Hey guys,

I do sports betting recreationally from time to time and I have been wondering about this question for a while now. I can not figure it out.

The question is:
Is 50% vs 50% event at sport betting really a 50% vs 50 % chance?
I think this a lot more tricky question that it appears at first sight.

For example: we have over/under(for both teams) at some random NBA game at 200,5 points.
Odds for less than 200,5 points are 1.9 and odds for over 200,5 points are 1.9. I understand it is 50 percent vs 50 percent. But it is 50 percent vs 50 percent just by the odds. I understand that betting house uses previous stats, current situation,... when they came up with the number(in my example with 200,5 points). But that was mostly made out of the past events. When they are playing is new event (not related to past). And also, we do not know if this is really 50 vs 50 chance because teams(in question) do not play like 10000 times so we could just calculate real odds. It is a lot different 50 percent vs 50 percent chance from the original coinflip (if we really flip a coin: heads or tails). We can repeat coinflip 100000 times and we see that this is really 50 % vs 50% chance(also it is easy to calculate this).

This is maybe very stupid but i will say it: 50% vs 50 % at sports betting is probably more like 60% vs 40%(but do not know for which side).

I hope you understand my question, I do not speak english very good.

Thanks for your effort to answering me.

Look into "confidence interval". I think it is what you mean.

@NewOldGuy
Thanks for answer. I googled confidence interval and read a lot about it, but I do not think this is the key to answer to my question.
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This is some underquestion:
Let´s say(for better understanding) in my above mentioned example there is in reality 30% vs 70% percent chance (the 200,5 points example).But we do not know which is favourite(over or under). And let us say there is no way to figure this out(just for better understanding). If we do not know if 70% percent is in favour for over 200,5 points or 70% percent chance is in favour for less than 200,5 points, Is it actually a 50 percent vs 50 percent for us?

There are several related issues packed into your questions.

(1) Subjective vs. objective probabilities:

(2) How betting odds are determined:

Typically, as I am sure you know, betting odds are set to generate a lot of betting on both sides. This generates vig or juice for the people setting the odds (the bookie or the house).

So, any bet that is listed at 50/50 (even odds) is not necessarily a true 50/50 bet. For one thing, since people have different subjective views on the underlying true odds, you can think of the bookie trying to set the listed odds at or around the median of people's subjective views of the true odds. This is not at all saying that the underlying true odds are actually 50/50.

This is the total nature of sports betting. If the line suggests that it is 50/50, and you believe that it really is 50/50, then there would be no reason to bet. By betting, you are essentially saying that your side has a higher percent chance to win. Anyone taking the other side is thinking that they have a higher percent chance to win. That is why people bet - because they think they are smarter or otherwise have some edge.

As you say, there is no known probability like there is with a coin flip. If the actual probability were known, bookmakers could make a perfect line every time. Nobody would think they have an edge, because they would know that they don't.

To look at your example, no matter what the actual probability is (if there were such a thing) it is a 50/50 proposition for you because you have no information. You could make your choice by flipping a coin, and you will pick the winning side 50% of the time, even if 1 side is really a 90/10 favorite. That is because the coin doesn't know which side is a favorite - it is equally likely to pick the favorite or the underdog. If you let a coin flip decide your choice, you should win 50% of your bets, no matter what the odds are. But you will lose money doing this, because the bookmaker has to make a living.

It depends on the sport. Namely it depends on how much luck is involved. If a bookmaker makes George 50% against Bill in chess or the mile run it is probably more like 90 or more percent but we don't know which one. In other words if they competed again tomorrow the winner today would be a giant favorite. But if it was a small poker freezeout or a game of baseball that the bookie rated as even, the real chances were probably 55% or less and the result of one contest doesn't change it much.

In sport betting I think that the correct approach is to forget about the "true odds". There aren't any "true" odds. In sports you have a couple of competitors and whoever scores more points wins.

This is a knowledge issue: you simply don't know who is going to score more. If you knew in advance what every party is going to do during the game (any decision, action, but also body movement and so on), well, physics law are still in play and you could determine who is going to win. But of course you can't. You then guess the outcome based on your information (past games, reported conditions on competitors and many other factors).

