Sixth Sense & Lady Luck

Sixth Sense. It’s a card which many players have strong feelings about, and a card which many others likely haven’t even heard of. After all, it’s been banned in the OCG for over 13 years, and it was only legal the the TCG for one half of a format at the end of 2013 – even then, it was Limited immediately on its release to the TCG, and banned pretty soon after. So what does it do?

First, you choose two numbers, and then you roll a die.

If the result is one of the numbers you chose, you get to draw that many cards!

If the result isn’t one of the numbers you chose, you mill that many cards.

Simply put, the two numbers you should choose are 5 & 6. That goes without saying – card advantage is much more relevant that a big mill. For the most part, drawing 5 or 6 cards off of 1 activation will net you the win. I say “For the most part”, since it’s not impossible for you to lose that game, but after rolling a 6, the odds of your victory have certainly gone up. But what are the odds surrounding Sixth Sense?

Ad Infinitum: The Dream Scenario

Because there are six sides on the die, you have a 2/6 chance of rolling one of the numbers you chose – that’s a 33.33% chance. Pretty simple. Although those aren’t amazing odds, imagine if you miraculously opened Sixth Sense in your opening hand every game you ever played, and you always got to go first.

That’d mean that you’d always get to activate Sixth Sense turn 1 every game.

Since you have a 33.33% probability of drawing big each time you activate Sixth Sense, and we can more or less just assume at this point that, “If you hit a 5 or a 6, you win“, we can say that you’d immediately win one third of all of your games. That’s pretty sweet, and a good reason concerning why the card is busted. A free win one third of the time, with no opportunity cost of putting random combo pieces in your deck, is certainly a feature that gets a card banned.

De Facto: Chances of Opening

Sadly, this isn’t going to be a reality most of the time: You don’t get to go first every game, and you’re not able to open Sixth Sense every game. So what are the chances of that actually happening?

Well, first I’m going to warn you that there’s quite a bit of nasty maths ahead. I’m aware that not everyone knows their statistics (Although you should probably try to read up on it a little – card games are all about chance!) so I’ll keep the numbers and workings to a minimum.

Pulling numbers straight out of my trusty hypergeometric probability distribution calculator, I can tell you the following statistics. Note that nothing below factors in card draw, and considers you only playing 1 sixth sense in your deck (I’m also working to 4 decimal places).

In a 40-card deck, your chance of opening Sixth Sense turn 1 is 0.1250, or 12.5%.

In a 40-card deck, your chance of opening Sixth Sense turn 2 is 0.1500, or 15.0%.

Because you’re just as likely to first as you are to go second, we can find a mean average using the above figures [(0.01250+0.1500)/2], which gives us 0.1375, or almost 14%.

That’s only about once in every 7 games.

If we factor in card draw, and mange to essentially cut down our deck to 35 cards (I’ll spare you the workings this time), that’s still only a mean probability of 0.1571, or about 16%.

That’s still only about once in every 6 games.

Nevertheless, the ability to more or less just win one in every 2 matches immediately, on the first turn, with the use of a single card, and not have to play any cloggy combo pieces in our deck, likely still warrants a ban. However, there are still a number of factors that affect our likelihood of the dream “victory” that Sixth Sense can bring. For a start, the “once in every 6 games” statistic doesn’t include the fact that we only roll a 5 or a 6 off of Sixth Sense One Third of the time.

De Facto: Chances of Drawing & Rolling

It was mentioned earlier that you have about a 33% chance of rolling a 5 or 6 with Sixth Sense. Since the probabilities of Opening and Rolling are independent, we can multiply them together to find out how likely it is to: Draw sixth sense, on either the first or second turn, activate it, and then resolve a 5 or a 6.

This one is easy to calculate: 0.04538 (about 4.5%) in a 40-card deck, and 0.0524 (About 5%) in a 35-card deck. These numbers aren’t very hopeful at all. Realistically, with these figures, you’re only going to play out your dream roll on your first turn once every 20 games! Those odds are pretty dreadful.

I’ve heard another argument time and time again: “Uh, milling is just as good as drawing cards, and Sixth Sense mills cards, so it’s not a downside when you mill”. I’m going to address this straight away so that I don’t have to refer to it again:

Milling cards isn’t really a downside of Sixth Sense. That’s correct.

However, E(X), the expected mill of Sixth Sense, is only 2.5 cards [(1+2+3+4)/4].

A trap card that mills 2.5 cards on average, with no other benefit, is a straight -1. The fact that you might mill a card that has a graveyard effect – playing 10 cards with graveyard effects still only gives you a 50% likelihood of milling one useful card. On top of this:

You don’t get to choose the cards you mill.

You might mill a card that your deck needs.

You might mill a card that you can’t get back.

Sixth Sense is a Trap Card, so you have to set it first

Hitting a useless mill is a -1

Trap cards that make you lose card advantage generally aren’t very good

I hope you can now agree that, at the very least, the milling aspect of Sixth Sense is practically irrelevant.

With that out of the way, I’m now going to cover what the chances of drawing Sixth Sense on a turn later than the first turn of the game, since that’s all we’ve covered so far.

