Last week, the ABC set to bashing bet365, bringing to light some of the huge betting company’s unsavoury practices. To which we respond, “Well done”. And, “Well, duh”.

The ABC noted a number of dodgy tactics employed by bet365, writing it all up as astonishing revelation. Perhaps the ABC reporters and their cloistered readers were astonished, but many Australian gamblers would have simply yawned. *All* gambling companies employ similar tactics and they’ve always done it. It is not new and it is not news. It is all part of the standard super-rigging of gambling.

To begin, it is no secret that gambling is rigged; even bad gamblers know that the odds are stacked against them. Mathematically, the rigging of a game is expressed in terms of *expectation*. In a fair game the average or “expected” win is zero. For example, flipping a coin in the natural win-lose manner is fair. By comparison, roulette has 37 possible outcomes but the payouts are calculated as if there were only 36 numbers. (The payout is “even money” if you bet on “red” or “black”, and the payout is “35 to 1” if you bet on a number.) This implies that the average loss per spin on roulette is 1/37 of the amount bet, or an expectation of about -3%. The expectation being negative indicates the rigging.

Given that gambling institutions intend to offer only rigged, negative expectation games, what can punters do about it? Lots, and not much. They can cheat, of course. Or, they can be become experts on horses or golfers or whatever. Or, they can look for mechanical or human flaws. There’s a surprising number of avenues to explore as well as, of course, many dead ends. (To illustrate the subtlety, we’ve included a few gambling puzzles at the end of the post.) Finding and exploiting opportunities, however, takes work and/or sophistication and/or capital. There’s lunch there, but it’s not free.

So, as a general rule, punters are left with only losing games to play. But how, then, does a gambling site entice a punter to play a game of negative expectation?

Yes, it’s a stupid question. Obviously there’s no shortage of punters willing to bet on appallingly bad games. But, if you run a gambling site, the real question is how to get the punter to gamble on *your *site. And that’s where one form of super-rigging begins. Super-rigging is making a betting opportunity appear better than it is. This is built in to the way poker machines work, and betting sites do it as a matter of routine.

In betting, top sites have various ways of enticing punters. To begin, there are sign-up bonuses. So, for example, you might sign up with a $200 deposit and the site will throw in $100 of “free bets”. That’s akin to signing up for ten sessions at a gym and getting a few “free” lessons chucked in. It’s basically fine, with what you see being pretty much what you get. After that, however, there are innumerable betting “promotions”, many blasting out from the TV and destroying everyone’s enjoyment of the footy. (Unless you’re a Saints fan, in which case any distraction from the actual game is considered a plus.)

The effect of gambling promotions is to change the expectation of the bets. For example, a very common offer is “money back” if the punter bets on a horse and that horse comes 2nd or 3rd. (That “money back” is most commonly in the form of a “free bet” equal to the size of the original wager, which is an important distinction but one we can ignore here.) Then, given a good horse may have, say, a 30% chance of coming 2nd or 3rd, an expectation of about -10% may become an expectation of about +20%. There’s no guarantee of winning on that race, of course, but it’s now a sensible bet. These promotions are obviously attractive to punters.

How do the betting sites avoid losing a ton of money on these promotions? Often they don’t have to do much of anything. To begin, most promotions will come with a relatively small maximum bet size, of $50 or so; this is fair enough, just the same as Coles limiting some sale item to “five per customer”. Beyond that, the promotion can be pretty much what it appears to be, in itself a loser for the company but good advertising to get the punters onto the site to bet further. But there are also traps and nasty tricks.

First of all, betting promotions vary dramatically in value, with more than a few being close to worthless. They can be analogous to Motor Heaven blaring that a car is “50% off”, after having doubled the price the previous week. Secondly, even valuable promotions can be used poorly. The horse promotion above, for example, would be essentially worthless if used to bet on a massive favourite or a sluggish also-ran. Again, one might compare this to a commercial situation, say Harvey Norman giving $10 off on any one item in the store and someone using that offer when buying an overpriced TV.

Amidst all the noise, however, there are many good promotions that can create positive expectation on small bets when used intelligently. So, what happens then? Then what happens is what the ABC story is all about.

