Posts Tagged ‘the house edge’

The reasons for why people gamble are many and varied and there is no magic blanket that can be thrown over the gambling population that has a universal explanation for their motivation.  One of the reasons should be to make more money than you gamble, which should be the goal of every punter.  But often it isn’t.  People gamble for many reasons, and making money isn’t always the number one agenda.  Is it fun to lose money to the sports bet outlets regularly?  I wouldn’t think so, but it should still be fun trying to win money consistently and land your occasional white whale.  When it’s no longer fun and dissatisfaction dominates your gambling emotions, you should be examining your motivation for betting.

The Champ Bros have always found it is more fun to be winning money than to be losing it.  It is very frustrating for us to lose money, as Kenny will attest to this year and I have experienced in many previous years.  We don’t see the point in betting money and not caring about losing.  This is not the attitude we carry into the challenge of trying to make a profit from sports betting.  We want to win, and we want to find the strategy which gives us a chance of winning.  And this isn’t easy.  We don’t kid ourselves about this and openly say from the outset that turning a consistent profit is difficult, where most years breaking even is a good result.  But buyer beware, as ‘breaking even’ is actually winning more than you are spending.

Picking winners and finding ‘good bets’ is just the beginning to staying in front and maintaining a profit for the long haul. To do this you also have to beat the bookmaker’s edge (aka vigorish/ vig or take or juice, or in poker terms, the rake), which means that you have to win more than merely breaking even to compensate for what you are giving to the sports bet agency EVERY SINGLE BET.  Just as poker players have to beat other players PLUS the casino rake and time charge to make money over time, the sports bet punter has to pick the winners and surpass the bookies vig as well.

I always look at a head-to-head match as having two possible outcomes.  This is important as the odds often distract the punter from this reality. Ideally you would want to get 2-1 on every bet you make on a head-to-head match; you bet $10 and win $20 if you get it right (which includes the $10 you wagered).  No one else takes a cut of this money and your win is based solely on picking the winning team.  But the book makers would have you believe that no two teams are ever evenly matched (or rarely so).  If you go through all the head-to-head sports it is very rare that two teams will have the same odds.  Have a look through the matches in the AFL, NRL, NFL, MLB, NBA, WNBA, NBL etc.  It is uncommon to find two teams with the same odds to win.

And when you do, you will see the bookmaker’s vigorish straight away.  Below is a typical list of odds for head-to-head games from a selection of Australian sports betting agencies (this list is for the MLB):

Bet365:  1.95/1.95

Centrebet:  1.93/1.93

Sportingbet:  1.93/1.93

Sportsbet:  1.92/1.92

IASbet:  1.92/1.92

Unibet:  1.91/1.91

Tom Waterhouse:  1.91/1.91

Luxbet:  1.91/1.91

TAB Sportsbet:  1.87/1.87

As you can see, TAB Sportsbet generally has the lowest returns of all the agencies, but ironically is probably the most popular in Australia.

Note: I couldn’t always find the basic head-head odds at bet365, but I think they call it the ‘Money Line’ and it is at 1.95 v 1.95 (it also shows up as ‘to win’ and ‘result’ with some sports too).

 

With the Tennis qualifiers, there is a drop in the odds offered compared to what is offered above, which was for Major League Baseball, so there is some variance between sports for what odds the agencies will offer when they deem it to be an even contest.

E.g. for the ATP Petange Challenger Qualifiers (9th Sept 2013), the head-to-head odds below were available. As you can see, they are significantly lower than what is offered above for the MLB.

Sportsbet:  1.87/1.87

Centrebet:  1.87/1.87

Sportingbet:  1.87/1.87

Tom Waterhouse:  1.86/1.86

Bet365:  1.83/1.83

My guess as to why this is the case?  The tennis players involved would be relative unknowns and hard to find any form lines on, so the betting agencies offer these matches with lower returns to protect themselves from match fixing, which would be easier to achieve with individuals than team events at this level.  Tanking or not, Bet365 is making 8.5% on any bets for this match, regardless of who wins (see below).

