2-7 TD Variance

[jeccross]

Hi, I have just started playing 2-7 TD after reading the section in Super system and playing it in a home dealer's choice game. I feel i've picked up the strategy fairly quickly and am a profitable player. Now here's the but.
I have suffered dome heavy losses over the last 2 days, about $600-700 at 5/10 limit (about 10 hours play). There's been plenty of hands where i've been drawing 1 with a better draw heads up against another drawer or pat with an 8/9/10 with against a drawer and lost, and I still feel I'm making good decisions and getting my money ahead. Is 2-7 a much higher variance game than limit holdem? Is it reasonable that this is just variance? I can handle losing the amounts and have the bankroll for it, I just want to be sure I'm a profitable player befoer I continue with the game.

[Guruman]

variance comes from the two variables in the game:
-the card
-the way people play the same hands.

the fewer card variables you see and the more differently you play from your opposition, the less variance and the greater profit (or loss) you'll encounter.

Since there are 4 total ways to make the best hand in holdem (royal flush x four suits) and there are 1024 different ways to make the best hand in TD (4 deuces x 4 threes x 4 fours x 4 fives x 4 sevens) the variance introduced by the card variable is actually less. The reason is that the suit of a specific card is close to irrelevant in most situations. Because you're essentially only using rank to determine hands in TD as opposed to using both rank and suit in Holdem, you're introducing fewer variables into play.

The balance to this is the second variable - the way that someone plays a hand. because there are significantly fewer card variables in the game, ok players naturally begin to gravitate towards very similar strategies more quickly. When two people would play the same hand the same way, the net result is variance. When one would play the hand differently than the other, the net result is profit and loss.

thus, the variables that are reduced by the card structure of the game are then to some degree re-introduced by the limited range of profitable strategies.

read this, then play a bit and ask yourself:

"how differently would I play the hands that I see my opponent showing down?"

If the answer tends to be "very differently," then a significant edge exists between you and the other player in one direction or the other.

"would the difference have won or lost bets in that hand?"

if your way would have lost bets then you must consider the possibility that other player has the edge over you in this game. If this answer shows up repeatedly, you should be adjusting your game.

if your way would have won bets, then you are likely to be the one with the edge. If this answer shows up repeatedly then you should not adjust your game.
----
My personal opinion is that triple draw is possibly solvable by humans in conjunction with computers. If the game is ever solved or even partially solved then no one without the answer will ever win and the game will implode.

Until that point, the biggest edge probably lies in the combination of having a winning strategy and finding players that are significantly worse than you to exploit. I know that sounds simplistic, but variance will swing you wickedly in this game if you've only got a narrow edge.

[Biggle10]

[ QUOTE ]
Hi, I have just started playing 2-7 TD after reading the section in Super system and playing it in a home dealer's choice game. I feel i've picked up the strategy fairly quickly and am a profitable player. Now here's the but.
I have suffered dome heavy losses over the last 2 days, about $600-700 at 5/10 limit (about 10 hours play). There's been plenty of hands where i've been drawing 1 with a better draw heads up against another drawer or pat with an 8/9/10 with against a drawer and lost, and I still feel I'm making good decisions and getting my money ahead. Is 2-7 a much higher variance game than limit holdem? Is it reasonable that this is just variance? I can handle losing the amounts and have the bankroll for it, I just want to be sure I'm a profitable player befoer I continue with the game.

[/ QUOTE ]

I don't have a nice solid explanation like guruman, but empircal evidence shows it to very high variance.

[DeathDonkey]

The short answer is yes, a $700 loss at 5/10 can easily be variance...I call that amount a rough hour, not even a downswing. It's a sick game.

-DeathDonkey

[Murakawa]

What is, pray tell, then a good BB/100 after 10,000 hands?

[MarkGritter]

While I agree with much of what you say, I'm not sure that it's a particularly good explanation for variance. Even a player who won 100% of the time would still have sessions that were less winning than other sessions. Yet such a player would not necessarily go back and adjust his game. Increased playing skill doesn't automatically lead to reduced variance (though it does result in fewer losing sessions, which is generally what players complain about.)

I'm not sure what I think of the notion of reciprocality in a draw game anyway since you often don't know what the opponent threw away--- or, in some cases, even what he kept.

