probable max losses in a row

[imofe]

What would be the correct way to calculate probable max losses in a row at a 45% winning clip over 1000 trials?

[Robert Fischer]

What would be the correct way to calculate probable max losses in a row at a 45% winning clip over 1000 trials?

I'm going to have think more about the subject to really give you any info weighing the pros and cons of drop down formulas and other options, but here is a quick answer:

1000 trials = a maximum of 12 consecutive losses

10000 trials = a maximum of 15 consecutive losses

formula for excel "=ROUND(LN(1000)/-LN((1-A1)),0)" where A1 is "x" or whatever cell you have the win% and "1000" is the number of trials.

[imofe]

Thank you Robert. I have an acquaintance at the track who asked me this and I said I would get back to him. He is a big bettor who was recently offered 8% on all his bets. He thinks he can obtain 45% winners at 97 cents on the dollar return. Because he is very aggressive and a rare bird (my dad use to say this) he wants to bet progressive style and wanted to know about losing streaks. I don't know what will happen , but from an entertainment perspective, you can't beat it.

[Ray2000]

There's a streak calculator at

http://www.pulcinientertainment.com/info/Streak-Calculator-enter.html

giving chances for a streak or 2 steaks in so many bets

[TrifectaMike]

It is not to difficult to calculate the probability of a losing streak when we start with a loss. Since we start with a loss, it is just the probability of a single loss raised to power of consecutive losses.

So, if q equals the probability of one loss, the probability of k losses simply equals q^k (q raised to the k power).

Example:

q (50% winners) = .5 and k =10 (10 consecutive losses)
q^k = .5^10 is approximately .001

However, let's ask a slightly different question. What is the probability that at least one losing streak of length k will occur somewhere among n independent wagers?

If k is less than n, this probability will be greater than q^k. Why would this be so? Because there now will be many opportunities to start a losing streak (each newly lost wager can be the start of a losing streak).

A good approximation for this probability is

P(>= 1 losing streak of length k in n wagers) is approximately equal to [1 + (n-k)p]q^k, where p is the probability of a win.

As expected this is greater than q^k.

Suppose you make 200 wagers in a month. With a win rate, p, of 50%, the probability of a loss q = 1-p, which is 50%. Most would calculate the probability of a losing streak of 10 losses as q^k = .5^10 = 0.001, or 1 out of 1000.

However, what is really needed is the probability of getting at least one losing streak of length 10 at some point during the 200 wagers. This probability is much higher. It is higher by the factor of [1 + (n-k)p].

[1 + (n-k)p] = [1 +(200 - 10)(.5)] = 96

So, the actual probability of at least one streak of length 10 over 200 wagers is 96 times as large as q^k or (96)(0.001) = .096 (nearly 1 out of 10).

That is quite a difference.

Mike (Dr Beav)

[Stillriledup]

you gotta eat a LOT of chalk to have 45% winners...but, it can be done if you just pick and choose and stick with prime horses who are 1-2 odds or lower.

[imofe]

you gotta eat a LOT of chalk to have 45% winners...but, it can be done if you just pick and choose and stick with prime horses who are 1-2 odds or lower.

Yep. And I don't think this guy has the patience not to make action bets. Especially if he starts to get some bad breaks, he could go on tilt.

[davew]

Thank you Robert. I have an acquaintance at the track who asked me this and I said I would get back to him. He is a big bettor who was recently offered 8% on all his bets. He thinks he can obtain 45% winners at 97 cents on the dollar return. Because he is very aggressive and a rare bird (my dad use to say this) he wants to bet progressive style and wanted to know about losing streaks. I don't know what will happen , but from an entertainment perspective, you can't beat it.

the parimutual system is designed to take money from people who bet too much into a pool

[imofe]

True Dave. I guess for me it is very entertaining to watch because I am overly conservative without too many mood swings. This guy is like a roller coaster ride.