Remember also that a bookie's job is not to predict event outcome; rather they have to guess how bets will distribute. In your example, if the total amount of bets is equally split between the two options, the bookies did a good job: no matter the result, they are going to win (because of juice). If instead a side is selected by bettors much more than the other, the bookie did a bad job and they risk to lose a lot.

On the other hand, the bettor must evaluate how much likely are the events according to their subjective assessment. Then, they decide whether to bet or not, depending on the offered odds.

To summarize:

- there aren't any "true odds"
- the likelihood of events in sports betting is subjectively assessed, based on the available information
- bookies offer odds in such a way to win in any case: they have to predict how bets will distribute
- bettors assess likelihood on events and bet whenever offered odds are convenient based on their assessment

What you wrote is only true of mediocre bookies. Bookies who are excellent handicappers will often put up a line that is not expected to get equal action and in the long run will do a "better job" than an equally talented bookie who tries to split the action. As a mathematician I know you get this. And I would normally forgive you for not realizing this is sometimes how it works in real life. Normally. But not given your screen name.

Of course you got much more experience than I on the subject and obviously in many instances a good bookie will incentivize bets on events they think to be very unlikely.

Still, the primary concern of bookies is to predict the action and only then the event (of course they are correlated). That's why good bettors can beat bookies: a good bettor has to be better than the field in predicting, while the bookie must be primary good in predicting the field.

I don't think that just predicting the action makes you a mediocre bookie (I might be wrong here since not an expert in the field). I was (very little to tell the truth) exposed to the pipeline of assessing odds for big online bookies. Basically, the opening odds are made by experts, but from then on, the odds are algorithmically adjusted based on running bets. Those adjustments are generally "agnostic" (are the same regardless the underlying event) and aim to get the most bets while giving the bookie the most safe outcome. For many events, in little time the initial odds are "forgotten" (i.e. odds are basically determined by the market and they tend to be the same value regardless the initial assessment).

This just to tell that it might be more important for a bookie to develop good algorithms that efficiently follow the market rather than looking for an extra edge based on the sport knowledge. A good algorithm let you open market even for events and sports you don't have any specific knowledge.

@ whosnext, VBAces, David Sklansky, nickthegeek

You all know a lot about probabilites and betting. All the answers really helped me with my question (I understand better everything now). You guys are the best (thank you for your effort).
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I have another 2 different questions:

1.)Which sports are the most »lucky« sports (and you can bet on them at bookies)?

I would say that the most lucky sports are the ones at which one change of the result that happened in a game, changes the »live odds« dramatically. I think this means that these sports have the lowest under/over at points or goals,... I assume soccer is one of the most »luckiest« sports? If we compare it to basketball: at soccer we have in many cases over/under, 50 vs 50 odds at 2,5 goals and at basketball for example we have this number usually above 200 points (at NBA). If one team scores a goal(in soccer), it changes our »live over/under 2,5 goals odds« dramatically. If some person scores a point in basketball, the over/under odds do not change that much. Am I looking this correctly?Am I way off?

2.)Distribution of results in my cases?

I am totally out of my math comfort zone with my second question (i will try to explain what I have in mind; maybe I do not use correct terms: please correct me). I am not sure how to calculate it (if it is even possible?). This is theory/math question, I think(some variables are out). There is 1000 different basketball games (different oponents) that will be played in the future, in our problem. At each game we have two possible outcomes of the event that we are interested in : over/under at x points (x is different number at different game). The odds for winning each outcome is 1.9. We have 3 different cases now:

Case 1): Lets say that the real odds for one of two possible outcomes (over/under x points) are 50 % vs 50% (exactly): 1000 different games (different oponents). There will be equal number (close to that number) of overs and unders (games that will end up with less/more than x points) in 1000 different games. And the results will be distributed in the exact same way as they are at coinflip (flipping a coin; heads or tails,…)?

