use this to figure out your optimal bet size?

thanks.

formula_2002
01-15-2003, 11:51 PM
Well, I guess it would go like this. Say your win rate was 20%.
Therefore the loss rate is 80%

probability of losing two in a row is .8x.8=.64
three in a row .8 x.8 x.8=.51
four in a row= .41
five in a row=.33
six in a row=.26

so you have a 26% chance of losing 6 in a row providing your loss rate was exactly 80%

In reality, you have to know you win rate in each odds group and your edge or lack of edge in each odds group and then adjust that for Volatility, which is the standary deviation...And thats where I have to leave it...

Good luck and visit my home page for some interesting reports.


Joe M

formula_2002
01-15-2003, 11:56 PM
"Commonsensense Betting" by Dick Mitchell, chapter "Money Management", may be worth the read. He covers the topic there.

Again
Good Luck
Joe M

hurrikane
01-16-2003, 05:59 AM
I posted the formula here somewhere. Do a search. I can post it later if you don't find it. Came from the mathematics of horseracing.
Formula is right. It is based you your win %

Rick
01-16-2003, 10:47 AM
Try VI by Mason Malmuth in this paper. It should be reasonably accurate. In order to answer the question you need to specify the number of plays, know what the variance of your payoffs is, and decide on an acceptable probability level. There really is no absolute maximum number of losses, because their's always some very small probability that you'll lose them all.

http://wiretap.area.com/Gopher/Library/Article/Gaming/ruin.txt


formula,

Dick Mitchell's analysis is wrong because it only looks at how likely a losing streak is over 100 plays. Also, the calculation you showed for losing six in a row is only accurate for exactly 6 plays. If you had 1000 plays, for example, their would be 995 (1000 - 6 + 1) sequences of 6 plays and you could lose in any of them. It gets messy to analyze this way.

hurrikane's formula isn't bad but is based on an approximation (Chebyshev's theorem) that is kind of a worst case guesstimate. It's weakness is that it doesn't consider the number of plays. But it is easy to calculate and following it probably won't get you in trouble.

BMeadow
01-16-2003, 10:59 AM
Check out Jim Bayle's booklet, Gambling Percentages and Probabilities, in which the length of possible/probable losing streaks is calculated for any win percentage you can muster.

Essential problem is that your streaks with 15-1 shots are going to be much longer than your streaks with 8-5 shots, so that mixing and matching may lead you to false conclusions.

Rick
01-16-2003, 11:24 AM
Simulation is the best solution if have a large sample of results and can do a little programming. I've done some of that and am convinced that Malmuth's estimate is pretty close, for my data anyway.

By the way, don't try using Bayle's analysis using your average odds on winners. That won't give you an accurate answer.

Rick
01-17-2003, 06:56 PM
A couple of things that I forgot to point out before. First, longest losing streak is not the same as the largest number of units you might be behind. You can lose 20 in a row, get one small winner, and then lose another 20 in a row. It doesn't make you feel much better to have that one winner and your bankroll is a lot worse than 20 units behind. Second, all of these estimates of how many units you should have in your bankroll assume that you never take any profits. That's OK if you're just building a bankroll but not if you're trying to make an income. If that's the case, I'd recommend a bankroll at least twice as big based on my simulations.

jackad
01-17-2003, 08:20 PM
Rick,
Could you save me the headache of trying to apply Malmuth's formula and just give me your bottom line?
In your opinion, a bankroll shoud be how many times bet size to avoid ruin? Assume 25% win frequency and 20% ROI.

Thanks
Jack

Rick
01-17-2003, 08:57 PM
jackad,

Unfortunately it's not that simple. It depends on the variance of your payoffs which you'd have to calculate. The average odds can be the same for distributions of payoffs that are very different. Use hurrikane's formula if you want the simple version. But remember that the maximum losing streak is not the same as the worst loss. For a 25% method that formula would come up with about 39 for the maximum losing streak. I wouldn't use any less than 50 units (2%) when building a bankroll and 100 units (1%) when taking profits but I'm pretty conservative about risking my money.