The gambling sites simply nobble any punter who is not a loser, in any manner they can: they will refuse to offer the promotions; they will limit the size of bets to approximately zero; they will lower the odds. What does that leave? It leaves the betting sites screaming out their offers, everywhere. But, any gambler who is halfway successful is banned from their offers, if not entirely.

And that is the super-rigging. The betting sites pretend they are offering positive expectation, but they will only continue that offer for people who use the offer in a useless manner. And, unlike the other aspects we have mentioned, such nasty practice has no commercial analogy that anyone would regard as acceptable. Imagine going into Harvey Norman and being shoved out the door, with some thug yelling “You only buy items on special, so we don’t want you here”. It is unthinkable at Harvey Norman but, in the context of gambling, it is universal.

How can the betting sites get away with this nastiness? Because the ACCC, the federal body responsible for overseeing and enforcing consumer law, is all bark and no bite. And, because the state governments and government regulators only care about whether they’re getting their cut of the loot.

It is obscene. And, as we indicated, none of it is news.

**PUZZLES**

Here are three gambling puzzles. If you are familiar with the puzzles and are sure you already know the answers, then please refrain from commenting for a while, leaving others free to think about them.

**Puzzle 1.** You are gambling on roulette, which has 18 red numbers, 18 black numbers and 1 green number (the zero). You watch the wheel spin and the ball lands on a red number. What colour should you bet on next, red or black? Or, doesn’t it matter?

**Puzzle 2. **A casino gives you a free bet of $10. You can place the bet on any standard casino game, or on a horse, or whatever. If the bet wins, you get your winnings as usual. (For example, if you bet “red” on roulette and win, you’d win $10.) Win or lose, the casino keeps the coupon. How much is the free bet worth?

**Puzzle 3. **You have found a betting game with positive expectation; it’s win-lose (like betting on “red” or “black” in roulette), but you have a 55% chance of winning and only a 45% chance of losing. You start with $1000 and hope to double your money. What is the probability that you will succeed before losing your $1000?

Just on the point about the ten dollars off on the Harvery Norman item, there’s a Vsauce video where he says it doesn’t matter whether you get ten bucks off on a million dollar item or an eleven dollar item, it’s still ten bucks either way. Or is your point that the TV is “overpriced” and there’s a cheaper alternative for the same TV elsewhere? Here’s the clip from the video: https://youtu.be/Pxb5lSPLy9c?t=263.

Thanks, Craig. Interesting video, and Vsauce is wrong.

Yes, I included “overpriced” to try to make the point clearer, and it actually corresponds to the real world of gambling. The “prices” (i.e. odds) that gambling sites offer can vary dramatically, and are often super-ripoffs. But the point holds even without including “overpriced”.

This example offers a very good illustration of thinking about how real-world gambling (and shopping) works, and why cartoon versions in the classroom usually miss the mark. (Maybe we need more teaching of numeracy …) Think about what you would do with the $10 offer. How would you actually use it, if at all? Why? People’s intuition is more accurate than Vsauce’s cleverness.

Having not used any betting sites, I’m a little confused as to what happens in Puzzle #2. Isn’t it the case that, when you normally bet on roulette and win, that you pay $10 to bet and get $20 back? If so, why do we win only $10 when we win with the free bet in this scenario?

Thanks, eddie, and a good question. Yes, if you bet a normal $10 casino chip on “red” on roulette and it wins then you get back $10 + $10 = $20. If you play a number and it wins, you get back $10 + (35 x $10) = $360.

However, it’s pretty standard in gambling to distinguishing between the stake (the amount of your bet) and the wager (the event of betting). That’s reflected in the “35 to 1” language of roulette odds, with the 1 representing the wager and the 35 representing the potential winnings from that wager. So, the gambling sites would say that “free bet” means they’re only giving you the bet/wager, not also the stake.

Hi punters ,

The worse odds I’ve seen for a roulette wheel with 37 possibilities was 18 to 1 for a specific number on a ferry between New Haven UK and Dieppe France in the last millennium . Because you only gamble on board outside of any country the company could set any odds they liked.

