The least understood concept in tournament poker

Let's imagine you have a rich clueless friend who doesn't understand probability. He shows up at your house every so often offering to flip a coin. If he wins, you give him 1K. If you win, he gives you 2K. Should you take the bet?

The answer is "usually".

Leaving aside moral considerations (like you may not want to take advantage of the poor sap), worries about him welching, or the coin being bent, or other red herrings, there is still sometimes a clear reason not to take this plus EV bet.

Imagine you have an even stupider richer friend who just rang you up and said he'd be round this evening to flip. Because he's stupider, he gives you 5K if you win. If the 1K you're flipping the first guy with is your last 1K, then you shoul turn down the first flip offer.

Why? Because if you lose, you'll be forced to turn down the even better plus EV offer of the second guy.

Here's the maths.

Half the time, you lose the first flip, and you're down 1K. EV -500.

Quarter of the time, you win the first, and lose the second, and you're up 1000. EV +250.

Quarter of the time, you win both to finish up 7K. EV +1750.

So overall this is a plus EV 1500 situation.

What if you reject the first one and accept the second?

Half the time, you lose, and you're down 1K. EV -500.
Half the time you win, and you're up 5K. EV +2500.

Overall this is a plus EV 2000 situation, and therefore preferable to taking both.

OK, so how does this apply to tournament poker? One thing I see a lot of good players (particularly good cash game players) say and do in tournaments is take on every single +cEV situation that presents itself, even the most marginal ones imaginable. This is always correct in cash games (subject to bankroll/variance considerations) but is clearly wrong in a tournament. Even at the start of a tournament, bubble factor is greater than 1, which means that taking a 50/50 when getting evens is mathematically incorrect. The deeper you go into a tournament, the higher bubble factor climbs, to the point that even if you think you're 2 to 1 against someone's range, it may be a mistake to call an allin getting evens.

But above and beyond that, there's a more practical reason for turning down marginal plus EV situations early in tournaments sometimes. If you believe that if you sit tight and wait patiently for long enough, you will almost certainly be presented with 60/40, 70/30 or 80/20 situations, then it's wrong to take even a 55/45. Because if you lose that 55/45, you're out, and won't get to avail of the better situations that would have presented themselves in the future. Furthermore, if you believe you have a massive skill edge, particularly post flop, then you may be missing out on future situations where you're 100% when the money goes in.

A lot of the skill of tournament poker is not just accurately assessing the likely odds compared to those offered by the pot but also intuitively sensing how fast you need to play due to structure and stack size in different tournament situations. In essence, knowing whether you need to be seizing every available +cEV situation (as, for example, when you're short stacked short handed nowhere near any level bubble) or whether you shoul be sitting there rejecting marginally +cEv deals as you patiently wait for much bigger ones.

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