Case 2): we know that bookie give us 50% vs 50% (1,9 each: two possibilities) betting odds chance on the event, but real odds are 100 percent vs 0 percent: over/under x points (and let us asume there is no way we can figure it out which side is 100 percent vs 0 percent;«bookie« also do not know which is 100 percent vs 0 percent). If we know that. Can we asume that there will be equal number of overs and unders in 1000 games? 50 percent of times there will be over and 50 percent time there will be under(1000 different games)? Bookie´s mistake that he do not know on which side the real odds are, will »even« by some number of games because he basically can get it right or he can get it wrong (50 percent vs 50 percent)? Distribution of results?

Case 3): Same as case 2, with only difference that the real odds are 75% vs 25%. Distribution of results?

This is my question here. Will the results be distributed in the same way in all cases (different games; 1000 games)? How they are related? Short-term and long-term? I do not know how to answer this (and do not know how to calculate this).

Thanks for your effort.

If you adjust the line based on bets without regard for expert opinion you will do much worse than if you don't (You SHOULD move the line but to one half point away from the other bookies). Keep in mind also that if you are "off" in your original line and move to "balance" the action you risk being middled.

On a more general note I maintain that there is actually a "true line" for any sporting event based on the info at the time. Just like a flush draw is 9/47 even though cards are out.

This reminds me the "exploitive vs optimal" debate in game theory. You seem to support an exploitive approach while I'm for the optimal route. Optimal strategy however allows you a lot more: you can open markets without specific knowledge (or at least you don't need to be very good, just ok will be fine), you can follow live events more robustly (good luck in beating a good algorithm during a tennis game) and you (in this specific field) reduce volatility. This last point is very important: if you are good at predicting markets, you can reduce the juice significantly and this in turn will attract more bets and keep bettors away from competitors.

In odds adjusting you have two ingredients: your original line (the prior probability) and the adjusted line, given the bets received (the posterior probability). You need to be good at assessing both. However, the latter is much more important. If I adjust well, I'm good for any popular event, in which the market will dictates odds (this is probability theory: if you have a lot of evidence, you land to the same posterior, regardless your prior assessment). For not popular events I might be off (my prior is wrong and I got not much data to adjust properly), but I risk much less. The opposite happens for whoever doesn't adjust well (risking to lose in popular, high volume, events).

It's important to stress that you can keep the concept of "true line" only if you specify that "truth" here belongs to info and not to events. Probability is about information. An event doesn't have a "true" odds. Even in your example: the guy with a flush draw will assess the probability of hitting as 9/47. In the same hand, another guy at the table who folded a couple of hearts and see the showdown will assess the probability differently. You can call both odds "true", if you like. But they are different and depends only on information. In sports betting they depend also on how you rate your information.

I have read again everything what everybody in this thread said.

I do not thing that this is correct. I think distribution of results (with big sample) will be a bit different in this case. I think it will be very close to "coinflip" distribution of results, but a slightly different. Maybe I am wrong?

Think about the following scenario. You conduct this experiment.

Step 1: You prepare an urn with a very big number of fair coins. You instruct a guy to randomly draw a coin from the urn, flip the coin and register the result (H/T). The guy repeats the above N times.

Step 2: Same as step 1, except now the urn shall contain half of the coins with two heads and the other half with two tails.

At the end the guy gives you the two H/T sequences without telling you which one comes from which step. Do you think you can tell a sequence from the other?

Half the time you will win x% and the other half (100-x)%. Add them up, divide by 2 and get 50%.

That's a very interesting example.

@David Sklansky and nickthegeek

Thanks for answers. Means a lot to me.
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No, I am sure I can not tell difference in this two cases. Thanks for nice scenario and better explanation. I really do not want to troll here, but I am still not sure about this. I would like to "get this".

Look at this:

example #1): we are flipping 1000 fair coins. Our results will be(sequence): H, T, H,H, T,T, and so on. and at the end our results will be 500 H and 500 T(close to that number).

example #2): we are flipping 1000 unfair coins. Our results will be: first 500 flips will end up with heads and last 500 flips will end up with tails. Results will be still 50% vs 50% and if we would look only the end results everything would look good. If we would look only unfair coin´s end results we would easily mistake them with "fair" coin´s end results. But the difference is in sequence(or distribution of results: do not know the correct word).
This two examples i just give because want to show my "thought problem".

