Some interesting thoughts byron.
Ok so let's clarify the maths.
To think mathematically is indeed to hold the opinion....
to focus on the math is to make an accurate appraisal of the situation, and then apply mathematical concepts to try and figure out the best way to play a situation.
But essentially the basis of this thought process is...Example - "Do I have the correct odds to draw to my flush?"
The mathematical equation for making this decision is simply deciphering how many outs you have and whether the probability of hitting one of those cards is compensated for by the odds the pot is offering. To be aware of the figures (but to choose not to allow them to entirely dominate your thoughts) and simple ignorance of them are two different things altogether. To suggest otherwise is being silly. The problem is that a mathematical equation is not situational or contextual it is a constant. So once you understand that tournament play is purely situational you will begin to appreciate that trying to fit a constant into every contextual decision is actually quite restrictive.
To produce an equation based on pure probability is too simplistic for tournament play. This is so because the maths doesn't take into account so many of the factors that need to be considered before making a decision as to the best way to play in a particular situation.
Time, stack-size in relation to the blinds/average/leader, opponent's behaviour/actions, position to the money, current table image/future table image, situation etc...are all variable factors nowhere to be seen in the ever constant probability equation. So I think being driven by the maths is more "guessing" at what to do because you are only taking one factor into account. To be aware of the maths and to also take every other detail into account is a far more comprehensive way of coming to a sound decision. Maths is not flexible...but you need flexibility of thought when you play a tournament. Making a decision at any point has many implications...those implications are not just about whether you answered the sum correctly or not here and now.
Getting lucky is another factor that has no place in this equation. But the fact is you do need to get lucky to win a tournament. This does not mean you see the sense in relying on luck again and again and again but that you simply recognise luck is a factor. Again, recognising something and being driven by it are different. To suggest otherwise is being silly.
If you play a solid game, then you recognise a situation to step to outside the maths and your position improves dramatically you are actually playing creatively. And creativity is essential to tournament progress. Focussing on maths can stifle your creativity because of it's inflexibility and you may miss situations you can exploit.
I think having a mathematically dominated strategy you become a bit one dimensional and this can make your mind inflexible to considering the more creative thoughts that can often be necessary if not wholly desirable in any given tournament situation.
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