Rick
01-18-2003, 11:23 AM
Here's some more info for those who may be interested. If you use the Malmuth formula as is, you're calculating the 3 standard deviation value, which corresponds to a confidence level of 99.87%. If you'll settle for 99%, you can use 2.33 in place of the 3 in the equation. If 95% is acceptable, use 1.645 instead. For my method that gives the following values:

3.0 (99.87%) 81.95
2.33 (99%) 49.43
1.645(95%) 24.64

The 99% level seems adequate to me and that's about what I use. The longest losing streak (99% confidence) according to the approximation mentioned by hurrikane is 35.41 for my data, somewhat less than the Malmuth worst loss value at the same confidence level. The actual longest losing streak I've had was 29.

The Kelly percentage calculated based on average odds is .0607 (16.47 units), but the true Kelly percentage based on the actual variance of outcomes is .02746 (36.42 units). Notice that the correct percentage is only about 45% of that based on average payoffs. Nearly everyone calculates it that way and if they use full Kelly they're probably overbetting by at least twice what they should. If you're familiar with Kelly you know that doing that could totally eliminate your advantage and cause you to lose money with a winning method. That's probably why so many with experience use 1/2 Kelly or less.

I hope all of this gives some perspective to the subject by making actual comparisons. Just for the record, I used 40 units early on and didn't like the experience when my longest losing streak followed my largest payoff. After a lot of study and running simulations I decided on 50 units for building the bankroll and 100 units for taking profits. I only keep about 50% of my bankroll in the account I use for wagering because it's really rare to ever go down below that level. The other 50% is readily available but kept in a different account. That also provides some protection against the possibility of my betting outlet disappearing.

Fastracehorse
01-20-2003, 08:09 PM
.............and true intellectual.

Do you have any additional insight you may want to add about what I could be looking for when I track the results of my selections??

I'm interested in p-3's but I am only following win % and ROI based on win bets in a few simple categories.

fffastt

Rick
01-21-2003, 12:40 PM
fast,

When I play Pick3's I use two horses in each leg and get better that 50% (maybe 53%) wins on each leg using the two horses. Even though betting all of my top two selections in every race to win would result in a loss, the leverage you get from Pick 3's makes it a profitable bet anyway. As I've said before, its one of my favorite ways to bet if I want to have something on every race.

When I developed my method for win betting I found that I'd get much more repeatable results if I used looked at the top two selections. If you optimize win + place payoffs on the top two the results are usually better when you look at a new sample than if you used the top selection only or if you only look at win payoffs. It didn't seem to help any to go to 3rd selections or show payoffs though. Also, if you try to optimize by using finish position, make any finish worse than 5th count the same as 5th. These horses with no chance for a piece of the purse just introduce additional noise into your predictions.

hurrikane
01-21-2003, 01:38 PM
Rick, could you clear up the leverage piece. Are you saying if you parlayed the money on the top 2 over the 3 races you would have a losing prop but in the p3 pool it is a winner?

Also, where can I get your book?

Rick
01-21-2003, 04:24 PM
hurrikane,

That's exactly what I'm saying. I explained why several times in the past in other posts, but I think you understand anyway. I didn't realize until a couple of years ago that I could have won a lot of money by playing Pick 3's and exactas a long time before I every had a profitable win betting method. When I first started out I played mostly spot plays so that wouldn't have worked but once I learned how to do reasonably well playing every type of race I should have capitalized more on the "leverage" of exotics.

I can't think of anything more boring than writing a book but I like trading thoughts with people here. The one way communication of books, seminars, teaching etc. just doesn't appeal to me. I'm more of a reader than a writer but thanks for the kind comment.

Fastracehorse
01-21-2003, 11:29 PM
>When I developed my method for win betting I found that I'd get much more repeatable results if I used looked at the top two selections.

1) Do you bet 2 horses in a race and if you do do you need higher odds??

2) What type of win mutuel are you usually looking at? - because if it is on the lower side I'd be very impressed that you could make a profit - I do believe you.

fffastt

Rick
01-23-2003, 10:32 AM
fast,

I only bet one horse to win normally. I don't like the lower win % of second choices but they would show a profit if the odds are high enough. I don't use actual odds to look for overlays. I can use either morning line odds or last race speed ratings and a jockey factor to look for overlays without monitoring the tote board. The average odds on my winners is about 7-2 using morning line odds and a little lower (with a higher win %) if I use speed ratings (in a negative way). If I did use actual odds, I'd probably look for about 3-1 minimum odds.

