I’m so unlucky!
The majority of Texas Hold’em games played today are of the No-Limit format, which differs from limit poker in that any bet at any time can be as big as a player wants (and has money to back it!). The implication of this is that every hand puts your entire chip stack at risk, meaning that there are many tactical variations from ‘correct’ limit play. More specifically it means that many hands which can be bet and raised for value in limit play need to be handled differently in no-limit play. An example would be where you hold top pair top kicker (TPTK) on a board with no flushes or straights. In limit poker you will almost always want to raise and re-raise in this situation, while in no-limit poker you may often have to fold if you (strongly) suspect you are beaten – i.e. your opponent holds two pair or a set.
In fact, a set is such a powerful hand in no-limit that many people base their entire strategy around ‘set-camping’, i.e. playing pocket pairs for any reasonable amount and hoping to flop a third card to match their pair. Many players find it very difficult to lay down hand like top pair top kicker or two pairs, and they will be in a world of pain if you flop your set. In such a scenario, the holder of the set will often ‘stack’ their opponent (i.e. win all their chips). It is a pretty nice feeling to play, for example, 55 to a small raise (say $2 on a 25c/50c table) and stack your opponent to the tune of $100 when his AK hits a board of AK5!
However, lets say your opponent held AA or KK (both consistent with his pre-flop raise) instead of AK. Now it is you who is in a world of pain, and your opponent who is licking his lips at somebody giving him such heavy action. Set against Set is one of the most profitable situations (for the higher set!) that occur in NL-hold’em. The lower set is playing for 1 out – the ‘case’ card to make 4 of a kind. The question is how you know you are up against a higher set? Well obviously if you have top set, you don’t have that worry, and if you have middle set, you are less worried than if you have bottom set.
However, even with bottom set, how can you be convinced that your opponent doesn’t just have TPTK, or top two pair or even a pair and big draw? Most top professionals and poker writers will shrug their shoulders and say that you can’t – this is just one of those situations where you have to put your chips in the middle and hope for the best – the logic being that you’ll win more than you’ll lose. Personally I’d agree with that advice too, as a general rule. There are times where you have to fold a set, e.g. you play TT to a pre-flop raise and the board comes QJT single-suited and two people go all-in front of you. There is just too much chance you are beaten to continue. However, in most cases, it is a terrible error to fold a set on the flop.
OK, so we know that we shouldn’t (in general) fold our set on the flop – but what happens when we run into a higher set? Simply, we lose our chips! It is one of the toughest beats you get, and it feels HORRIBLE! But how often can you expect this to happen to you? If it happens to you 5 times in 1 month, are you cursed, or is it just the way things happen? The answer of course will depend on how often you play, and prompted by some discussions at another forum, I decided to investigate.
The first thing to do is to make some (simplifying) assumptions about the problem. I assumed that I was playing at a 10-handed table, and that anyone with a pair would see the flop. Furthermore I neglected those rare times where one player flops a full house and another flops a poker. I was only considering those cases where two (or more) people made a set on the flop – some of these hands would already be behind in reality to flushes and straights, and some would lose on subsequent rounds.
To actually do the simulations I wrote some very simple code in Excel – essentially performing a Monte-Carlo simulation of a poker deal. The logic looks something like this:
- Shuffle cards
- Deal 10 pocket hands and a flop
- Check if I hold a pair
- If I do, then check if someone else holds a pair
- If they do, then check if I make a set on the flop
- If I do, check if anyone else makes a set
- If they do, check which one of us wins
- Repeat for a large number of hands
I ran 1 million simulations, i.e. 1,000,000 ‘deals’. Of those deals, I made a set (while someone else had a pocket pair) just over 2900 times. Of those 2900 times, I made the highest set just under 300 times and a lower set about 330 times. The reason for the slight difference is because some of the times where 2 people make a set on the flop, a third person also makes a set! You therefore make top set a little less than half the time where you are involved in a set over set confrontation. The above figures are approximate of course and will change slightly every time you run the simulation – however they are ‘reasonably accurate’ – i.e. I would be surprised if the ‘true chance’ was more than a few percent (of the above) different.
What this simulation is telling us is that if I play 1 million hands I can expect to be on the losing side of a set over set (on the flop) about 330 times, i.e. once in every 3000 hands. Playing online poker, one can expect about 60 hands per hour, so that equates to about 50 hours of gameplay! Obviously for someone who plays a lot of poker, especially where they multi-table, that is going to be far from irregular. Bear in mind too that this is the chance of one particular player losing in this scenario – the chances of seeing such a confrontation at a 10 handed table are obviously a multiple of this – i.e. something you should expect to see every couple of hours on average, at most.
Just goes to show – even the ‘most unlikely’ events can happen more often than you think. That’s poker!
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