Playing versus drawing

[Titanium Dragon]

Today's (8/31/2007) states that in organized play at the GP and PT level, that people on the draw win more often than people on the play. I wonder if this is true of Vintage. Looking at the situation, you see there's a lot of possible combinations, but assuming you always choose to play and you're equally likely to win or lose regardless of being on the draw or on the play:

Win - win = 75% of the time you're on the draw
Win - lose - win = 50% of the time you're on the draw
Lose - win - win = 50% of the time you're on the draw
Win - lose - lose = 50% of the time you're on the draw
Lose - win - lose = 50% of the time you're on the draw
Lose - lose = 25% of the time you're on the draw

This shows that if you win twice, you've got a very high chance of being on the draw for both games. Now, this is assuming that you have equal chances regardless, but let's say that being on the play is advantageous, but not nearly as important a factor as, say, the deck matchup. If you have a highly advantageous deck matchup, or you are a much better player, you're going to win a lot of matches where you were never on the play, and thus the win percentage for the draw will be higher even though you were at a disadvantage, it just wasn't enough of one to make a difference.

My question to you all is: do you think that being on the play is advantageous? In vintage tournaments, does being on the play convey an advantage? And in your own personal games, have you ever kept track of whether you win or lose more often on the play or on the draw?

[Webster]

My question to you all is: do you think that being on the play is advantageous? In vintage tournaments, does being on the play convey an advantage? And in your own personal games, have you ever kept track of whether you win or lose more often on the play or on the draw?

Keeping in mind that there are actually people out there who ask honest questions, I'll entertain this topic as one of those with this concise answer:

The speed of a format dictates the amount of an impact that going first in a given game will have on that game. Building decks with that afformentioned knowledge in mind is a tribute to exactly how monumentous the die roll is. The die roll changes the way games are played out so much that one might confuse a specific game, broken up into two different categories (one where deck A plays first and the other where deck B plays first), to be two completely different unrelated games with totally different mulligan/play order decisions; the reality of the situation is that the observation is 100% correct. The classic example is stax vs pitch long. Both players know the list that their opponent is playing. The sample hand for pitch long is:

black lotus, dark ritual, dark ritual, cabal ritual, demonic tutor, misdirection, chain of vapor.

On the play vs stax this hand is a goldfish hand. On the draw, if you kept this, you'd either be a fool, a fool with balls, a miser with balls, or you're just plain unbeatable and the force is with you. You risk losing to chalice of the void, sphere of resistance, and trinisphere almost flat out.


Two sides of the coin; two different game scenerios; the die roll dictates which one gets played out.

[LotusHead]

Two sides of the coin; two different game scenerios; the die roll dictates which one gets played out.

In short, in a classic game of Webster vs LotusHead (and there were many), if Web wins the die roll game 1, he Duresses me and I can do nothing about it. If I win the die roll, Web counters my first turn Chalice/Sphere cuz he mulled to 6 or even 5 to get that Force.

Games two and three are where the real games are. But if I win game 1, then I'll at least get to go first on game 3, and that is very important.

[zeus-online]

Vintage is way too fast for it to be a good idea to go second.
I've lost plenty of games which i would've won if i had gone first, the card you get from drawing is almost nothing compared to the tempo gain from going first - And in type1 the player who goes first will often be drawing cards faster then the other guy because you'll have more mana to cast your spells. (Which generally kills your opponent or gives you insane card advantage)

/Zeus

[Harlequin]

Aside from the speed of vintage - which is a valid point.  This is a great example of a "False Possitive."

By virtue of the system of "looser's choice" and assuming that all players given a choice will choose to play first, then the players who win many rounds will in turn be forced to play and win more games on the draw.  This does NOT provide any information about a the win % of a player on the draw.  So it does not support the conclusion that a player on the draw will have a higher win %.

Consider the expected number of games played on the draw, where the prob(play)=prob(draw)=50% on the first game... and the Prob to play on the nth game played (where n>1) is = 0 | game(n-1)=W; = 1 |game(n-1)=L

Event = the count of games played "on the draw"

Round Win: 
E[W-W] = 1.5
E[W-L-W] =  1.5
E[L-W-W] =  1.5

Round Loss:
E[L-L] = 0.5
E[L-W-L] = 1.5
E[W-L-L] = 1.5
=================

So the player who wins more rounds has a slightly higher Expectation of games played on the Draw. 

[Implacable]

When playing with Flash, depending on whether you're on the play or the draw, there is up to a 15-20% variance in win percentage.  Combo decks in particular garner a huge advantage from being on the play, and I quite literally have NEVER seen a competent player of any deck go on the draw willingly in Vintage.

[GrandpaBelcher]

I played against Michael Simister last summer when he came out of retirement briefly to play Belcher.  I was playing Fish with Null Rods, Stifles, and Forces.  He won the die roll and chose to play.  He won easily with Wheel into Belcher and Welder.  Game two I said I would play, but he asked me if I was sure, saying he could use the extra card.  I said I was sure and drew a hand that let me Duress and Force and get Null Rod into play.  Game three, he elected to draw and beat me after playing Belcher and using Memory Jar to get his last land out of the deck.

Now that I think about it, that's a reasonable strategy for decks like Belcher and Flash against Force of Will decks like the Fish deck I was playing.  You get an extra card to play with while they have fewer cards to stop you.  Unless you fear Duress greatly or some permanent hate like Null Rod, Pithing Needle or a Sphere with the first turn, you'll probably face a similar amount of hate turn two as you would turn one.  Then too they're drawing one card to your two by turn three.