The other easy way to see what the different sports bet agencies are offering for an even bet is to look at the line betting.  When they offer the line, you will see the return for either team will usually be the same, as they have squared them up by offering the points difference.

Vigorish

What all this basically means is that the bookies are making money on EACH and EVERY bet you make, even if you win.

If Kenny and I both pick a team in a match deemed to be even, say with TAB Sportsbet at 1.87, and we each bet $10, one of us stands to win $18.70.  TAB Sportsbet gets $20 out of us, and then gives the winner $18.70, keeping $1.30 on the transaction, which is 6.5% profit for them.  So you can imagine if $100 000 was bet on the match with an even spread of bets between both teams, TAB Sportsbet would make $6500 REGARDLESS OF THE OUTCOME.  Think about that, wouldn’t that be nice.

Where it gets interesting is when the matches aren’t evenly matched.  Say TAB Sportsbet is offering 1.20 on the fav and 4.60 on the upset in a head to head match.  They have deemed one team to be much stronger than the other and are prepared to gamble on this result.  Now if Kenny and I again both pick a team and bet $10 each, one of us stands to win $12 and the other $46.  TAB Sportsbet get $20 out of us.  On the 1.20 win they will make $8, but on the 4.60 upset they will lose $26.

The same match is listed as 1.23 and 4.40 on Sportsbet and in the same scenario, we can win either $12.30 or $44, and they will either make $7.70 or lose $24.

So how do they make their money in these matches?

The majority of punters will be betting on the favourite hoping to win $12 from their $10 bet (a $2 profit).  Those picking the upset are trying to win and make a profit of $36. For the bookie, they just need to position the odds so that the result gives them a profit no matter what the outcome is, as seen with the odds above.

Say 10 people bet $10 each on the upset.  They have bet $100 and the bookie would have to pay out $360 extra to cover them.  That would require 36 bets on the favourite of $10 each.  So overall there was $460 bet.  If the fav does get up, it has to payout those 36 punters $12 each, which is $432, and a profit of $28.  In this balanced scenario, even if the upset did occur, they still wouldn’t lose any money.  But if say 40 people bet on the fav and 10 on the upset, they will make a profit with either result.  $500 bet.  Fav wins = payout $480 ($20 profit).  Upset = payout $460 ($40 profit).

So as I hope you can see, it wouldn’t be difficult to keep adjusting the odds of either outcome depending on how much money was being spent on which result, so that the sports bet agencies always made a profit on EACH and EVERY bet they offer to the punters.

Vigorish Formula

There is a formula where you can easily calculate this bookmaker’s edge/ vigorish, and it doesn’t take many calculations to see how much profit they make from every bet they offer the punter.

v = 100 * (1 – (p*q/ p+q) )

Where v = vigorish, and p and q are the decimal payouts for each outcome.

In the TAB Sportsbet scenario for an even match, p = 1.87 and q = 1.87

v = 100 * (1 – (1.87*1.87/ 1.87+1.87)) = 100 * (1 – (3.4969/ 3.74)) = 100 * (1 – 0.935) = 100 * 0.065 = 6.5%.

Hey, same as my calculation above!

In the second TAB Sportsbet example, p = 1.20 and q = 4.60

v = 100 * (1 – (1.20*4.60/ 1.20+4.60)) = 100 * (1 – (5.52/ 5.8)) = 100 * (1 – 0.9517) = 100 * 0.04828 = 4.828%

So believe it or not, TAB Sportsbet are still making 4.828% out of the 1.20 v 4.60 match no matter who wins.  Again, an easy way to make money; I’ll take people’s bets on any sport they like, give them odds so they can gamble on winning some money, and then take 5% of every single transaction regardless of the result.

Who Pays the Vigorish

There is some debate as to who actually pays the bookies juice; the winner or the loser.  It is a bit of a perspective dilemma, whether you view it from the winner’s perspective or the loser’s perspective, but I like to keep things simple and this is my explanation.  The winner pays the vigorish.

