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Does a tournament with 500 places in the money and 5,000 players require a different strategy than one with 50/500, or one 10/100? I see that in an extreme case in a tournament with 1/10, everyone is your enemy, no matter what, and you might need to play more aggressively. But for the rest, could a player just pull a small-ball strategy and obtain the same results?

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Lets assume you are talking about a tournament with normal speep, starting stack and 9 players per table: The smaller the field is around the money-bubble (10/100) the more likely it is that you will sit on a table with less people than intended capacity, with results in a more aggressive play then on full table. Also, the more player are in the field, the more likely are players with huge stacks 150BB+ whose are able to push around people with an average stack.

In theory, your expected return on investment should be the same, but it depends highly on your personal playstyle. also for tournaments with a large player base 5000+, the payouts for the top 1% increases stupendously fast, which again might not fit your style.

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First off, I think there could be a small difference in your strategy mostly because bigger fields tend to have weaker players on average.

Therefore you could pass slight +EV plays to avoid busting out if you know you are likely to find much more profitable spots later on.

Unlike the previous answer, I do not think that your return on investment is the same since it should be bigger against weaker players, but what is surely bigger is your variance and you need to account for that.

That being said, I think small ball strategy is only effective against really weak players since it can easily be exploited even by average competitors, so that should not be your main strategy no matter what field you have.

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