[Stillriledup]

Yep. And I don't think this guy has the patience not to make action bets. Especially if he starts to get some bad breaks, he could go on tilt.

The only way you can beat the game, in my opinion, is to bet on horses who look bad on paper but in real life, they're not that bad. Horses who look good on paper are short prices for the most part and horses who look great on paper are shorter prices still yet. The greatest players are able to sniff out the horses that the general public THINK are slugs, but really aren't.

[TexasDolly]

It is not to difficult to calculate the probability of a losing streak when we start with a loss. Since we start with a loss, it is just the probability of a single loss raised to power of consecutive losses.

So, if q equals the probability of one loss, the probability of k losses simply equals q^k (q raised to the k power).

Example:

q (50% winners) = .5 and k =10 (10 consecutive losses)
q^k = .5^10 is approximately .001

However, let's ask a slightly different question. What is the probability that at least one losing streak of length k will occur somewhere among n independent wagers?

If k is less than n, this probability will be greater than q^k. Why would this be so? Because there now will be many opportunities to start a losing streak (each newly lost wager can be the start of a losing streak).

A good approximation for this probability is

P(>= 1 losing streak of length k in n wagers) is approximately equal to [1 + (n-k)p]q^k, where p is the probability of a win.

As expected this is greater than q^k.

Suppose you make 200 wagers in a month. With a win rate, p, of 50%, the probability of a loss q = 1-p, which is 50%. Most would calculate the probability of a losing streak of 10 losses as q^k = .5^10 = 0.001, or 1 out of 1000.

However, what is really needed is the probability of getting at least one losing streak of length 10 at some point during the 200 wagers. This probability is much higher. It is higher by the factor of [1 + (n-k)p].

[1 + (n-k)p] = [1 +(200 - 10)(.5)] = 96

So, the actual probability of at least one streak of length 10 over 200 wagers is 96 times as large as q^k or (96)(0.001) = .096 (nearly 1 out of 10).

That is quite a difference.

Mike (Dr Beav)

Thanks for the post TM. It was appreciated by me. I am surprised that imofe didn't comment,maybe he missed it.

[imofe]

Sorry about that. Thank you Mike and Ray. Mike's post and Ray's attachment were both very helpful.

[imofe]

Okay. This should be interesting. His planned progression based on the probable consecutive losses will be a step up in one unit after three losses to a max of 15 plays ( losses). So max losses would conclude after three 5 unit losses. Looks like he can lose 45 units if 15 in a row go down. He said he will start over after a win even if he has not broke even for that session. He is confident he can do 45% at 97 cents on the dollar ( 8% back). I won't see him again until Friday, so I'll update then.

[overthehill]

i dont understand why he thinks progression will help him. if anything there is a likelihood that 1. he is in a slump that will be exacerbated by progression, 2. his increased betting size will effect the pools. in my opinion it is very difficult to project 45% winners with confidence under any circumstances. yes it may average out that way over thousands of bets, but its a fallacy to think that therefore there is any certainty that for any race or small group of races that the odds of winning is 45%. horse trainers jockey are not machines and the surface changes and weather effect results as well. i think there have been sequences at new york tracks of a favorite not winning for three days.

the only person i have heard of making money from some sort of progression was a guy i met years ago, who seemed like an astute handicapper though he was an admitted alcoholic. he said he made a living by playing a couple of place parlays a week. he said he would hit 50% of the time and get better than $7 back.

[thaskalos]

i dont understand why he thinks progression will help him. if anything there is a likelihood that 1. he is in a slump that will be exacerbated by progression, 2. his increased betting size will effect the pools. in my opinion it is very difficult to project 45% winners with confidence under any circumstances. yes it may average out that way over thousands of bets, but its a fallacy to think that therefore there is any certainty that for any race or small group of races that the odds of winning is 45%. horse trainers jockey are not machines and the surface changes and weather effect results as well. i think there have been sequences at new york tracks of a favorite not winning for three days.

the only person i have heard of making money from some sort of progression was a guy i met years ago, who seemed like an astute handicapper though he was an admitted alcoholic. he said he made a living by playing a couple of place parlays a week. he said he would hit 50% of the time and get better than $7 back.