Let’s use the head-to-head match where both teams are paying 1.87, and Kenny and I bet $10 each on a team to win; he picks Collingwood and I choose Richmond.  At the end of the game, one of us is going to lose $10 and one of us will win $18.70.  When you bet $10, you assume that if you lose, the $10 is lost.  If the odds were a true reflection of an even match, the winner would expect to double their money and collect $20.  However, they are only going to receive $18.70, and are paying a tax of $1.30 to the bookie for handling their money for this bet.

It can be argued that because the bookie was holding both our bets as a $20 pool, the winner gets back their $10 bet and the $8.70 from the odds, which is what they were expecting, and the loser has in fact paid the $1.30 tax out of their losing $10, with $8.70 of their losing bet going to the winner.  The problem I have with this view is say only 1 bet was placed on the event and it wins.  There is no loser to pay the vigorish, so the bookmaker must be paying it for you.  This could be argued theoretically, but the bottom line is, the sports bet agencies don’t EVER pay even money for evenly matched head-to-head events, and the reduction in the odds below 2-1 is what the punter is paying as a tax to the bookies if they win their bet.

With betting exchanges like Betfair, they take a flat rate (5% less incentives) of the NET PROFIT the punter may make on any event they have bet on, where the loser just forgoes their investment with no further loss incurred. This to me is what the sports betting agencies do as well, except they often take more juice and it is factored into the odds before you make the bet.

The next post is going to look at the formula for calculating vigorish for events with 3 outcomes, which will be applied to the soccer.

Beaner

The Champ Bros see sports betting as one of the more likely ways of making a profit through gambling, as you can minimise your risk and maximise your chances of winning money over time through discipline, research and understanding the odds structures of the book makers, and most importantly, avoiding the ‘sucker bet’ (and the NRL on a Monday night).

Sports betting has its own pitfalls with the odds offered by the bookies being less than the true odds for the event, where a $1 bet on a head to head match between two evenly matched sides only returns $1.87 for either side to win (TAB) or $1.92 (Sportsbet), obviously less than $2 it should be in a perfect world.

This view of ours is the result of years of dabbling in other forms of gambling and betting and learning how the other types of gambling and games out there function.  The following is a brief analysis of what the punter is up against when playing the pokies or gambling in the casino, and why gambling and especially poker machines can easily lead to gambling addiction.

It must be noted here that gambling addiction is very real and that no punter at any level or in any form of gambling is immune from it.  Our approach is that gambling is supposed to be fun and a challenge, where we know what we’re up against and we are trying to find the edge that gives us an advantage over the book makers.  As mentioned before, we are low ball punters who are very disciplined in not deviating from our strategies or in how much we bet, which adds to the challenge and makes turning a consistent profit all the more rewarding.

Poker Machines

How Victorian Poker Machines Work

Poker machines (pokies) are a popular form of gambling, but make no mistake, pokies are designed to earn revenue for the venue operators and not for you. This is known as the ‘House Edge’.

Each machine has an inbuilt computer program that randomly generates 1000s of possible outcomes every second.  When you press the button:

1.    The machine will randomly pick one result from the many thousands of possibilities in a millisecond.
2.    The next second it will generate thousands more.
3.    It does this continuously, every second all day and night, without thinking or remembering.

The machine accepts any credits bet. If the machine determines a win, credits are paid.  If not, the machine continues to generate outcomes until the button is pressed again, each press completely unrelated to the last.

Bonus Features

Game bonus features are designed to give you the feeling that you are getting something for nothing or a second chance to win. However, everything that happens on a poker machine, including ‘game features’ and ‘free spins’ are included in the calculations made by the poker machine manufacturer. So even when it appears that you’re getting free spins, the fact is, you have already paid for them with the losses you’ve had already on the machine.

Surely some money must return to the players?

The ‘return to player’ setting is the average amount won by players as a share of the total amount bet. By law, Victorian poker machine venues and the casino must return at least 87 percent of the total amount that is bet each year to players.

It takes millions of games for a machine to reach its ‘return to player’ setting and it’s important to note that there is no legal requirement for any individual poker machine to return the expected rate (87%) in any given period of play.

