swings in shorthanded play

[Lunar Tweak]

why are the swings in shorthanded bigger then in a full ring game?

thx

[Jason Pohl]

Two main reasons.

First, the game is faster. So, if the game changes, it can take a while to adjust, causing large variations. Also, a larger sample size (i.e. # of hands/hour) is going to allow a larger variation.

Example: You flip a coin 10 times. The coin lands on 'heads' an average of 5 times. It probably wouldn't be surprising for heads to come up as few as 3 times or as many as 7.
If you flip the coin 100 times, you will see 'heads' an average of 50 times. However, here's the catch. It is far more likey that since you flipped 100 times, your results might fall at 40 'heads' or 60 'heads' results. Percentage wise that's not as big a difference, but that's +/- 10 actual flips. So, if you had $10 on each flip, your variance would be larger if you flipped 100 times in an hour versus 10. Does that make sense?

Second, the decisions are more marginal. In a ring-game, it's a lot easier to put players (especially low-limit) on hands. There are a lot of automatic plays. Short-handed, there is so much semi-bluffing, bluffing, and slim value betting/raising that it is much, much harder to read your opponents. Thus, your overall edge is smaller.

The truth is that the variance has not changed due to the small edges. If your session results fell between $-100 and $900, the variance would be $1000. If your sessions fell between -$400 to $600, the gap would still be $1000, but you would notice the variance more because you'd be losing a lot more. In other words, you're more likely to have a losing session with such small edges, making the variance more obvious. Hope that helps. Good luck.

--Jason

[Lunar Tweak]

[AceHigh]

"First, the game is faster."

Won't this decrease the variance? More hands, means more chance for the law of averages to catch up, doesn't it? If I'm a winning player, aren't I more likely to be winning after 1000 hands than 500 hands?

Using your coin flip analogy, won't the % of heads flipped after 1000 tosses be likely to be closer to 50% than after 10 tosses?

"Second, the decisions are more marginal. "

I think this reason is closer to the mark. Marginal decisions and good poker skills are more in play in short-handed games. A lot of full ring poker games are about math and pot odds, if the game is loose enough. Short-handed games are more about reading players and making decisions based on probabilities. If you make bad assumptions, you can make a lot of bad decisions in a short amount of time.

[Jason Pohl]

I'm impressed AceHigh. I actually wrote an article that included mention of these factors October 12th for 'www.pokerpages.com'. You point out something I should have clarified further.

With a higher sample size, the results will tend to be closer to average on a percentage basis, but the actual numeric range can be higher (measured in big bets). So, over 100 flips or 1000, you are far less likely to see a 60% 'heads' result than in 10 flips, but still more likely to see a wider range of results. In reality, we're talking about the difference between 80 hands and 120 per hour, but those extra 40 hands make a difference. The speed factor also plays a part in decisionmaking ability, as you mention.

BTW...you mentioned, "If I'm a winning player, aren't I more likely to be winning after 1000 hands than 500 hands?" The answer is 'yes', but the range of possibilities for you is larger because of the increased sample size. In other words, it's possible to win or lose a lot more in 1000 hands than 500. After enough hands, if you are truly a winning player, your results will be virtually guaranteed to be positive...but the real question associated with variance at that point is: "How much?"

As for your comment regarding marginal edges, I agree completely. Theoretically, a good player will continue to average +EV through a clustering effect of mostly good decisions mixed with some bad judgment decisions. However, reality dictates that a lot of players get stuck for a time on bad assumptions...and as you say, "you can make a lot of bad decisions in a short amount of time (in short-handed poker)."

Also, we're simplifying a bit...there are other factors. For example, a change in just one player from fish to shark will definitely change your results dramatically, whereas a change in one player at a full game will have a less pronounced effect. The whole structure of the game is based on a less predictable, volatile format. That's why it's popular IMO. Good luck,

--Jason

[AceHigh]

Well, I don't have any stats to prove it, but my guess is "good" short-handed players make more money and have less variance than "good" ring game players. They play more hands/hour and the fish get chewed up by the poor pot odds.

I think the "average" winning player might have a higher variance because, he's just not very good at short-handed play. That combined with more marginal decisions means more mistakes and more variance.

[Glenn]

Nope, the variance is higher short handed. I don't always use pokerstat but I do have about 30000 hands of heads up play in a ps database and my results confirm this. The per hour variance is MUCH higher due to the greater number of hands. The per hand variance is also greater compared to a ring game according to my stats as well. I think you are making the often mistaken assumption that variance means losing. It is possible to have a high variance but still usually win because your win rate is extremely high.

[AceHigh]

Yes, you will have a higher variance in terms of $$$, because a higher % of your hands are playable, in terms of time and hands dealt. Variance would be less by hands played.