I have a hard enough time with this game when I am sober...

[imofe]

i dont understand why he thinks progression will help him. if anything there is a likelihood that 1. he is in a slump that will be exacerbated by progression, 2. his increased betting size will effect the pools. in my opinion it is very difficult to project 45% winners with confidence under any circumstances. yes it may average out that way over thousands of bets, but its a fallacy to think that therefore there is any certainty that for any race or small group of races that the odds of winning is 45%. horse trainers jockey are not machines and the surface changes and weather effect results as well. i think there have been sequences at new york tracks of a favorite not winning for three days.

the only person i have heard of making money from some sort of progression was a guy i met years ago, who seemed like an astute handicapper though he was an admitted alcoholic. he said he made a living by playing a couple of place parlays a week. he said he would hit 50% of the time and get better than $7 back.

The previous weekend I did not see him, but I saw him two days ago on Saturday. Up to this point he said he is winning with the progression hitting in the low 40's and getting back 95 cents on the dollar. The problem is he has lost the winnings on pick 4's and carryover pools. He is now thinking of hiring someone to place his bets so that he is not at the track losing the profit on other bets.

[thoroughbred]

you gotta eat a LOT of chalk to have 45% winners...but, it can be done if you just pick and choose and stick with prime horses who are 1-2 odds or lower.

Stillriledup,
Very true.
There have been analyses which show that if you bet every race and choose only one horse to WIN, then it is just about impossible to have a win rate of 40%.

I've thought about why this is so, and concluded it is basically for the same reason that no major league ball player has had a batting average of 400 ever since Ted Williams did it in the 1950's. While the physical parameters of horse racing and baseball are so different, the same kind of limiting restraints are at work.

[ultracapper]

1941. I'm a baseball junkie. Couldn't let the Williams inaccuracy go. By the way, that was the same year DiMaggio hit in 56 straight games. DiMaggio's batting average during the streak was .406, exactly the same as Williams's on the season. Joltin' Joe batted .356 for the year and took down the MVP. If the voters would have known that .400 would probably never happen again, I'm sure Williams would have gotten it, even though the NY media hated him with a passion. Last time a NL player hit for .400 was Bill Terry of the NY Giants in 1931. John McGraw was the manager. How's that for historical perspective. The same McGraw that refused to play in the 1904 WS because he considered the AL an inferior league and wouldn't subject his brilliant team to a "World Championship" series with a minor league champion. That was all a very, very long time ago now.

I digress. Carry on.

[thoroughbred]

1941. I'm a baseball junkie. Couldn't let the Williams inaccuracy go. By the way, that was the same year DiMaggio hit in 56 straight games. DiMaggio's batting average during the streak was .406, exactly the same as Williams's on the season. Joltin' Joe batted .356 for the year and took down the MVP. If the voters would have known that .400 would probably never happen again, I'm sure Williams would have gotten it, even though the NY media hated him with a passion. Last time a NL player hit for .400 was Bill Terry of the NY Giants in 1931. John McGraw was the manager. How's that for historical perspective. The same McGraw that refused to play in the 1904 WS because he considered the AL an inferior league and wouldn't subject his brilliant team to a "World Championship" series with a minor league champion. That was all a very, very long time ago now.

I digress. Carry on.

Ultracapper,
Thanks for the date correction. At my advanced age, many dates of long ago sort of blend together.
As a baseball junkie, you may wish to know my conjecture as to why Williams was able to do what is obviously a difficult thing to accomplish, i.e. bat over 400.
I have read, from time to time, that when Ted Williams was entering the Navy in World War II, the examination of his eyesight showed that it was exceptional. I understand, that in all the time since then, again from what I read from time to time, no other recruit has equaled his great eyesight. It was this extra capability, that I believe had him bat over 400.