Fastracehorse
01-23-2003, 08:10 PM
If U had a higher average win mutuel, but fewer plays, would your strategy change much??

fffastt

Rick
01-24-2003, 01:44 PM
Fast,

That's a hard question to answer. It's always nice to have a higher ROI but it almost always comes at the expense of lowering win % and reducing the number of plays. A lower win % may cause a lower bet size for the same level of bankroll safety and result in less $ per year. A smaller number of plays results in more variance in annual income so that the worst years might be unacceptable.

JustMissed
01-24-2003, 02:12 PM
Originally posted by Rick
fast,

I only bet one horse to win normally. I don't like the lower win % of second choices but they would show a profit if the odds are high enough. I don't use actual odds to look for overlays. I can use either morning line odds or last race speed ratings and a jockey factor to look for overlays without monitoring the tote board. The average odds on my winners is about 7-2 using morning line odds and a little lower (with a higher win %) if I use speed ratings (in a negative way). If I did use actual odds, I'd probably look for about 3-1 minimum odds.

Rick, Could you help me out?

I understand an overlay by definition is an underbet horse. I believe most player determine if a horse is underbet by comparing their own Estimated Fair Odds(EFO) to the toteboard(public)odds.

If I read your post correctly, you are comparing your EFO to the MLO. Since the morning line odds are the estimated fair odds of a track employee, are you not in fact comparing an estimate to an estimate when you should be comparing an estimate to a real expected payoff.

HELP, what is it that I am misunderstanding?

Thanks,

JustMissed
:confused:

Rick
01-24-2003, 02:40 PM
JustMissed,

You're absolutely right. I've found that it doesn't cost me much in ROI (actually maybe nothing according to my records) and saves me a lot of time. Statistical analysis shows that about 80% of the variance in actual odds can be attributed to the morning line so it's not all that inaccurate anyway. And, if your horse is bet down in actual odds compared with adjusted morning line odds it's a little better bet anyway. The same thing is true to a lesser degree with last race speed ratings. I want to determine my overlays compared with "dumb money", not "smart money".

Here's an idea for someone to look at that likes to do research. Eliminate the morning line favorite, the horse with best last race speed, and the horse with highest average earnings. Then handicap the rest of them using your favorite method. My guess is that you'll have a much better ROI doing that.

JustMissed
01-24-2003, 03:02 PM
Thanks for taking the time to explain.

I play Tampa Bay Downs which at this time of year is loaded with tons of snowbirds with pockets full of Motown pension and social security money.

Some days I'll have a good horse ready to pop with a MLO of 7-2 and by 4 minutes to post he'll be bet down to 4-5. If I bet based on the morning line I'd go broke for sure.

Of course it works the other way also with the longer odds horses especially. I've seen good horses at 8-1 MLO not drop a point.

Anyway, thanks for clearing that up. I see what you are doing and good luck to you.

JustMissed
:)

andicap
01-24-2003, 03:07 PM
What a fun idea!

Thanks for the suggestion!

Interestingly, when Ragozin determined that he made a profit (I think it was a Sports Stat study) with the best of his last 3 figs at 4-1 or above (not a huge sample and I don't think the Raggies believe it will hold up over time), they found the ROI improved if the best figures was derived two or three races back.
That is, if you eliminated any race where the best fig was the last race, their ROI improved!

Rick
01-24-2003, 03:42 PM
Fast,

It turns out that increasing your ROI has a much greater effect on overall average profit than increased odds does. You can increase odds by a factor of four if you can increase ROI by a factor of two and still show the same average profit. The odds ratio goes up as the square of the ROI ratio. So, an ROI that is 1.1 times as much (10% increase) allows for an increase of 21% (1.1 * 1.1 = 1.21) in odds. I'm assuming here that you'd change your % of bankroll bet based on the optimal Kelly calculation or some fraction thereof. But it also assumes that you'd make the same number of bets per year, and that wouldn't be the case if you were "tightening up" a method to produce a higher ROI. So you still might wind up worse off by trying to squeeze out that extra couple of points of ROI. Every case is unique though and you really have to make your own comparison. My goal is high annual profits with low variance without needing a large bankroll. Not too much to ask, right?

Fastracehorse
01-24-2003, 11:42 PM
Thanx again.

Another question: How many plays do you expect to make in an average year??

Fast.

Rick
01-25-2003, 11:49 AM
fast,

I should get about 1800 plays if I'm not lazy, maybe only 1600 if I take a lot of time off. I looked at several possible scenarios for comparison if I changed the number of plays using the same method. These are just based on guesses as to how my win %, ROI, and number of plays would be affected.

