Lets suppose there are 2 types of tournaments, and we have played 100 of each, both have a buy-in of 1$. In 'game A' we have EV of ROI 130, and in 'game B' we are expected to get ROI 90.

After playing 100 games of both, in 'game A' we have result of winning 170$ (70$ profit) In 'game B' we have won only 20$ (80$ deficit) Comparing to expectations A= +40$ above ROI, B=70$ below ROI.

Here is the question: If you can now play exactly 10 games of only the game you choose before moving to new town, which game do you play?

This could evolve to discussion of psychology as well.

Surely nobody picks the worse game on a poker forum. Come on.

So you're asking if people would play the better game where they've done better or the worse game where they've done worse? Not to be rude, but are you ******ed?

Maybe OP is employing a form of Gambler's Fallacy, meaning he will win more with B to get back to the 90 ROI. That's nonsense of course.

I've seen strawmen like this before. This is - I believe - exactly what is being suggested.

Lets cut the bs (i mean by bs either gambler's fallacy https://en.wikipedia.org/wiki/Gambler's_fallacy " its due" or just mocking it and moving on lol) and make the thread interesting if possible to learn something.

What if in fact there could be a reason to choose the "worse" provided both where winning events but the second had a more consistent results distribution and the first was rather less consistent but included a big final table win to put it significantly above the other.

Surely there may be a point where an argument can be made for going for the lowest historical return avg tournament (assuming they are not the same for some other reason ie different place and it wasnt a stupid discussion about 1$ events lol but something more substantial and it remained same in performance so ok it may not even be a poker case but something else) if you think the first one is involving an outlier result and the remaining samples dont look all that great in comparison to the other one.

The question is at which point and under what mathematical arguments if you have 2 samples of equal populations in each do you go for the inferior avg event if at all.

Lets say we know the distributions both have to obey but not the parameters.

We can discuss examples that this makes sense.

My example was not able to make clear point: So based on this discussion I'll improve it.

500$ HU-games with no rake. Expectation against opponent A is ROI120, and result is 9 wins out of 9 games. Expectation against opponent B is ROI110, and result is 0 wins out of 9 games. Now you get exactly 1 more game, which one do you play?

I think its good to have something so improbable in these conversations like my way of thinking. I can clearly create something new, because its so difficult to attach to mainstream.

Why ever choose B? Makes no sense.

Your example doesn't make your point, because your point is wrong.

I don't know where you're trying to go with this, but again the higher ROI game is the correct choise

But it's won 9 in a row. How can it possibly win again?

Your examples both make clear that your premise involves the gambler's fallacy. You should look that up. If you bet on a fair coin flip and heads comes up 9 times in a row, the next flip is still 50/50.

Right, BUT, if you had to bet again wouldn't it make sense to bet heads again just in case the coin isn't fair?

Answer = A

Now perhaps you mean that the player should change his expectation for each based on the results observed? If that's what you mean then it is a more complex question, depending on some unknown factors.

except he ran good at A and ran bad at B so it's even more A.

This is a good point, there are clearly times when it is better to give up some expected value to remove risk (insurance). We can construct some examples, but I am not sure how much there is to be learned as each person's risk preference will be different.

Haven't read responses .....


Are we assuming that the expected ROIs of 130 and 90 are definitely correct? Or are we not assuming that and are supposed to reevaluate based on the actual results of the last 100 of each? If the former, then Game A. If the latter, then I guess someone has to do some math and I don't think there is enough information given.



EDIT:

Read question too quickly. I assumed it was going to say that the higher expected ROI game has had worse results over the last 100 trials than the lower expected ROI game. In fact what it actually says is that the higher expected ROI game had better results over the last 100 trials than the lower expected ROI game.

So, obviously Game A.

To answer the question I bolded, A.

There most be some adv for you to have played B at all. Perhaps your expectations are not to very exact, so suppose B is worth it for some un said reason and the numbers are not completely true. I would play B because in the "expectation" model, the so called expectation must be met , you now have none if you quit you will loss all of it; thus we can presume that the cause of taking B was it is a side game during free time from A. Thus you most continue in B or loss the whole adv of it leaving you with only a +10 ev not the average both