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If you play a tournament and you consider yourself being better than average players, how will the chance of winning the tournament be affected if the very same tournament now instead have twice as many entries?

If you are better than average players in the tournament then the chance of winning it maybe wont be twice as hard just because the entries are twice as many. Am I wrong?

  • This may be a factor in low-man SNGs, for example your starting equity is a bit bigger, but nothing more. I can't imagine how a better than average could work in an full-variance MTT, filled with thousands of players. – user1165 Oct 12 '15 at 13:57
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    It will be twice as hard. But the payouts will also be twice as big (if payout is based on entries). – paparazzo Dec 27 '15 at 14:29
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I have a decent ROI in on-line MTTs (70%+ at low-mid stakes)

The larger the field the harder it is to cash (ITM) and harder it is to outright win the MTT but it is easier to get a high ROI

If you examine the results on OPR/Sharkscope for top-ranked players in different formats, you will see what is achievable

For a top mid-stakes player in turbo or faster format it's roughly:

6 players:- ITM 35% and ROI 5% (+3-4%)
18 players:- ITM 25% and ROI 15% (+5-6%)
50-100 players:- ITM 20% and ROI 30% (+10-12%)
101-1000 players:- ITM 19% and ROI 40% (+12-15%)
1001 + players:- ITM 17% and ROI 50% (+15-20%)

Figures in brackets are for slow and ultra-slow

The big field MTTs is where you find the big prizes. To win these you need a lot of luck no matter how amazing you play. If you use GTO, it's fairly easy to guarantee a profit over a large sample.

If you are a good player, your edge is greatest when the field is large and the blinds are slow. It gives the field more chances to make mistakes and gives you the ability to be more selective and informed about when to be aggressive

The smaller the field and faster the blinds, the more important luck becomes

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Short answer:

Let MTT has the following structure: all players play heads-up, the winner goes to the next round, the looser eliminates. In such tournament the number of players at each round halves. That is, to show the same performance when the total number of players doubled, the player have to win only one more heads-up match.

Long answer:

Let x(t) be a number of (active) players in MTT at time t. If there are total N players at the beginning, then the following approximation holds:

x(t) = N * exp(-r*t)

where r>0 is some constant depends on MTT's blind structure. One can treat player's performance by the time T he or she remeins active in the tournament on average.

Suppose, player usually takes p-th place, that is he or she must remain active for the time

T= - log(p/N) / r

However, if we double the number of total players (N -> 2N) the time player have to remain active (in order to take p-th place) will increase only by a constant log(2)/r, which is not equal to 2T.

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  • Question is not time in tournament. – paparazzo Dec 27 '15 at 14:26
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Consider Tiger Woods at the peak of his game. Yes is was better than 99% of the golfers. There were tournaments were he was even money to win against the field. Still his chance of winning versus 100 player is less than versus a field of 300 players.

So if you are better then 60% of the players and you double the number of players then you still have twice as many players above and below you.

.60 * 100 = 60
.60 * 200 = 120

If the last 100 that sign up are fish then good but your odds still go down. You still have to beat the people already in. A fish is not likely to win but can still draw out on you when you got your money in with the best hand. That is what makes putting a player all in more powerful in a tournament.

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  • If payout goes up with number of entries then it would be a wash. – paparazzo Feb 8 '16 at 16:50
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The answer would require quantifying the skill levels of all players, or at least a very general estimate of where you see yourself compared to the others. Even if more players are added, your estimation of yourself would remain the same unless there are specific players added whom you believe to be ‘better than you’. Assuming you believe yourself the 10th best player in a field of 100, and an additional 100 ‘fish’ join the tourney, your estimated position would still be 10th best player, now in a field of 200.

Your odds in that scenario would change from 1-in-10 (100players/top 10) to 1-in-20 (200 players/top 10). Your odds would change from 10% to 5%, but again these would still be arbitrary estimates. The only thing this thinking would or should actually affect is how you play your hands in different stages of the tournament. If there are more bad players, you may play more aggressively early on, building a stack for later on when the blinds have escalated several levels. Since you start with more players, you have more players than usual still active as the blinds become higher and higher. The fewer total players, the more you might benefit from being passive and ‘picking your spots’. But since there is so much ‘dead money’ at the beginning of the tourney with 100 additional weak players, it becomes more urgent that you build your stack.

But based on pure math, obviously, your chances are ‘1 in however many total players there are in the tournament’. Estimating your skill relative to others will only affect how you play at different stages of the tournament, but also bear in mind that the higher the field, the more pay-out positions there are.

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  • And if it helps, I have won a tournament before of about 540 players. – GoodWillGustin Feb 9 '16 at 21:46

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