In Victoria this is a minimum of 87 per cent. This doesn’t mean that every time you play you will get 87 per cent of your money back. It means that if you could play enough spins to cover every possible combination on a machine (about 80 million) then you could expect to get 87 per cent of your money back. This also means the operator can count on 13 per cent of your money. For this reason the operator doesn’t ‘cheat’ and the machines aren’t ‘rigged’, they simply have a built in advantage for the operator—there are many more losing combinations than winning ones.

Why are poker machines so addictive?

While there is little research actually taking place in Australia about this problem, there is some research from the USA about their slot machine epidemic and the role of dopamine in the brain, and I also have my own theories related to operant conditioning.

Dopamine

When dopamine is released in the brain, it can give a feeling of pleasure or satisfaction. E.g. Food and sex release dopamine.  These feelings of pleasure and satisfaction become desired, and to satisfy that desire a person will repeat the behaviours that release dopamine. Several studies have been conducted which targeted neural response to rewards. The results were unanimous in the fact that when someone performed an action over and over again, and was given a reward randomly, dopamine levels rose. If the reward was given consistently, i.e. every fourth time the action was performed, the dopamine levels remained constant. Finally, if no reward was given, the dopamine levels dropped. This also explains why eating new foods or eating food when travelling overseas is usually more pleasurable, and why having spontaneous sex is more exciting; the ‘freshness’ of the experience acts as an unexpected reward, releasing more dopamine into your brain.

These same random rewards can be seen in gambling and especially with poker machine payouts. Because the outcome is based on chance, a player does not know prior if he or she will win. Therefore, if the person wins (a random reward), dopamine levels increase.  From this it has been concluded by some that only people whose dopamine levels are naturally low become addicted to gambling.  When pokies players are on a losing streak though, their dopamine levels would drop (no reward being given) and this leads to them feeling miserable when they have lost their money.  Their solution? To play the pokies again trying to get the win (the unexpected reward) that will once again increase their dopamine levels.  This chasing of the pleasure and satisfaction dervied from dopamine is a losing battle though, as the brain won’t release as much dopamine when the action is repeated without something new happening, and the expectation of the reward also suppresses the release of dopamine.

This is a similar cycle that leads to cocaine addiction, as cocaine chemically inhibits the recycling of dopamine in the brain, causing a flooding of dopamine and intense pleasure in the user for about 30 minutes.  Tolerance soon builds though as dopamine is also released when something pleasurable and unexpected occurs.  Routine limits the release of dopamine, and as the cocaine user gets an expectation of the pleasure, the pleasure won’t be as intense as less dopamine is released with the similar action.

Interestingly, medications which boost dopamine can cause compulsive gambling. Parkinson’s disease results from a severe dopamine shortage caused by the death of dopamine-producing cells in mid-brain structures that are involved in bodily movement. Some Parkinson’s disease patients who received drug therapy to increase their dopamine levels developed gambling problems.  Soon after the drug therapy ceased, their gambling addiction also ended.

One patient, a 52-year-old who had only occasionally gambled before taking the Parkinson’s medication, became a compulsive player, losing $100,000 in casinos. A month after discontinuing the drug, his gambling stopped and his wife said she had her “old husband back.” Another patient who developed a compulsion to play poker machines said he saw a report on the strange side-effect of the medication on the Internet and had a “eureka!” moment. His desire to gamble vanished three days after he stopped taking the drug.

Operant Conditioning

I believe another factor at play when people become addicted to poker machines is a form of operant conditioning.

Operant conditioning is a type of learning that occurs through rewards and punishments for behaviour, where an association is made between behaviour and a consequence for that behaviour.

For example, a rat can be trained to push a button and get food as a reward, reinforcing the behaviour of pushing the button.  This is a Positive Reinforcement.

Now a rat in a cage will also learn very quickly that if the same portion of food is dispensed (say from a tube) each time the button is pushed, it can come back any time and push the button and the same amount of food will arrive.  In the meantime, the rat will sleep or go about its business without any stress worrying about its next meal.

