Why I Don’t Play The Lottery: The Winning Paradox

Good news: there is a sure-fire way to win the lottery.

Bad news: you will need to have £14m available.

To win the National Lottery here in the UK, you need to match 6 numbers from the draw of a possible 49.

There are about 14 million 6-number combinations between 1 and 49. At £1 per selection, and given that National Lottery organisers Camelot don’t do bulk-buy discounts, you’ll be looking at a £14m outlay, to guarantee yourself a £5m jackpot (give or take).

And of course, if someone else is lucky enough to have also picked the winning numbers, your jackpot is halved.

The Winning Paradox

This is what I call the Winning Paradox. Spending £14m to win £5m is clearly not a profitable approach.

Anyone who thinks about this for more than half-a-second can recognise that it is not a viable strategy. The upside does not get close to matching the downside.

In other words: even when you win, you lose. £5million in returns has cost you £14million in outlay. Ouch.

Winner winner!

Winner winner!

Poker Players and Sports Bettors Beware

Yet poker players and sports bettors fall for the Winning Paradox time after time.  They chase draws without the correct odds, or back short-priced favourites at the bookies even when the risk/reward ratio is terrible.

The problem with this strategy lies in those two simple words that unfortunately a lot of the gambling community forget to consider: risk and reward.

Unfortunately, it is all-too-easy to lose your discipline. Backing short-odds favourites may lead to a lot of small wins, but that is of little use when the big loss comes in that wipes out all of your profits – and then some. The Winning Paradox in all its glory.

Or picture the poker player who can’t resist chasing gutshots when they are being offered 3:1 – even though the ‘correct’ odds for making this loose play are around 10:1.

Feedback Loop

Admittedly, the waters are muddied because, in poker and in sports betting, the feedback loop is misleading. It feels good when you win the hand (or the bet), so it is perfectly normal to attempt to replicate the success.

And because you are playing every hand and placing every bet in a batch of one (rather than in a batch of 14 million, as with the lottery example), the downside can be camouflaged. This is why discipline is the key.

When placing a wager or considering a call in poker, it is imperative that you ask yourself one simple question:

Is the juice worth the squeeze?



Do you always ensure that you are getting good value for your investment when playing poker or sports betting? Let me know in the comments, add me on Skype (search ‘casy151’), or follow me on Twitter.

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Are You Too Quick To Give Your Poker Coach Credit?

Beware of falsely attributing an upturn in your poker results to a good coach. This one can be extremely tricky, so you have to be on your guard. Here’s a scenario for you:

Mike is a long-term winning reg in the mid-stakes 6-max Sit N Gos. However, in the last couple of months he has been losing a chunk in his normal games, and he is worried that the other regs have figured him out.

On the recommendation of another reg, he contacts a coach to see what can be done to end his slump.

Sure enough, after five expensive coaching sessions, Mike’s results start to improve. Before long, Mike is back to his old win-rate, beating his normal games at a decent clip.

The coaching worked!

Or did it?

The Poker Coaching Conundrum

As a coach, I can assure you that most players seek out my services when they are suffering a bad run of form. They think that it must be addressed urgently, and hiring a coach must be the most efficient way of getting back to form.

I am always very wary of accepting coaching applications from such players. Indeed, I reject a lot more of them than I accept.

The reason is simple – it is immoral for me to take credit for aiding these players’ recoveries. 90% of the time, what they experience is a simple case of regression to the mean.

Poker’s Regression Obsession

Regression to the mean is when things naturally settle back towards their ‘true’ level over time. For example – in poker, an average player who binked a massive tournament win was almost certainly extremely lucky, rather than someone who had developed poker genius overnight.

Before long, they will dribble some of their money back to the poker community as the luck wears off and their typical skill level emerges.

When a football team sacks their manager, it is usually because they have been under-performing relative to their normal standard. The new boss gets appointed, and lo and behold, results start to improve. Miraculous!

Well, not really.

The reality is that the team were likely going through a run of bad luck and fragile confidence – a temporary blip that would rectify itself naturally in time.

Do you see where this is going?

Let’s get back to Mike

Mike’s poor recent run was overwhelmingly likely to correct itself over time – assuming, of course, that the bad luck would not provoke bad decision-making.

The real solution to Mike’s sticky situation is to simply keep doing what he does best: grinding away, until variance rights itself and he regresses towards his typical, impressive level.


So how best do we avoid getting into this sticky situation?

I always encourage my students to strengthen from a position of strength. That means that they should look to work hardest on their poker homework when things are going well for them. It is during such times that their thinking is at its clearest, and my students are at their most responsive to new ideas.

