Let's start with a bland deck: six cards for each colour with one pip each, one card for each colour with two pips and five multicolour cards with two pips each. That means that for any colour there are eight cards with one pip in that colour (six single colour and two multicolour) and one card with two pips. The character with this deck is trying an easy task (requiring one pip) and has a score of two in the skill in question. He can thus draw two cards.
The chances of not getting any success at all are (31/40)*(30/39), or 59.6%. There is thus a (slightly more than) 40% chance of success.
The task gets more difficult; now the character is facing an average task (requiring two pips). He can still draw two cards; there are two ways in which he can have a success; either draw two cards with one red pip (possibility A) or draw the card with two red pips (possibility B).
Possibility A: (8/40)*(7/39)= 3.6%
Possibility B: 1-(39/40)*(38/39)=5%
Total possibility: 8.6% - a drastic reduction. But then, the character only has a level of one in the skill.
Difficulty stays average, but now the character has level 3 in the skill; the player can draw three cards. Computations get a bit more difficult now.
There's again the two possibilities described above.
The chance that the card with two pips is drawn now rises to 1-(39/40)*(38/39)*(37/38) = 7.5%
Let's split the chance for possibility A into the chance that the player draws three pips (I mean, three cards with one pip) and the chance that the player draws two pips. The chance for three pips is (8/40)*(7/39)*(6/38)= 0.6%
The chance for two pips is (8/40)*(7/39)*(32/38)*3! = 22.7%
Total chance is thus 31%
This gives some idea for the chances. Things start changing when the player would decide for instance that the character is a very good fighter, and thus puts twenty red pips into the character's deck, and reduces blue and white pips to five each. Chances also depend on how those red pips are divided; twenty cards with one pip each give the player a 50% chance with each card drawn that the card has a red pip, but with fewer cards but more pips per card there is a chance that the character can succeed in very difficult tasks.
Imagine that a character has a combat skill of 3 and has to fight a monster with a defense of 4. If the character's deck has 20 cards with one red pip, the character will never be able to overcome the monster alone, even though he has an even chance of drawing a red card with each card he draws. However, if the character has five cards that each have four red pips (like Flame Wave), he has a decent chance (33.8%) to kill the monster, even though only one in eight cards drawn has red pips. If the deck contained ten cards with two red pips each, the chance would have been 28.5%.
So it seems that if you want to succeed often at simple tasks, you should spread your pips. Get many cards with just one pip. If you want to have a decent shot at difficult tasks, however, put a few cards with more pips in your deck.
In the above analysis we left out the effect of cards with the same theme as the challenge. If a character often dealt with goblins (as shown by an amount of goblin cards in his deck) and now has the task to spy on them, successes are not only generated by cards with black pips, but each goblin card also counts for one success. If the player would have a Marsh Goblin card (cost: BR) in the deck, the card would be worth two successes; one for the black pip and one because it's a Goblin card.