[fnurt]

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My head hurts. I don't get your math here. [img]/images/graemlins/confused.gif[/img]

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Thus, the total of all the outcomes is (10% * 435) + (30% * 74) + (40% * 20) + (10% * 3), which comes out to exactly 74. Sometimes, rounding error may cause a slight difference to appear.

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For example why is 10% * 435 used instead of 10% * 535, since $535 is the cash equivalent of buying into step 3? How did you calculate the whole thing, start from the buttom and work up? Please clue me in.

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$435 is the correct number because it's the actual value of the buy-in that matters, not the displayed value. For example, the value of a free entry into a $500+100 event and a $500+200 event are exactly the same - either way your EV is $500. This is the phenomenon that makes many of these tournaments bad investments - not only do they take a rake up front, but a big chunk of the prize pool is already earmarked for the purpose of paying rake into your next tournament.

You're right that it's a circular result - the only reason I know the value is $435 is because I've done the math and found it to be $435. That's where algebra comes in; I expressed the EV of each step in terms of an equation, and then solved them all. For example, for Step Higher, you can easily calculate the EV for Steps 4 and 5. You can then express the EV for Steps 1-3 as X, Y, and Z, respectively, and create equations like Y = (10% * X) + (30% * Y) + (40% * Z) + (10% * 3). This is the exact same equation I used in my original post.

Once you have 3 equations using 3 variables, solving them for a numerical result is just basic algebra - by which I mean I probably would have been a lot faster at it 20 years ago!