If they wait until something goes wrong (ie. a downswing) before attempting to appraise their game, then their outlook will be cloudy. They will be tempted to attempt root-and-branch, reactionary surgery when a few tweaks were all that was needed.

My advice to Mike

In future, look to engage the services of a coach when things are going well. Don’t fall into the trap of bolting the barn door after the horse has departed. When things are going badly, it is not the time to clutter up your mind with new concepts and it is very difficult to objectively appraise your game.

And most of all, don’t assume that the upturn in results was down to the genius of the expensive coach! In all probability, in a swingy game like poker, it was a simple case of regression to the mean.

A good coach will be able to say no to applicants who are suffering a temporary blip – or at least, they must be willing to hold their hands up and say that they had little to do with the sudden upswing in the student’s results!


What do you think – are you too quick to seek out coaching when you hit a downswing?  Are you the sort of person who wants to pat the coach on the back when you should really be applauding yourself? And most of all, do you truly understand the nature of variance and its sister – regression to the mean?

Let me know in the comments, or drop me a message on Twitter or Skype (just add me – ‘casy151’)


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Do You Have This Costly Leak? Introducing the Diamond Star Effect

I was coaching an excellent player this morning, when an interesting scenario arose. We were reviewing a Sit N Go that he had played, in which he reached Heads-Up against a guy who is generally considered the best player in those games.

A particularly strange hand saw villain take an extremely non-standard line, which left my student flummoxed.

What was his thought process? I encouraged my student to talk the hand out from the start. Several different possible reasons for villain’s strange decision-making in the hand were discussed. None seemed credible.

‘Why did he decide to make that move?’ asked my student, obsessed with unravelling the truth: ‘he must have had a reason’.

Here’s the thing. Villain did have a reason. It’s just that the reason was not what my student anticipated.

Villain screwed up.

Nothing simpler, nothing more complicated. He misplayed the hand. He lost track of where he was, of the flow of the hand – a side-effect of multi-tabling. His move made no logical sense, because there was no logic to it.

My student had made the cardinal error of associating villain’s undoubted technical quality with infallibility. Of considering an elite SNG player to be superhuman and incapable of error. His reason was understandable, if misguided.

To understand this, you must appreciate that villain is something of a legend in the low-midstakes games; a regular leaderboard-topper, who plays more tables with a better winrate than anyone at those stakes.

The Halo Effect is when a Person A’s judgment of Person B’s character is skewed by their overall impression of Person B. For example, it is common for us to think a movie star a cool person because of a role that they played. Or that a politician is a good decision maker because they dress well and have a strong physical presence.

This was its poker equivalent: the Diamond Star effect.

On Sharkscope, Diamond Stars denote the top players at each limit. Villain possesses several Diamond Stars. However, that does not mean that he makes the optimal decision at all times.

It takes him a few days to play one thousand games; errors are guaranteed. My student gave too much respect to villain’s reputation, and attributed merit where none was due.

We see this in football. In Scotland, Celtic rarely get beat at home, regardless of how poorly they play. They have a bigger budget and better players; however, this is not the sole reason for their imperious home form. Their apparent invincibility is a daily topic in the red-tops and on the sports shows. Players at ‘lesser’ clubs are treated as irrelevant by the media, whereas Celtic’s players are rated as demi-Gods. When they take to the turf, the visitors afford their exalted opponents too much respect, and might as well be 1-0 down by kick-off.

Deference does not win battles. Opposition that you consider to be of superior ability can be overcome by playing them, not their reputation. If you are a profitable, hard-working player, then you must trust your decision-making and problem-solving skills, regardless of your opponent.

Sure, the best players make fewer mistakes than most; however, you can be absolutely certain that these do occur on occasion.

So if it looks like a mistake, and it smells like a mistake, then it probably is a mistake. The esteem in which my student held his opponent determined his reaction, despite the evidence that suggested that villain simply misplayed the hand.

How often do you fall into the trap of thinking that excellent players always play every hand optimally? I know that I have made this mistake before, and I would bet that I will make similar errors in logic in the future. However, the first step towards eliminating a leak is to recognise it.

Christy Keenan is a poker coach, writer, and player. He has a Master’s Degree in Sport Psychology, and specialises in decision-making in competition.

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The Strategy of 18-Man SNGs (pt 2)

18 Man Strategy – Part Two

Last month we took a look at the early game strategy of 18-man Sit N Gos. With a very limited amount of time until the push-or-pass blind levels come into effect (BB 100 and higher), there is an onus on the good players at the table to accumulate chips in the early stages.

As such, starting hand requirements can be lowered if there is reason to believe that Hero’s post-flop edge will counterbalance his hand’s weakness. In other words, the cards matter less than position when facing a fish. With the bubble factor being so low (the further from the bubble, the lower the bubble factor), then risks can and must be taken in order to give yourself a competitive stack at the endgame.