So to go back to my over/under x points at basketball. I still think there will be different sequence at results in sports betting 50% vs 50%(by odds) if we compare it to coinflip sequence. I mean, I am sure at the end both will have very close to 50% vs 50% results. End results would be the same. But sequence: I am still not sure.

This would be incredibly unlikely (and, btw, as likely as it would be in example #1).

Why you think that in example #2 the first 500 coins will be heads and the last 500 tails? Remember, you draw your coins randomly, so extracting the first 500 coins of the same type is so unlikely (as likely as flipping the same face for 500 times with a fair coin).

Thanks for this. Yes, I understand now what you are saying. I get it now.

Yeah, I am still not sure that we will have same "most likely" distribution of results(sequences) in "sport´s 50 vs 50" and coinflip(yes, end results would be very close). I also give bad examples in previous posts.

In sport´s 50 vs 50 we have "human error" ("bookie´s mistake":With that I mean that for what ever reason bookie did not give us exactly 50 vs 50 (possible bigger profit for bookie;a bit wrong prediction by bookie,…: all the things that you guys wrote here)), which I do not think it can be calculated easily(end result can be calculated easily: but frequences not).

Is it theoretically possible (generally speaking; not in this case) that we would have same end results and different "most likely" distributions of results (sequences) in two different long term 50% vs 50% situations(one is totally random and one is not)? I think yes and in some cases (also possible because of "human error")? Correct or not?

Sry that I did not answer this before. Yes, that was really bad example. You are correct with this.

I can be very wrong here:
I think that we can not equal "sport 50 vs 50" with any kind of coin example, because we do not know every "sport 50 vs 50"´s chances (which side will be favourite, and by how many this site will be favourite;every "sport 50 vs 50" is different chance and we do not know which is which), like we do at coins. We also do not know our next in line "sport 50 vs 50"´s chances,...

I really respect your knowledge (math, probability,..), I am very curious what you have to say (or somebody else) about my previous (to this) post (second and third paragraph). Is it stupid? Correct? Possible? Why?

Thanks for your effort and your time.

Yes, I read again everything what I could find on google on distribution, coinflips, and more. I guess I really confused a lot of things. You guys were correct. Thanks everybodies here for your time. You guys are the best.

POSSIBLE EV+ BET at roulette?

Very little chance it is...but still

I will just post my question here, so I do not open another thread. I hope somebody with good math and programming knowledge(basically I need somebody that do know how to write simulation) will be interested. I am thinking of some kind of roulette bet that is maybe EV+(I do think it is very unlikely that what I have in mind is really EV+ bet, but I would really like to see some results). I would like that somebody do simulation and data gathering for this possible EV+ bet at roulette. I am not saying what I have in mind here, because this would not be smart. I do not mind saying this to 1 other person, pretty sure this person will not say what it is about to anybody else(if it is really possibly EV+ bet in roulette; very little chance for it, but still). Why I think this person will gave me correct data and simulation. In case results will be negative, I will ask another one to repeat simulation and data gathering. The more people know this, the more terrible it is.

I am not paying anybody nothing and it is very likely that what I do have in mind is not EV+ roulette bet, so you will be probably doing this for free. If you are interested, please PM or write here.

Thanks.

This system wins you a dollar in roulette 99.98% of the time:


(It's called the David Lyons Patented Roulette System, and requires a 50,000 bankroll)


Bet $1 on every number other than 29 and zero, if you win - stop (up $1)
If you lose (down $35 overall), bet $35 on every number other than 29 and zero, if you win - stop (up $1 overall)
If you lose (down $1260 overall), bet $1,225 on every number other than 29 and zero, if you win - stop (up $1 overall)
If you lose (down $44,135 overall), then *oops* you are broke.

But the chance of those three losses in a row are 2/37 x 2/37 x 2/37 = 0.000158%
Which means the chance of winning the dollar is 99.98% every single time.

I do not have any kind of "martingale variation system" in mind. I do have in mind a system that is a lot more complicated. I do get lost with my calculations, because it is so complicated.