An Intermittent Reinforcement is when the reward is given at random intervals, and/or the reward is a random amount.  It has been found that a participant is more likely to act when they only sometimes get what they wanted.  So when an action’s reward is unknown and not guaranteed, there is a greater response (no doubt related to the release of dopamine).

So if the rat in the cage pushes the button and starts getting random amounts of food at random intervals (not every time the button is pushed), it is going to be in a more agitated state as its next meal is not guaranteed.  The result?  The rat will keep pushing the button and waiting at the end of the tube for the food to arrive, as it no longer knows when it is coming or how much food there will be.  Does this action remind you of anything?  Why don’t they just get up and walk away…

If you push the rat one insidious step further and gave it a diminishing amount of food over time, say only 87% of what was delivered in the previous hour, what do you think would happen?

The rat would sit at the end of the tube and keep pushing the button until it starved to death.  And this is also the unfortunate fate of the poker machine player.

The poker machines pay out a random amount of money at random intervals, and this Intermittent Reinforcement of an action quickly leads to addiction.  And when you include the factor that poker machines only return 87% of what is invested over time, every addicted player will eventually go broke, starving to death while sitting at the machine and pushing the button.

Why do the people who are less well off tend to gamble the most?

I can’t answer this question definitively as it is a highly complex issue, but I can share a hypothetical scenario I used to present to my students when I was teaching at Swinburne University.  It was a simple proposal and it was always raised after the gambling lecture in the subject Popular Culture, when the students would inevitably want to discuss this very issue.

My proposition was that they could gamble their final grade on the flip of a coin.  They win and they get a high distinction, they lose and they get a fail.

After their initial shock and unsure laughter and then my promise that it was just a hypothetical and wouldn’t impact on their actual mark, there would always be at least one student in the class willing to risk a fail for the chance to win a high distinction.

The student would choose heads or tails and I would get another volunteer to flip the coin so there was no bias, and we would look at the result.  A win would often result in a fist pump and cheers, while a loss would be followed by a shrug of the shoulders and a, “I was going to be lucky to pass anyway” style comment.

The brighter students in the class would get my point straight away; that the ones most likely to gamble in this scenario were in fact the ones who had the least to lose.  It would be very unlikely that someone who is already heading for a distinction would risk that grade for a fail, undoing all their hard work and study on the flip of a coin.  But the same hypothetical is very enticing for a student who is looking at just a pass or a fail anyway, as they have just about nothing to lose in gambling their poor grade.

Now I understand that this analysis may be a fallacy when it comes to explaining why some people in the poorer demographics tend to gamble more than those in the richer areas, but I think for some people there would be a relationship between the respect you have for the money you’ve earned through time and hard work and the likelihood you would risk losing it all through gambling.

Casino Gambling

When you step into a casino to gamble it’s easy to be overwhelmed by the number of options in front of you. With rooms of pokies, card tables, dice games and spinning wheels it’s a good idea to find out how each game works before you play. Otherwise, you may find yourself losing more money than you imagined.

Each game has a house margin which is the overall percentage of money bet that is kept by the casino or house. Skilled players may be able to reduce the house margin slightly to be in their favour in games of skill, but in games of chance, the margin always remains the same.

Skill-based games are never an assurance of winning and the odds are always in favour of the house.  Just like the poker machines, this is how the casinos make their money.

BLACKJACK is a card game of chance and skill where players may improve their chance of winning by using a better strategy. After receiving two cards from the dealer, the player can choose to be dealt more cards so as to have a total score closer to 21 than the dealer’s total – without going over 21. Face (picture) cards count as 10, aces count as 1 or 11 and the cards 1 to 10 count as their face value. The house margin for Blackjack is generally less than 1% for skilled players.

CARIBBEAN STUD POKER is a game of chance and skill where an initial “ante” or “stake” is bet and players receive five cards face down. The dealer receives four cards face down and one face up. If a player thinks they can beat the dealer’s hand they must double their original bet. If they don’t think they can beat the hand, then they forfeit their original bet. The best poker hand between the player and the dealer wins. Jackpot bets are also available, but even with an allowance for the jackpot, the house margin is around 5.5 percent.

