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rdiam 11-21-2019 08:28 PM

Optimal Betting
 
There have been a lot of opinions on betting expressed on this board recently regarding "how to bet". Instead of opinions, let's deal with facts, since optimal betting can be precisely defined by math and statistics.

Briefly, optimal betting is defined as "you bet when you have an edge, you pass when you don't have an edge". Now "edge" is sometimes hard to precisely define and may be subjective, but is roughly approximated by the formula "is the horse paying more based on its implied odds than I estimate the horse to win?" So if you think a horse can win more than 50% of the time, it is a bet at 1-1 or better. Similarly, if you think a horse can win 25% of the time, you should bet at anything better than 3-1. Otherwise, you pass.

The best way to calculate how much to bet is to determine your percentage "edge", divide it by the odds, to show the maximum percentage of your bankroll to bet. You bet more on low odds horses, and less on high odds horses. In words, this is Kelly betting, and is very aggressive. Most will cut this bet size in half or even by 1/4, with some even cutting it by 1/10. This will maximize the growth of your bankroll and minimize your chance to bust out.

Now, here is where it gets a little tricky. Humans tend to be risk averse, feeling more pain when losing $100 than the pleasure received from winning $100. So when you bet while only considering your edge, you may be subject to large runs of losing bets before your edge kicks in. Even when betting even money shots, you will lose 3 in a row 12.5% of the time. How many of you can push the money in and make that fourth bet after such a mild losing streak?

Enter Dr. Sartin, who recognized that the psychological aspect of betting also needs to be considered, and came up with a bankroll smoothing technique of 2 horse betting. More precisely, as long as your 2-horse bet has an "edge" to overcome the losing bet, you will increase your win probability over a 1 horse bet, be able to bet a larger percentage of your bank, have fewer and shorter losing streaks, and watch your bankroll grow faster.

In fact, there is nothing magical about 2-horse bets: if you can find an edge with 3 horses (including your "losing" bets), then bet 3 horses. If you only find an edge with 1 horse, then bet 1 horse.

Finally, it is often advantageous to include a low odds horse in your group bet that, on its own, may not show an "edge", but when combined with another horse creates a group of bets that not only show an edge but create a higher win probability from the group enabling you to bet a larger percentage of your bankroll and grow it more smoothly and faster. For example, some will bet an 1-1 favorite to "breakeven" if it wins to cover the group bet, and let the longer odds horses provide the profit when they win.

Bottom line, look for your edge, check to see if by including a low odds horse will maintain your edge, and bet as many horses in your group that will keep your edge: in any given race, it might be none, one, two, and maybe even three. Be flexible and not dogmatic.

Richard

Mitch44 11-22-2019 09:15 AM

It's true that an excellent selecting process will not make up for a poor money management techniques and those that don't give money management its just dues will soon depart from their bankroll. I know very few that give money management the respect it deserves.

Depending on the situation and I can make a profit I'm not adverse to betting more than 2 horses a race. In difficult races that are part of a series (DD,P3 etc.) it pays to go deeper in races that are fraught with unknown factors or has many contenders. It pays to evaluate the race as much as a horse or two to access the degree of difficulty of each race. One race may only have 2 legit contenders and another may have 3 or 4.
I always try to design a bet based on my handicapping or analysis. There are many valid questions such as :Who is the only horse that can beat this horse? Can I make a better profit by betting an Ex. and not a win bet on this low odds horse? And of course; Should I just pass this race? I've made some killer bets on legit favorites by looking at the race before and after for a nice DD. Players tend to ignore ugly horses and play too conservative in wide open races. I ask; Why not? and include unknown factors in my analysis, plus many just can't pull the trigger on good price horses. I don't have that problem, if you can't make the bet than you can't reap the rewards.

While Sartin's early thesis or studies of betting the "counter energy and class horses" for Ex. betting is still a valid concept there is no doubt in my mind he would have evolved from this if he was still with us. Basically through his research etc. Well he gave the foundation for research, all one has to do is take it to the next step. A ha, there is that nasty word again, WORK. What is getting or producing many place horses?