De Facto: Drawing on turns 3+

It’s important to remember that, at these late stages of the game, it’s possible that your opponent might have a response to your Sixth Sense, or even be able to destroy it on the turn it’s set; It’s quite possible that even if you draw Sixth Sense past this point, it might still be negated or get blown up before it can resolve.

For maximum likelihoods, I’m going to be covering the probability of opening Sixth Sense with an effective 35 card deck – So all of your draw spells count towards this limit.

Also, bear in mind that Pot of Desires is pretty likely to banish your one-of Sixth Sense!

Here are the probabilities of drawing Sixth Sense, then rolling a 5 or a 6, anywhere within the first 9 turns of the game:

Turn 1: 0.1429 (14%). You have a (~4.7%) chance of drawing it, then rolling a 5 or a 6.

Turn 2: 0.1714 (17%). You have a (~5.6%) chance of drawing it, then rolling a 5 or a 6.

Turn 3: 0.2000 (20%). You have a (~6.7%) chance of drawing it, then rolling a 5 or a 6.

Turn 4: 0.2286 (23%). You have a (~7.5%) chance of drawing it, then rolling a 5 or a 6.

Turn 5: 0.2571 (26%). You have a (~8.4%) chance of drawing it, then rolling a 5 or a 6.

Turn 6: 0.2857 (29%). You have a (~9.4%) chance of drawing it, then rolling a 5 or a 6.

Turn 7: 0.3143 (31%). You have a (~10%) chance of drawing it, then rolling a 5 or a 6.

Turn 8: 0.3429 (34%). You have a (~11%) chance of drawing it, then rolling a 5 or a 6.

Turn 9: 0.3714 (37%). You have a (~12%) chance of drawing it, then rolling a 5 or a 6.

Most of those numbers aren’t exceedingly useful, as past the first 3 or 4 turns of the game, as (If the game hasn’t ended by then) the fact that Sixth Sense is a trap card becomes increasingly relevant. Having to set a card, hope it doesn’t get blown up by an opponent’s set Mystical Space Typhoon, Galaxy Cyclone, Heavy Storm Duster, or Twin Twisters, really is an issue.

A lot of the time, it’d just be better to play a more useful card that can be searched. On top of that, it can easily be a dead card if your opponent can OTK you before you get to actually use your new hand of cards.

Even if you can make it to turn 7 without the game already ending, you still only have a One in Ten chance of drawing, then pulling off your 5 or 6 roll. That’s ignoring the chance of your opponent having an out. There’s one out in particular that sees a lot of play already:

De Facto: Cr(ash) & Burn

Ash Blossom & Joyous Spring. It’s a semi-new card, and a card that can completely shut down a Sixth Sense resolution. Just by discarding it – regardless of who goes first – your Sixth Sense it toadally nullified. What’s more, it’s a heavily sided (and even maindeckied) card in the current format – and likely most formats going forward.

If your opponent has 3 copies in their deck, in a 40-card deck they have a 0.3376 (34%) chance of opening it going first, and a 0.3943 (39%) chance of opening it going second. If they were ultra-lucky and managed to Maxx “C” you before then, it’s even more likely that they’ll draw into it.

Because of the existence of Ash Blossom, all of our previous statistics now change. I’m not going to rework all of the probabilities past the second turn, as the game changes too much after then. It’d be important to factor in other outs, like a set MST (Which can also destroy a set Sixth Sense turn 2), as well as the chance of Ash Blossom being used on something else, other than Sixth Sense.

We can easily use mean probabilities to work out the likelihood of drawing, flipping, resolving, and rolling a 5 or a 6 with Sixth Sense on either the first or second turn:

{[P(0.1429 ∩ 1- 0.3943) + P(0.1714 ∩ 1- 0.3376)] /2}*0.3333

= {(0.08655453 + 0.11353536)/2}*0.3333

= 0.1000*0.3333

= 0.03333 (~3%)

Three percent. Three percent. The chance of drawing, flipping, resolving, and rolling a 5 or a 6 with Sixth Sense within the first 2 turns in a competitive environment is three percent. That means that you’ll likely pull it off once every thirty three-games. That’s once every eleven matches.

I’d finally like to add that just drawing 6 cards doesn’t win you the game outright. Somebody who doesn’t know what he’s doing will very likely still lose. An opponent with an amazing hand could still beat you, and it’s possible that you’ll get OTK’d before you even get to use those cards.

Conclusions

It should still be said that Sixth Sense is a sacky card. But my point here is that it’s not a competitive one – the payoff is just too difficult to achieve. because of this, a Sixth Sense resolving should be seen as a very Timmy move – Drawing six cards is awesome …and because of the probability aspect, it’s fair.

It’s fun to do crazy things within the limits of Yugioh, especially when they don’t come up too often.

If you really want to argue that “Nobody should be able to end game on the spot, ever!”, I’d suggest that you also advocate to getting these cards banned:

And there are a lot more than that. As you can see, just because you can end the game with one move, doesn’t mean that doing so is consistent.

This is one of the main reasons that Sixth Sense is Proscribed on the Trinity Banlist – Proscribing it renders it unsplashable. If you don’t know what the Trinity banlist is, you should check out my previous article.

Until next time – Stay Groovy!