BACCARAT is a game of chance in which cards of 10 and below count as their face value, aces count as 1, and 10s and “face cards”, such as Queens and Kings count for 0. Two cards are dealt to each of the players and the banker with an optional third. The total of the hand’s value works by dropping the first digit (a hand totalling 15 would be counted as 5) the aim being to get a hand value closest to 9. Bets can be placed on the player’s or the banker’s hand, or on the hands being tied. The house margin for Baccarat is around 1.2 percent.

SIC BO is a dice game of chance in which three dice are rolled and players try to predict possible outcomes and totals of the dice rolls. Players can bet on the dice rolls amounting to particular totals, combinations of two dice, single numbers being rolled through to specific triple rolls. There are no betting strategies to reduce the margins of Sic Bo, depending on the bet placed the house margin remains between 2.8 and 16.2 percent.

ROULETTE wheels in Australia have 37 numbers on them, 18 red, 18 black and one zero. Double Zero Roulette has an additional zero to make 38 numbers. The wheel is spun and a small ball is sent spinning in the opposite direction. Bets can be placed on the ball landing on specific numbers or colours (red or black), on odd/even outcomes or on “low” or “high” numbers. The house margin is 2.7 percent for roulette and 5.26 percent for Double Zero Roulette.

PAI GOW is a chance-based game played with 32 tiles. 22 of these tiles form 11 Identical Pairs and the remaining 10 tiles form 5 mixed pairs. After the game has been dealt, each player and the Bank (house) needs to construct two separate hands with their four tiles called a Low Hand and a High Hand. The player’s hands and the Bank’s hands are then compared to determine who wins. Pai Gow has a house margin of 1.5 percent.

BIG WHEEL is a game of chance in which a wheel is divided into 52 compartments, each one showing one of seven different symbols. Players simply bet on a symbol and win if the wheel lands on that symbol. The house margin for Big Wheel remains consistently at 7.7 percent.

POKER at Crown Casino in Melbourne has become very popular since the dedicated room downstairs was started and the Aussie Millions is held there every year.  A lot of poker players believe they are playing the casino game where they have the most control over their fate, and that a good player can always make money.  In a pure cash game this may be the case, but at the casino there are some factors that make turning a consistent profit much more difficult.  With the hourly time charge and rake from every hand, the bottom line is that if players sat down with the same amount of money and no extra money was added to the table, the casino would end up with the majority of their money over time, with only one player having what was left.

As of 2012, Crown Casino in Melbourne takes the following rake per hand from the low limit cash game:

$1/$2 – 10% capped at $15 (plus $5/hour time charge)

Lottery Games

I’m not going to go into great detail about playing the lottery as it is a pure game of chance.  The following are some common Australian lotteries and the odds of your numbers actually coming up.

LOTTO draws are made on both state and national levels. 45 balls numbered 1 to 45 are combined and six balls are randomly selected to create the winning combination, with another two balls selected as the supplementary numbers. At least four games are played per Lotto card and your chance of choosing the six winning numbers and receiving the Division One prize with a single game is 1 in 8 145 060.

POWERBALL uses two machines each containing 45 balls numbered 1 to 45. Five balls are drawn at random from one machine, while one ball, the Powerball, is drawn from the second machine. You must play at least two games in a draw. Your chance of matching all five balls plus the Powerball is 1 in 54 979 155.

KENO is played in a registered venue such as a club, hotel or casino and consists of 80 numbers (1–80) where 20 numbers are drawn at random. On a $1 game players choose 10 or 15 numbers. If a player chooses between 7 – 10 numbers, a proportion of their bet is allocated to a jackpot. Your chance of winning the jackpot on the 10 number game is 1 in 8 911 711.

Beaner

References

http://www.gambleaware.vic.gov.au/know-odds/how-gambling-works

http://serendip.brynmawr.edu/bb/neuro/neuro05/web1/isiddiqui.html

http://www.addictscience.com/gambling/