The way I play now gives about 1800 plays with 27% wins and 20% ROI. Using 0.2 * Kelly as a fixed bet size with a $10,000 bankroll gives $116 bets and $41,760 estimated income. Now, here are the results for some other combinations:

2400 bets, 28% wins, 15% ROI - $97 bets, $34920 income.
1200 bets, 25% wins, 25% ROI - $125 bets, $37500 income.
900 bets, 24% wins, 30% ROI - $136 bets, $36700 income.

So, if these are reasonable assumptions about how the variables would change, then any changes I made would just result in a lower income. Also, reducing the number of plays results in a larger standard deviation in annual income. For the 1/3 reduction shown above it would increase by about 22% (square root of 3/2 = 1.22). So the bad years might be 12,200 lower than average rather than 10,000 lower than average for example.

LOU M.
01-25-2003, 12:48 PM
How often do you take profits?Does when you do affect your overall return? What rules would you institute if one wanted to live off the profits?

Rick
01-25-2003, 02:12 PM
Lou,

When I'm building a bankroll I bet about 2% at convenient dollar intervals. When my bankroll is up to the desired level for profit taking, I bet 1% of the full bankroll (fixed bet size) and check the bankroll level once a month (about 150 plays). If there is a loss, I don't take anything. If there is a profit, I take it all. I may switch to doing that at 3 month intervals since there is almost always a profit after that many plays while at one month there is a significant chance of a disappointing result (maybe 15-20%). In the unlikely event that I would lose down to half my bankroll, I'd go back into the bankroll building mode with 2% bets and not take any profits until it was replenished.

LOU M.
01-25-2003, 02:22 PM
Thanks, sounds like a solid idea.

anotherdave
01-25-2003, 02:58 PM
Rick do you decrease your bets when your bankroll drops or do you stick with the same bet? I do a very similar thing to you (I think). I bet about 1-2% until I reach my maximum bet threshold, and then I stay at that flat value. It only goes up, not down, until I reach my threshold.

I've always had trouble with decreasing my bet in a winning streak, because it is invariably broken by a 10-1 winner which I had too little on. It may be riskier, but I only bet 1% at that point so doesn't worry me much. So if I am at $10000 betting $100 a race (1%) and my bank drops to $7000, my bet is still $100. Just wondering what you do?

AD

Rick
01-25-2003, 04:50 PM
AD,

I do decrease bets on a losing streak but I use thresholds (going up and down) that make the changes in bet size less often. For example, if I'm making $20 bets at $1000, I won't raise the bet size until I get to $1250, when I'll jump to $25. So, it's more like 2% rounded down to a convenient bet size. I try to set the thresholds at least 20% apart so I'm not changing my bet size continuously. Also, I make all of my bets at the beginning of the day so they're all the same size based on the beginning-of-day bankroll. I'm not saying this is the best way to do it, but I really don't like complicated money management schemes.

Another interesting idea, suggested to me by socal fan, is to bet a percentage of the maximum amount your bankroll has been in the past. According to my simulations, my percentage should be about 20% less if I used that rule. So I would bet 1.6% of maximum instead of 2% of current. It does have the desirable property that you mentioned of never having to decrease your bet size. It's just as safe as long as you use the more conservative % of bankroll.

I had the opposite problem from you about a year ago. I had a large winner ($81.80) and increased my bet size by too much, which was followed by my longest losing streak (29). That experience made me somewhat more conservative. But I've had it go the other way too. It seems like if you have a long losing streak with a certain style of play that the odds go up a little on that type of horse. Say you're betting early speed types and they finish second for about 10 races in a row. It seems like everyone else betting them gets disgusted and decides to bet closers instead, which of course guarantees that an early speed horse will win and pay about $40. I think at most tracks they actively try to eliminate any severe bias, so it's more likely to go back to normal than to continue.

There also seem to be seasonal effects at some tracks that affect my profitability but I don't understand them well enough yet to be able to adjust my bet size. The patterns may disappear after I look at it for a few more years. It reminds me of some of the post position studies I've seen where there seems to be a clear bias one year and then the next year it's reversed or eliminated. Track management seems to be looking at the same information we do and making adjustments accordingly. I've seen some trainer pattern data too that flipped back and forth like that from year to year.