In my mind, the following factors contribute to the high-variance nature of triple draw:

1) The best starting hands are not all that large a favorite over other decent or even mediocre starting hands. You cannot just "play tight" and dominate your loose opponents; you will often be getting money in as a narrow favorite instead of a big one. (Except, of course, for those lovely situations in which your opponent is drawing dead.) Hand values may vary more from street to street than in other games (although that is just speculative on my part.)

2) In a related fashion, the opportunities to get out cheaply are few and far between. A Hold'em hand might cost just 1-3 small bets before being folded. A good TD starter will usually cost 2-3 SB predraw, and 2-3 SB more to see the third draw.

3) It is a shorthanded game, and shorthanded games generally have increased variance over 9- or 10- player games (due to the increased blind cost per hand.)

4) It is a game of limited information; although you can easily judge the absolute strength of your hand, you usually cannot accurately estimate the strength of other players' hands. A flop or stud game gives more opportunity for hand-reading skill to reduce an opponent's range of holdings, while a lowball player often has a much wider range to consider.

5) Drawing rounds give extra opportunities for mistakes in addition to the betting rounds.

6) Many showdown hands are nut or near-nut holdings. When two big hands collide there is usually not any way for even a very skilled player to avoid putting in bets.

In summary, I believe that the variance is high because the structure of the game encourages many bets to go in on marginal edges. More bets per hand == more variance.

I think it's important to keep in mind that variance works both ways--- it's a well-defined mathematical notion, not just a term for "losing sessions".

[Guruman]

Hi Mark,

thanks for taking the time to go over my logic, I'm still kind of in the process of developing it. [img]/images/graemlins/smile.gif[/img]

1) The best starting hands are not all that large a favorite over other decent or even mediocre starting hands. You cannot just "play tight" and dominate your loose opponents; you will often be getting money in as a narrow favorite instead of a big one. (Except, of course, for those lovely situations in which your opponent is drawing dead.) Hand values may vary more from street to street than in other games (although that is just speculative on my part.)

I think this is generally just agreeing with my initial statement that the cards have less of an influence in this game than in holdem. Since the cards are variables, this means that the variance is reduced.

2) In a related fashion, the opportunities to get out cheaply are few and far between. A Hold'em hand might cost just 1-3 small bets before being folded. A good TD starter will usually cost 2-3 SB predraw, and 2-3 SB more to see the third draw.

I've stated elsewhere (not in this forum) that I believe bets and raises in poker amount to pure amplifiers. They either amplify variance (if there is a showdown) or profit/loss (if there is a fold). So while bets and raises may amplify variance, they may also amplify profits and losses - which by definition are the opposites of variance and thus counterbalance it.

3) It is a shorthanded game, and shorthanded games generally have increased variance over 9- or 10- player games (due to the increased blind cost per hand.)

This was recently actively disputed in


MHSH, and its there that you'll find the rest of my thoughts fleshed out a little more. Suffice it to say that shorthanded play equaling greater variance is not a settled argument.

4) It is a game of limited information; although you can easily judge the absolute strength of your hand, you usually cannot accurately estimate the strength of other players' hands. A flop or stud game gives more opportunity for hand-reading skill to reduce an opponent's range of holdings, while a lowball player often has a much wider range to consider.

this is a valid argument for more variance, and I think that it coincides with the balance argument that I made as well.

5) Drawing rounds give extra opportunities for mistakes in addition to the betting rounds.

mistakes equal profit or loss - and profit or loss is the opposite of variance. With that said, I disagree that more drawing rounds equates to more mistakes because it introduces more cards (variables) and makes it more correct to attempt to suckout. So, I agree with the effect while disagreeing with the premise. [img]/images/graemlins/smile.gif[/img]

6) Many showdown hands are nut or near-nut holdings. When two big hands collide there is usually not any way for even a very skilled player to avoid putting in bets.

another good argument for more variance.

[HOWMANY]

[ QUOTE ]


2) In a related fashion, the opportunities to get out cheaply are few and far between. A Hold'em hand might cost just 1-3 small bets before being folded. A good TD starter will usually cost 2-3 SB predraw, and 2-3 SB more to see the third draw.