Guess what the biggest mistake commonly made at the final table is? I’ll give you a clue: it’s exactly the same as the biggest mistake commonly made in the early game. That’s right; forget what you think you know – tight is WRONG!

Most players instinctively nit up when short or medium-stacked as the bubble approaches. Their logic, which runs along the lines of ‘I’ve invested too much time and concentration in this tournament in order to bust without any cash’ is fundamentally flawed. I’m going to show you the numbers in order to explain why.

Let’s take an 18-man SNG on Pokerstars. Entry costs $13.89 + $1.11, with prizes of $100, $75, $50 and $25 for the top four finishers. A lot of novice/intermediate players make the mistake of looking at the prizepool and deducing that a first-place finish is 4x as valuable as finishing fourth. However, this is not the case.

Let’s compare them when deducting the entry fee: $100 minus the $15 entry plus rake = $85 profit. $25 for fourth places equates to a measly $10 profit once the same $15 is subtracted. Put simply, one first-place finish is worth a monstrous eight-and-a-half fourth-place finishes!

So how does this relate to optimal bubble strategy? Well, in short, you should do everything within your power to ensure that you grow your stack on the bubble, rather than folding your way to a puny cash. The bubble must be treated like it’s an old friend; you have been here before and know how to cope with its idiosyncrasies.

Too many players fear the bubble and risk-aversion takes over. Of course, I’m not advocating ‘any-two-will-do’ recklessness; however, it is absolutely vital to identify the players who are only interested in locking up a cash and then you must bully them mercilessly.

Remember that, when the bubble period commences, the blinds are normally monstrous and the presence of antes are a double-whammy. Any opportunity to steal and propel yourself towards the chip-lead must be grasped with both hands.

Remember the maxim of Sit N Gos: shove wide, call tight. Fold equity is absolutely crucial; calling an all-in shove involves paying an enormous ICM tax unless the caller has a monster stack, so it is imperative to put your opponents to a tough decision.

The vast majority of the time, all but the LAGgiest of villains will err on the side of caution. Let’s take a look at two examples from a tournament recently played by one of my students:


In the early stages, risks should be taken in order to grow your chipstack and apply pressure on your opponents. Here, Luis has a tough decision when faced with a mini 3-bet. Reasoning that a higher pocket pair would probably 3-bet larger in order to juice the pot pre-flop, he decides to 4-bet all-in with Jacks for value. Villain’s call with pocket fives is consistent with the loose/passive play commonly found in lower stakes tournaments. However, that’s not Luis’s concern and he is happy to gain a full double-up with his Jacks. Now he is handily positioned to start pressurising the rest of the table.


Luis has successfully built upon his early double-up and approaches the critical bubble passage with a commanding chip-lead. He puts his chips to full effect by whaling on his opponents, making a number of loose open-shoves safe in the knowledge that, with such enormous ICM implications, his opponents will be (correctly) calling very tight. On the bubble, he picks up the 725 in blinds and antes four times in six hands, positioning himself handily to take down the whole tournament, rather than being content in waiting out the bursting of the bubble.

Luis ended up taking down this particular Sit N Go, and in reviewing his tournament afterwards I was proud to see the number of occasions in which he didn’t allow his terrible cards to dictate his decision-making. Recognising a good shove spot has little to do with your actual holding, and has everything to do with your fold equity. Weak players wait for others to do the dirty work in popping the bubble for them. Good players, however, see the bubble for what it truly is: an opportunity to set oneself up for winning the tournament.

SIDEBAR: Folding Can be OK!

Of course, we can’t always be reaching for the stars. Sometimes we will be in the gutter, short-stacked and scrapping to secure a min-cash. This is the nature of the Sit N Go; you can’t win them all, but you can do everything in your power to make the optimal play at any given moment.

When you are micro-stacked and your tournament EV is low, it can be strategically sound to attempt to fold your way into the money. Any return on your investment is an achievement in itself, but it is criminal to fold away into a position where you are rapidly blinding out. In Sit N Gos, fold equity is everything; preserving it by making some light shoves has to be done on occasion. And remember, you’re allowed to suck out sometimes too!

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The Strategy of 18-Man SNGs (pt 1)

***Here is a 2-part article I wrote last year for Poker: The Magazine ***


18man Sit N Gos are hugely profitable for two main reasons: with more entrants than their 9man or 6max counterparts and fewer regs, there is obviously more likelihood of finding a soft game. When this simple truth is coupled with the fact that there are some pretty basic flaws in the accepted optimal strategy, it is not difficult to see why the best regs at even the lowest stakes are making some serious coin.