Surprisingly some people were still playing

Steve R

Hi puzzlers,

The sample above is good and no doubt most have seen the Monty Hall problem but my

favourite is the 100 Red hat Blue hat collaboration problem supposedly used by Google amongst others to test their applicants.

https://www.independent.co.uk/news/science/can-you-solve-the-100-hat-riddle-set-by-google-in-job-interviews-a6886326.html

Steve R

Opinions on your questions:

It doesn’t matter but if I had to make a bet I would bet on red, just in case there was something funny with the wheel and it had a bias for red over black (no idea why this would happen in a modern casino, but there was a historical case of a group of Mexicans observing roulette wheel bias in Las Vegas many years ago and making quite a good return…)

If you only have one token, swap it with someone for a free drink. Otherwise, take 0 or any of the single numbers 1 to 36; the expected value is better than choosing red or black. The actual value is then 10*35/37 or about $9.46 (rough calculation), still a loss though.

depends on your betting strategy. If you bet the entire stake at once, the calculation is simple enough, but if you divide it into smaller bets (as some of the online gambling sites allow…) then I need more time to work it through and so will leave for someone else.

Well, RF, you’ve been to the talk. But mostly correct.

Plural. I’ve seen you a few times (and watched the vidoes). And read the Age articles. I still think there is money to be made in sports betting with a bit of Mathematics (and the right market) but otherwise entirely agree.

Marti,

My 2 cents on the hypothetical 3rd puzzle given p > 0.5 and ignoring minimum and maximum bets on an even money winning payout then chance of eventually doubling your cash would be 100%.

I think the way to maximise your accumulation of winnings would be to invest a fraction of (p-q) of your remaining cash at each bet. So with p = 0.55 this fraction would be 10%.

What do you think of the St Petersberg Paradox?

https://en.m.wikipedia.org/wiki/St._Petersburg_paradox

Steve R

Thanks, Steve. The (as close as you like to) 100% is spot-on, and the p – q gives the sophisticated approach to getting there. Is that knowledge of gambling, or probability? As for the St Petersburg thing, yes it’s fun weirdness, though not really a paradox.

Marti,

The St Peterburg paradox is interesting to me because most people wouldn’t pay $25 to play even though the theoretical payout is infinite …probably due to the perceived risk of default by the bank?

My interest in statistics and probability is inherited from my grandfather who was a physicist and strong bridge player . So I spent a couple of years studying actuarial mathematics working for a derivatives trading firm a while ago . As you know options etc are a zero sum game with many trading and insurance strategies which these days are usually run by competing algorithms .

Steve R

Thanks, Steve. Of course, the mathematical point is the proper definition of expectation in such infinite contexts. And the practical gambling point is that mathematics only gets you so far.

I’m curious about your grandfather. My great uncle was Charlie Goren, but I inherited absolutely none of his bridge-playing ability.

Marti,

I didn’t inherit my grandfather’s bridge skills either but it is a fun game at all levels where probability,inference and the occasional psyche will help you score well. I’m sure your ability to keep accurate count of a six deck blackjack game might have some recessive genes from Charlle G to thank. It’s not everybody who has a bridge playing convention named after them

My grandfather used to compete against Reece and other national players in the 60s when he retired with occasional success.

Steve R

Card counting is much, much easier than non-counters realise.

Theoretical payout… there was an article a few years ago on this in one of MAVs journals (I think it was ASMJ) and the interesting case was studied if one had the entire world’s GDP, a googol of US dollars and the like, where the “theoretical payout” becomes much more sobering.

Can’t find the journal in my bookshelf, so may be pre-2014.

Thanks, RF. it is interesting that so few teacher-aimed materials get to the heart of real-world gambling.

RF,

in the Petersberg lottery link above they use a ln utility curve rather than the theoretical expectation meaning a millionaire would be willing pay up to 2 plus a source of credit would max out at $3.35

Steve R

I doubt ASMJ is read by many teachers. Just the 10-20% who are not OOFT (which I know is something of a bug-bear of yours…)

No, but it is reflective of the materials teachers do see.