The Kelly system does work just like Richard says, so can betting on 3 horses to win(of course depending on the odds) The Kelly has stood the test of time and its designed to prevent ruin or run outs as simple as that. Some have problems understanding it but as Sartin always said; "grasp concept." The concept is a simple one but most have problems properly employing it, much of that is being caught up in the moment and the excitement of a race or the chase. I find it very difficult to employ it especially because I often play multiple tracks, actually impossible to employ with multiple tracks. Its much easier to employ when playing a single track but even then some have problems with it. What I have recommended to a few through PM's is to forget this after every race unless your really a math wizard and employ it after each day of racing rather than after each race. Problem solved. I like to think of it as the modified Mitch or Monkey version of Kelly.Of course you'll win more if you can employ it after each race however few can do that and the time can be better spent on the selection process. Know you're capabilities and limitations and don't try to juggle more balls than your capable of. Problem solved as you win your bets increase after winning days and decrease after losing days. This allow you to place more emphasis on each race rather than what amount to bet which really is a distraction and a bad one at that. I find this modified version of the "Kelly" to be superior to no Kelly. Like anything in horse racing its subjective and I'm sure there are nay-sayers. To each their own, find out what works for you and the nay-sayers should find out what works for them. No plan or no money management for sure doesn't work. Good luck.


Mitch44

raceman5 11-22-2019 12:48 PM

Good!!!
 
stuff guys!!!!!!


bob

CEW 11-24-2019 06:25 PM

Hi Richard & Mitch:

To me, Huey Mahl's article in the back of Follow Up #2 is tops, where he mathematically establishes, in a simple way, when to pass a race based on the individual player's win percent and average mutuel. And he explains the Kelly Criterion very nicely. I believe it was the single most important article out of everything Howard put out. Anyone else reading this may want to check it out.

Mitch - I play 10% of bank and always dutch two horses, sometimes three if I can get about a 75 cent return. I agree that Kelly is better than no plan at all. Way better, really. I used to think that I should try applying it to the stock market, but the market is way different in that you are pretty much all in most of the time.

I carry a copy of the 2 horse dutch chart for quick reference on the payoff (to know when to pass) and also the other quick reference chart to split the horses with the correct percentage of the bet on each.

I love this part of the game....especially when my two horses control a race and come to the wire ahead of the rest!

Best regards,

Chuck

Bill V. 11-24-2019 08:53 PM

Quote:

Originally Posted by CEW (Post 124653)
Hi Richard & Mitch:

To me, Huey Mahl's article in the back of Follow Up #2 is tops, where he mathematically establishes, in a simple way, when to pass a race based on the individual player's win percent and average mutuel. And he explains the Kelly Criterion very nicely. I believe it was the single most important article out of everything Howard put out. Anyone else reading this may want to check it out.

Mitch - I play 10% of bank and always dutch two horses, sometimes three if I can get about a 75 cent return. I agree that Kelly is better than no plan at all. Way better, really. I used to think that I should try applying it to the stock market, but the market is way different in that you are pretty much all in most of the time.

I carry a copy of the 2 horse dutch chart for quick reference on the payoff (to know when to pass) and also the other quick reference chart to split the horses with the correct percentage of the bet on each.

I love this part of the game....especially when my two horses control a race and come to the wire ahead of the rest!

Best regards,

Chuck

Hello Chuck

Recently I posted a winning ticket, where I bet 2 horses to win
My bankroll was $50 I bet $5 per horse. The odds on each horse
were 3.10 and 3.30 to one
A poster criticized me for making the bet
I want to see if you can tell me if the bet was okay
Thanks
Bill

Mitch44 11-25-2019 06:29 AM

CEW,
Dutching is an old concept that was around in the 60's and is still valid today as are many concepts if you can get the right set up and situation. Very late money from simulcasting coming after the race begins hinders and makes it difficult to properly employ. Ditto with Benter's concept and other concepts that beat the game.
While all still valid one must have a great deal of patience to employ them however the public does make mistakes every day.

Whenever the game gets beat it evolves to new ways in order to survive. I wouldn't hold my breath for tracks to change such as employing a strict cutoff to post time. That would reduce their pools and thus their profits on take.

The Kelly is a valid concept that is ignored by the masses even today. Most give little attention to money management.

There are many similarities of the stock market and horse racing. I suppose if one has very deep pockets positions can be Dutched. I.e play 3 or 4 different companies and have the one that survives etc. Your right for the small player in that your mostly all in.

Mitch44

CEW 11-25-2019 07:51 AM

Hi guys -

For anyone reading along, I use Huey's proportional betting based on the article in Follow Up #2, so anything I say below can be found thoroughly explained in that article. I've been doing it ever since I read it in the 1980s.


Bill - Two 3-1 horses dutched (split) evenly yields even money or a hair higher, as I am sure you know. Two things need to be applied to understand why Huey says this is the ultimate way to bet:

How to figure ROI and how to know when you have an advantage.