[/ QUOTE ]

I've always assumed this is one of the biggest reasons 2-7 is so swingy. Almost every 6 handed TD hand is going to go through 3 of the 4 betting rounds with bets going in basically guaranteed before the draw and on the first draw, and we're seeing the river quite often as well. You're also generally taking only a bit the best or a bit the worst of it in these situations. In Holdem we fold quite often on the flop, while we fold basically never after the first draw. When we do call the flop in a full game we generally have an idea of whether we're leading/drawing/bluffing (obviously not always, but you get the point).

TD offers even the worst players in other games the ability to play the first three rounds somewhat logically, while terrible players regularly light money on fire in all other games on every possible betting round with their stupid play.

[MarkGritter]

[ QUOTE ]
So while bets and raises may amplify variance, they may also amplify profits and losses - which by definition are the opposites of variance and thus counterbalance it.

[/ QUOTE ]

See, this is where we have the fundamental disagreement. You seem to be using "variance" to mean something different from what I expect it to mean.

In the commonly accepted mathematical definition, variance refers to how the values in a population (or a random variable) are spread around the mean ("expected") value. In particular it can be defined as "the average of the square of the distance of each data point from the mean."

It is a quite startling claim that increasing my expected value by winning more also results in a reduction in variance. (Heck, this may well be true for poker but it would require pretty substantial evidence.)

Here's a mathematical example. We'll play coinflips for $1 a flip--- you lose $1 on tails and win $1 on heads. The value of this game is $0. The variance is $1 = 0.5*(1)^2 + 0.5*(-1)^2

Now suppose you know the coin flip in advance, and could choose to bet either $2 or $0. The value of this game is now $1. (Half the time you win $2, the other half you lose $0.) The variance is still $1 = 0.5(2-1)^2 + 0.5*(0-1)^2. Playing the coinflip game perfectly didn't change your variance at all but it increased your average by $1.

Are you using "variance" in this strictly technical sense, or with a different definition?

[gergery]

[ QUOTE ]
variance comes from the two variables in the game:
-the card
-the way people play the same hands.

the fewer card variables you see and the more differently you play from your opposition, the less variance and the greater profit (or loss) you'll encounter.

Since there are 4 total ways to make the best hand in holdem (royal flush x four suits) and there are 1024 different ways to make the best hand in TD (4 deuces x 4 threes x 4 fours x 4 fives x 4 sevens) the variance introduced by the card variable is actually less. The reason is that the suit of a specific card is close to irrelevant in most situations. Because you're essentially only using rank to determine hands in TD as opposed to using both rank and suit in Holdem, you're introducing fewer variables into play.

The balance to this is the second variable - the way that someone plays a hand. because there are significantly fewer card variables in the game, ok players naturally begin to gravitate towards very similar strategies more quickly. When two people would play the same hand the same way, the net result is variance. When one would play the hand differently than the other, the net result is profit and loss.

thus, the variables that are reduced by the card structure of the game are then to some degree re-introduced by the limited range of profitable strategies.

read this, then play a bit and ask yourself:

"how differently would I play the hands that I see my opponent showing down?"

If the answer tends to be "very differently," then a significant edge exists between you and the other player in one direction or the other.

"would the difference have won or lost bets in that hand?"

if your way would have lost bets then you must consider the possibility that other player has the edge over you in this game. If this answer shows up repeatedly, you should be adjusting your game.

if your way would have won bets, then you are likely to be the one with the edge. If this answer shows up repeatedly then you should not adjust your game.
----
My personal opinion is that triple draw is possibly solvable by humans in conjunction with computers. If the game is ever solved or even partially solved then no one without the answer will ever win and the game will implode.

Until that point, the biggest edge probably lies in the combination of having a winning strategy and finding players that are significantly worse than you to exploit. I know that sounds simplistic, but variance will swing you wickedly in this game if you've only got a narrow edge.

[/ QUOTE ]

Great post, interesting read, I agree with many of the things you said, and liked Tommys article.

But your post has nothing to do with variance. Its more applicable to winrate.

As Mark pointed out, variance has a mathematical definition that is calculatable and is a measurement of dispersion around the mean result (play around in wikipedia). so games where lots of bets go in will by definition have higher variance. to have lots of bets go in you usually need aggression, and if players are any good at all they need a reason for their aggression (ie. hand values closer together, uncertainty around relative value of hand, ability for hands to change in value over time, etc.)

-g