Heads-up tourneys and variance

[TNixon]

After doing a bit of digging for information about the variance in heads-up sit-n-gos vs normal 9 or 10 player sit-n-gos, I found an article (through a link on the forums here) titled Basic Bankroll Management, which gives basic guidelines for bankroll requirements for various types of play.

The relevant quote about heads-up-tourneys is:


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Heads up sit and go tournaments are a variance monster all to themselves. Your win rate will have a massive effect on your variance in heads up play, and a player who is only winning 55% of his matches will have huge swings, while a really solid heads up player with a 70% win rate can get away with using numbers about twice the size of the regular SNG numbers in the chart above. The 55% player probably can't have a big enough bankroll no matter what he does; the variance is just too high.

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I'm having a little bit of trouble understanding why this would be true.

I can certainly see why it would be true that variance would increase heads-up for cash compared to a full ring game, with the reasoning being nearly identical to the reasoning for variance being higher at pot-limit omaha compared to no-limit holdem: because hands are often so close statistically, there are more marginal situations where it is correct to make big bets or calls, while being a slight favorite or underdog.

Similarly, when short-handed, it's less likely that your opponents have premium hands, so you end up putting in more money in marginal situations.

However, when playing a freezeout tournament, isn't your win/cash rate basically the *only* thing that determines variance?

The reasoning given for needing more buyins for a multitable tournament is that with more people, you will reach significant cash less often, so the reccomendation is for a higher bankroll to ride out the dry spells. The "average" player (whatever that really means) has an 11% chance to win a 9 person sit-n-go, but only a 1% chance to win a 100 person tourney. It seems quite obvious that there will be bigger gaps between bigger wins in the MTT situation.

Of course, the fact that you don't have to win to cash in a STT surely makes a difference, with the top 30% getting 2x their buy-in, the top 20% getting 3x, and the top 10% getting 5x, but in a heads-up tournament, the average player has a 50% chance to win. Shouldn't that fact alone *reduce* the variance of a heads-up sit-n-go in comparison to a full single-table tournament, making the dry spells that much shorter?

I have no clue whatsoever know how to calculate it, but I have a hard time imagining that a 20 buyin downswing is more likely to happen on a 50% average over other situations with smaller percentage chances to win bigger pots.

Before this weekend, I would also have said with certainty that my personal experience backed up my gut instinct about heads-up tourneys having less severe downswings, especially at low buyins, because I was having far smaller downswings playing $2-$10 heads-up than I was playing $5 STTs, after working $20 up to almost $200 on heads-up tourneys, playing with about a tenth of my bankroll or less in a single tourney. (if I had $120, for example, I'd play 1 $10 and a couple $5s).

Of course, we're talking about a super-small sample size, and I dropped back down to $20 again on a very long string of losses, but I did clearly identify some very bad tendencies on my part, especially in the $10 tourneys, so at this point, I really have no clue if the downswing was the result of a lot of poor play, combined with a little bit of bad luck, or if that's the normal expected variance playing heads-up?

My gut says that once I stop being stupid in the places I'm being stupid, heads-up tourneys are actually the safest way to slowly increase a bankroll.

Now, I realize completely that even if I'm right about that, $20 isn't really enough to start with (I actually started with $100, but dropped almost instantly to $20 on what was mainly a bad streak of luck on the $5 STTs), and my chances of going broke before getting a stable bankroll are pretty good anyway, but I wanted to get other people's thoughts on the matter.

If it makes a difference, I appear to be significantly better than a 55% winner at the $2 HU tourneys on full-tilt (closer to 70%), and before this weekends big losing streak, which, as I mentioned, appeared to be more me being a donkey and less normal variance, looked to be about a 60%-ish winner on the 5s and 10s.