1) Howard always suggested adding up your $2 mutuels and dividing by the number of winners in a given cycle in order to come up with your average mutuel. However, as Huey explains, this does not take into account the losing horse in your bet. The easiest way to figure the winner and loser together for the actual odds of your play is to take the gross return from the bet divided by the cost of the bet minus one. So in your example, you bet $5 each on two 3-1 horses. It pays at least an $8 mutuel (either $8.20 or $8.60) times 2 1/2 (since you bet $5 each). So on the lesser horse you get back $20.40. Divide by the bet of $10 then subtract 1. Your net odds were 1.04 to 1, which takes into account the winning bet and the losing bet. If the $8.60 horse won, you received 1.15 - 1. I write this number down after every play. After you have about 10 to 20 races, simply average these odds for your true average mutuel. This number is what counts when referring to everything Huey talks about in the article. (Mitch - by the way - if you do this quick calculation after each race, you can easily apply it to Kelly as you go along between simulcast races, but I sense you really don't need to based on how you describe your style using Kelly.)

2) Then the other step is to go to the graph on page 47 of Follow U #2. Say your average mutuel over a number of plays is 1.0 to 1 (even odds). Go up the left hand column to 1.00.....as you go to the right on the graph, you see that you have a positive expectancy as long as you win at least about 51% of your races. At even money and hitting the Sartin average of 63% nets a Kelly advantage of about 27%.

So the answer to splitting two 3 - 1 horses is as long as you are hitting half of your races, you are in positive territory. More likely you are hitting at least 60% whereby your advantage is over 20%. So any bank amount you start with will grow.

And lastly, as to when not to make a play....Huey uses .50 cents to one as the lowest acceptable odds in the article. This is based on the player's example and his win % and average mutuel. I have found that my low cutoff is around .75 cents to one.

Best regards!

Chuck

rdiam 11-25-2019 05:03 PM

Bill V.:

While the math mentioned above is well and good, you might want to consider the following simplified "rules" for win betting (unlike handicapping, rules DO work for betting and money management):

For 2 horse bets: rank your (4) contenders by whatever method you prefer.

If the top choice can be bet at 5-2 or higher, bet it

If the second choice can be bet at 4-1 or higher, bet it

If the third choice can be bet at 6-1 or higher, bet it

If the fourth choice can be bet at 8-1 or higher, bet it

If these rules have you betting 4 choices, you are missing something so PASS

If these rules have you betting 3 choices, your option to pass since the crowd does not usually make these kind of mistakes in most races

Exception to the rule: if your top choice can be bet at 3-1 or higher, OK to bet your second choice at 3-1 or higher.

If the rules above do not qualify a group bet, then bet a single horse to win if it can be bet at 1-1 or better AND any horse at 3-1 or lower IS NOT a win contender according to your handicapping.

In your example, your 2 horses were 3-1, so you have a valid bet according the exception criteria.

Hope this helps.

Richard

CEW 11-25-2019 05:47 PM

Richard -

In your post here from the 21st, you wrote:

The best way to calculate how much to bet is to determine your percentage "edge", divide it by the odds, to show the maximum percentage of your bankroll to bet.


Can you give an example or two? I like the way it sounds already!

Thanks in advance for your help!

Chuck

rdiam 01-08-2020 07:51 PM

Raptor:

You are confusing variance with edge. Since the edge in most gambling games is quite small (usually 5% or below), the variance tends to be high. High variance means that you can show a profit over a relatively small sample size but still be betting into -EV and having a negative edge. In fact, the whole idea of casino games such as craps, roulette, and slots, is the provide a positive edge (+EV) for the house and negative edge (-EV) to the player, but all showing a high variance so that in the short run there will be winners! If you win at craps or slots, you will be inundated with offers for meals and rooms to get you back in the casino. Why: because they know over a large enough sample size the player's negative edge will work in their favor and they will get the money given enough time.

The best gambling games are those with high variance but where those with skill can win over a large enough sample size. This is why lowball poker died (variance was too low and skilled players always got the money) and why no-limit hold em has become so popular (high variance, poor players can win in the short term, but skilled players can have +EV with proper playing and betting strategy). It is also why casinos try to ban blackjack card counters and shuffle trackers, since they know these types are playing with a positive edge, and will eventually win if they are allowed to play long enough. Similarly, most of the sportsbooks now legal in the US will limit or ban those bettors who bet with a pattern that shows them to have +EV. So if you are allowed to bet whatever your want with a sportsbook, you most likely have -EV since they welcome your action.

Since this is a horse racing site, consider that horse race betting also has high variance, especially in the exotics. Yes, you can have +EV and an edge, but having an edge has nothing to do with short-term results. And because of the high variance, with sample size needed for you "edge" to kick in is much higher than you might expect -- we are talking hundreds, if not thousands of bets.

Richard


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