In 6max SNGs, with two players getting paid and a pretty chunky payout structure of 65% for first place, 35% for second, each player’s tournament life is extremely valuable. Even in level one, with one-third of the entrants reaching the money, the bubble is not far away. Let’s contrast this with the payout structure of an 18man SNG:

Firstly, the payout is more gradual With four players making the money, it goes up incrementally from 10% of the prize pool for fourth place to 40% for first place. At no stage is there a payout leap as great as with a 6max or 9man money bubble. As such, locking up a min-cash (or, conversely, being the bubble boy) is not as significant in terms of prize pool equity as in one-table SNGs.

Of course, in actual dollar terms, the larger the field, the bigger the prizepool. Therefore, making the money consistently is fundamental to your bottom line. However, with only 22% of the field cashing in an 18man SNG and a larger proportion of weak opponents, the best regs will be on the front foot from the first level.

I advocate taking risks in the early stages, with the intention of building a formidable stack right from the start. The positive impact of this is three-fold. Firstly, achieving an early double-up affords you a comfortable buffer from elimination.

If you have your opponents out-chipped, then you cannot be eliminated in a single hand. Your opponent’s tournament life is at risk every time he plays a pot with you, but yours is not. As such, you generate more fold equity against those who fear being KOd.

Secondly, as mentioned, it is vital that you claim the weak players’ chips before your tough opponents do. Simply put, the best regs have a higher expectation in the tournament than the fish.

They will, on average, reach the end-game more frequently. If your opponent is a big donator in the games, then his chips are up for grabs. He will enter too many pots, play too passively, and spew off chips postflop with hands like Top Pair, Mediocre Kicker.

Of course, the only way to truly exploit his postflop deficiencies is to get into pots with him. Look to isolate his open-limps, and play liberally when in position. There is a difference between widening your range in order to exploit a weak opponent, and sheer recklessness.

You will have to have some deft post-flop manoeuvres in your arsenal, but the only way to develop a feel for this is by immersing yourself in post-flop decision-making. Remember that the deeper-stacked you are post-flop, the more pronounced your edge will be. This is because there is an increased likelihood that your opponent will have to make decisions on all three streets. More decision-making for your opponent = more potential mistakes for him to make. More mistakes from him = more money for you!

The third compelling reason why you should be inclined to take risks in the early stages is that accumulating a big stack will not just prevent your tough opponents from doing so, it will allow you to whale on them.

You will be able to wield your big stack; the good regs will know that their expectation in the tournament is high, and will be disinclined to tangle with another good player who has them out-chipped.

Their blinds will become ripe for your plundering, and their raises prime opportunities to re-steal. So not only will you accumulated a healthy stack to take into the end-game, but you will also be constantly increasing the disparity between yourself and the other good players by nicking away at their chips.

In summary; it is my opinion that too many good players approach the early stages of an 18man SNG with chip conservation, rather than chip accumulation, on their mind. They simply want to reach the push-heavy middle stages with a playable stack in order to exploit the holes in the fishes’ shoving habits. The flaw in this theory is that there is no guarantee that the soft money in the field will still be in their possession! If a good opponent gets to the weak player’s chips before you do, then you can guarantee that you will have a far trickier mission claiming those chips from him. His mistakes will be fewer and further between, and he will be able to whale on you with impunity. So don’t be afraid to get involved in some marginal spots in the early stages with spewy opponents. You do not have an infinite window to lay claim to their stacks, so you might as well get cracking right from the start.

SIDEBAR: The following hand demonstrates the need to trust your reads on a loose, aggressive opponent. Seeing that he has somewhat fishy stats, I elect to isolate in position holding AQ. The dry flop hits a part of his limp-call range (which I would anticipate to be 22-TT, A2s-AJo, and some general Broadway-type combinations such as J10, KQ etc), but there is no reason to do anything other than fire out a continuation bet, which Villain calls.

When he check-raises the turn, it would be easy to fold in the face of his apparent strength; after all, he is repping AJ, JJ or 3-X for flopped trips and my AQ would be very close to drawing dead. However, his stats indicate that he folds to continuation bets only 50% of the time. Therefore, I am happy to call his bluff and take it to showdown on the river, safe in the knowledge that I’m very unlikely to get called by worse and so I have received maximum value for my one-pair hand.

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Poker: The Magazine Out Now on Tablets

Hi folks,

The first edition of Poker: The Magazine is out now.  It is a tablet-based, fully-interactive free mag that features several articles and a short coaching video from yours truly.  If you have a tablet, download it from this link.

I will be a monthly contributor, so keep your eyes peeled for lots of strategy advice and commentary on the poker issues of the day.