I meant that there would be fewer losing sessions for a good short-handed player. The luck factor would be reduced because you would be called upon to use your skills more often.

[Glenn]

"Yes, you will have a higher variance in terms of $$$,"

As opposed to variance in terms of matchsticks???

"Variance would be less by hands played. "

I guess this is true but it seems fairly if not completely useless.

About having mostly winning sessions...again, this may or may not be true, but it doesn't matter at all. What matters is how much you win or lose.

I think one area causing contention is the fact that you may be using the term variance in a way different from us. I assume you know this but variance is a term from statisics which is defined by a formula. When we use it here we do not mean "that which varies" or "varied results". Obviously if you meant those things it is different.

Another thing, from stats and experience, you can have much bigger losing sessions short than full even if you are a winning player.

[Glenn]

also you generally need a bigger bankroll to play short at the same limit even if you are a very good player

[AceHigh]

My point was usually variance or standard deviation are related to hours when talking about poker. But hours shorthanded and hours in a full ring game aren't the same in terms of actual playing time. So my variance per hand played was an attempt to reflect this.

Sort of like measuring variance in BB/hour instead of dollars/hour so you can compare variance between different limits.

[Jason Pohl]

I agree with Glenn. I am a winning short-handed player, and I win in full games (at a lower hourly rate). However, the variance short-handed is tremendously higher in my experience, even though I feel my skill reduces that deviation significantly. Note, that although my win rate is higher in short-handed games, my variance (or range of wins/losses) as well as my % of losing sessions (I average 1.25 hours per session...so they're short) is much higher than ring games of the same length per session. You might expect the opposite, but it just isn't the case b/c the speed, range of possible wins/losses, and marginal edges cause large fluctuations to be possible.

BTW...Malmuth points out that Standard Deviation (variance) is generally less for a better player (in Gambling Theory and Other Topics). His explanation of why is pretty comprehensive.

--Jason

[AceHigh]

"as well as my % of losing sessions (I average 1.25 hours per session"

Won't shorter sessions, cause more losing sessions?

How is your win rate short-handed vs. full games? I don't have near the amount of short-handed time as full, so maybe my results are skewed, but my win rate is much higher at the same limits.

I think the better starting hand stand up a lot more in short-handed games.

[Jason Pohl]

Mentioning the length of the sessions was purely as a point of interest. Even the percentage of winning/losing sessions can be somewhat skewed. However, the critical stat is standard deviation in terms of BB/hour.

My deviation in BB/hour is much higher in shorthanded games, and my percentage of losing sessions is also higher in shorthanded games.

However, my win rate is higher at shorthanded by a lot, but I attribute that to two things. First, shorthanded affords me opportunities to make more +EV decisions, and secondly, I am simply better at shorthanded play that full ring games.

As for the better starting hand holding up, I have no doubt that they hold up more often in shorthanded games. There are usually fewer opponents and often heads-up competition, so naturally the better hand holds up more often.

On the other hand, people sometimes make truly bizarre calls and raises in short-handed play, leading to more bad beats caused by a bad read. In other words, opponents are a lot more likely to stick around in a 5-handed game with a thin draw.

--Jason

[AceHigh]

There's an excellent section in "Inside the Poker Mind" by John Feeney on short-handed play that's sums up the pluses and minuses very well. I think he says what you, glenn and I have been trying to say, but simpler and clearer.

[2ndGoat]

Short-handed play is a very different beast than full-ring limit games. *But* if the only difference was hands/hour, follow me on a trip through statistics.

Assume you are a 1BB/hour, 10BB/hour^1/2 SD winner at 40 hands/hour.

Now you play at a table that goes twice as first.
EV is 2 BB/hour, that's easy.
SD is sqrt(2)*40 ~= 14.1

IF session results were normally distributed, and it is generally accepted that they are not if your sessions are only an hour long, You would have a:

54% chance of being ahead after an hour in the slow game
55.5% chance of being ahead after an hour in the fast game
(according to normal distribution tables)

With a 5-hour session, which I imagine gives us pretty close to normally distributed results, (I'll spare the numbers)
58.8% chance being ahead in slow game
62.1% chance of being ahead in the fast game.
Mind you, the wins and losses will still be bigger in the fast game, and the long run is going to take a good amount of time to make the quick game "steadier" than the slow one. In a 5-hour session there is a 2.5% chance you'll be down 53BB, whereas in the slow one there is only about a .5% chance of that in the slow game.

Short-handed play of course, shows a much great increase in variance vs. a full ring game. You're playing many more than twice as many hands per hour, because you have to get involved more often. If you compared your short-handed results to your results in a full game when you're first in from late position or in the blinds vs only late position players and blinds (and compared results per hand rather than hour, since the time stat loses its meaning), i bet the hands/hr difference would nearly get you to similar results.

2ndGoat