Obviously one match isn't a big enough sample to make a difference, but even that he asked whether I was sure I wanted to play was enough to get me questioning that choice in some matchups.  I'll have to keep track of my records more closely in the future.

[Harlequin]

Simulation Example supporting my post a few posts up....

Player A (Alex) vrs Player B (Bob)

The Game:
Each player has a deck of cards starting with 1, then 2, 3, 4, 5, ...  Alex has a deck with 4 cards in it: 1,2,3,4.  Bob has a deck with 9 cards in it, 1 to 9.  The player who is "going first" reveals the top card of thier deck.  Then the player going second reveals the top card of thier deck.  The higher number wins the game.  In the event of a tie, the player who went first wins the game. 

The Tournement:
Normal Tournement '3 Games in 1 Round' set up.
Game 1 is decided by a 50:50 flip.
Game 2 and 3 are looser's choice, and the looser always chooses to reveal first.
Game 3 is only played if each player has 1 game win. 

The winner of the Round is the player who has 2 Game wins.

Player Win Probabilitys:
Alex's deck is much worse when compared to Bob's deck.  Bob has certain cards that will always beat Alex reguardless of if he is on the play or draw.   There are 4x9 = 36 possible outcomes of the 2 decks - each are equally likely.  6 outcomes will cause Alex to win, 26 will cause Bob to win - and 4 will be dependant on who goes first.

Prob(Winning a Game)
A 2nd   16.67% = 6 / 36
A 1st   27.78% = (6+4)/ 36

B 1st   83.33% = (26+4)/ 36
B 2nd   72.22% = 26/36
///////////////////////////////

100 Simulations:
In 100 rounds, Alex wins a respectable 12 rounds.  With Bob winning the other 88.   Note that 233 total games were played - which would be expected... because that means that 66 rounds were decided in 2 games (AA or BB). 

Notice that the "On the Play" percentage for Bob was much lower than 50%.  He only was on the play in 93 out of 233 games. 

Now the interesting part:
A plays first => Lost   108
A plays first => Win   32
A plays first => Lost   18
A plays first => Win   75
............................. ..
Win% Of all players who played First: 45.923%
Win% Of all players playing Second:   54.077%


Does this prove that A player will increase the odds of winning by choosing to play second? 
No.  Because remember, defined mathematically:
Prob(Winning a Game)
A 2nd   16.67% = 6 / 36
A 1st   27.78% = (6+4)/ 36
B 1st   83.33% = (26+4)/ 36
B 2nd   72.22% = 26/36

[agesga]

According to Implacable, who says that he hasn't seen a competent player going on the draw willingly, meditate about this:
Imagine you win the roll die so you decide to play (as usual); then your opponent says: How many cards should I let you draw in addition
to change your mind?

Personally I don't think that this kind of matter (playing vs drawing) could be modeled mathematically to extract conclusions. Other subject like playing vs drawing with 2 specific decks indeed can.

For the moment i only will let the opponent play first in test games.

[Implacable]

According to Implacable, who says that he hasn't seen a competent player going on the draw willingly, meditate about this:
Imagine you win the roll die so you decide to play (as usual); then your opponent says: How many cards should I let you draw in addition
to change your mind?

Personally I don't think that this kind of matter (playing vs drawing) could be modeled mathematically to extract conclusions. Other subject like playing vs drawing with 2 specific decks indeed can.

For the moment i only will let the opponent play first in test games.

On a whim, I would have to draw two extra cards (i.e., have 10 cards in hand after my Turn 1 draw-step) to play second.  When playing a deck like Flash, I would simply never do it, as giving them a chance to play Brainstorm/Duress/Sphere/etc...  is not worth it.

[emidln]

In Legacy with my U/B Draw4 deck I frequently elect to draw against opponents that I've scouted and know they only have Force of Will (and not Daze) and no Duress. That is the only deck I've ever encountered that really wanted to do that though, and the only time that would happen is when I knew there could be no penalty for it. In those scenarios, there was no reason not to take an extra card (my percentages of killing first turn jump almost 10% if I see that extra card).

[Implacable]

In Legacy with my U/B Draw4 deck I frequently elect to draw against opponents that I've scouted and know they only have Force of Will (and not Daze) and no Duress. That is the only deck I've ever encountered that really wanted to do that though, and the only time that would happen is when I knew there could be no penalty for it. In those scenarios, there was no reason not to take an extra card (my percentages of killing first turn jump almost 10% if I see that extra card).

But this is in Legacy.  I certainly agree that, in a slower format, there are considerable incentives for taking an extra card (especially if you're going to be reacting to whatever your opponent plays anyway, instead of playing proactively), but even Vintage control decks do not go on the draw by choice.  I simply have yet to see a situation where it's a good choice.

[hvndr3d y34r h3x]

I'm fairly confidant that being on the play is a major advantage. True you get 1 card a head on the draw, but there are some many opening plays you can make to undo those that advantage. A simple brainstorm puts your card vision to 10, opposed to their 8.

[Methuselahn]

Just to throw it out there,  Ichorid can elect to draw for the purposes of discarding a dredge spell on the first turn and then proceed to slow roll the opponent with returning Ichorids.  This may happen in the stax matchup, most likely, if at all.