In a deck built around flooding the board with minions, I've noticed Hunters tend to be by far the largest issue, because in addition to having access to easy and cheap board clear, they also have unleash the hounds, one of the most insane 2 drops in the game. I personally have two decks, paladin and shaman, that are built around having a large number of small minions on the field.
Firstly a word of advice based on your commented deck list. If your do really enjoy flooding the board using your power, I would highly recommend you consider cutting down some on your four drops and increasing your number of three drops and maybe even two drops. The advantage of this is that, it makes you more likely to be able to use all your mana in a turn for maximum efficiency. For Instance:
- Turn 2: Use Power or play relevant 2 drop, depending on board state and opponent power.
- Turn 3: Play 3 drop
- Turn 4: Use Power and play relevant 2 drop, OR play 4 drop.
- Turn 5: Use Power and play relevant 3 drop.
Alright, regarding your specific issues against hunters, one of the best counters to unleash the hounds is high toughness taunt creatures, or having a number of taunt creatures. The big issue is that most hunter decks will be running 2 silence owls, so oftentimes they'll simply silence your large taunt creature, and then attack past it. Some possibilities to fill this role include:
Sen'jin Shieldmasta: Hands down one of the best taunt minions in the game, Sen'jin can usually eat up anywhere from 3-5 hounds from unleash the hounds, depending on how much support your opponent has for the unleash. In addition, Sen'jin is relevant against a large number of other decks unlike some other large taunt creatures. I would definitely consider running 2 of these if you tend to have issues against aggro decks. The big downside of him against hunter decks, as is the case with most bigger creatures, is he dies to a kill command.
Tirion Fordring: A very powerful legendary creature, if you have him, I would highly recommend running him, as he's hard to kill and still impactful upon dying. The big issue with him is that he is one of the biggest blowouts if he's silenced, just becoming a measly 6/6 for 8 if he is.
Abomination: Abomination is, in my opinion, a very underrated minion. He is amazing against Unleash the Hounds specifically, almost always clearing all the hounds on his own, in addition to any potential support your opponent might play, such as timber wolf and starving buzzard. The big downside of him for you is that he basically acts like an exploding trap, most likely killing all your token minions.
Defender of Argus: Defender of Argus is an amazing creature, especially for a paladin, who is easily capable of making sure he has the creatures to use it with. The big downside of him in this case is that if your opponent has Timber Wolf, their hounds will just trade for your 2/2 soldiers. I would still recommend at least running one of him in your deck, if not two, because there are many times that he is relevant.
Sunwalker: One of the hardest to straight out kill taunt creatures, sunwalker can be very impactful upon the board. The big downside of him is that he's highly susceptible to silencing, and is somewhat high costing, especially if he gets silenced.
Fen Creeper: Generally considered to just be a worse version of Sen'jin, he is still not a bad consideration to put in to the deck if you're having that much difficulty against hunters. The benefit that Fen Creeper has over Sen'jin is that he won't die to a single kill command, taking both a kill command and a hound to kill, and still eating up between 3 and 6 hounds if they don't have kill command.
Sunfury Protector: A tiny version of Defender of Argus, I would be hesitant to run this in your deck, since you're most likely going to have only small minions to use her with. Still, her ability can be very relevant, as she'll force your opponent to clear two of your minions before they can attack you.
Mogu'shan Warden: As a last ditch effort, if Unleash the Hounds is absolutely the bane of your deck, I would run Mogu'shan. He is often very irrelevant against opponents, but against Unleash the Hounds specifically, he is one of the best minions out there. Again though, he's not very good against most other decks.
Worrying about clearing the board of an unleash the hounds after their turn is less of a big deal, as you should probably be saving your consecrations for just such an occasion if possible. If that is a concern though, you can also add Avenging Wrath to your deck, as it's an excellent board clear against Unleash the Hounds, and in general, is just a rather good spell, at worst being 8 damage to the opposing hero for 6 mana.
Regarding the other aspects of the hunter, having big taunt creatures also helps to avoid your creatures' divine shields from being removed, by protecting the smaller divine shielded minions. In addition, divine shielding a Sen'jin Shieldmaster or Abomination can be pretty powerful.
In respect to the explosive trap, unfortunately, there's not many counters to it in a paladin deck besides playing around it, or using divine shields. If you're truly worried about it, consider doing little other than using your power until your opponent uses their first explosive trap. If you bait out an explosive trap, you can much more confidently attempt to establish board control by playing a number of cards from your hand after it explodes. Divine shields though do suffer from the issue of being easy to trade a small minion in to remove it. It is why I would probably not run Hand of Protection, but would definitely still run Argent Protector, as a 2/2 with 'Give a friendly minion divine shield' is pretty good.
Best Answer
TL;DR: Skip to the plot at the end of this answer, and to the simple approximation that follows.
(Aside: This question is probably more appropriate for mathSE than it is for Arqade. The math is quite involved.)
Caveat
I first want to make the obvious caveat: don't take these numbers too seriously. The probability that UtH+Buzzard is in the hunter's hand is entirely dependent on the previous cards played, and that player's playstyle. A skilled player would of course not rely on the numbers alone, but would have to take into account all previous turns and all previous cards played. It is complicated if not impossible to get actual numbers on this; no matter how much I take into account there will always be more to consider, and any calculation will be making some sort of assumption about the hunter's playstyle.
Example 1. On the hunter's turn 3, you have three 2/1's out, but he/she does not play UtH. More than likely he does not have UtH in his hand. Or maybe he is saving it, due to having both UtH and Buzzard in his hand. Regardless, the fact that he does not play UtH on this turn alters the probabilities in some way.
Example 2. On turn 4, the hunter plays down to 0 cards. Then you know of course that neither UtH nor Buzzard is in her hand. Thus from this point onward, you can no longer trust the probabilities in (for instance) MikeR's table; they are far too high, for they have not taken into account that the hunter received neither combo card all the way up through turn 4.
My point is that these probabilities (computed later in my answer) are merely a very rough estimation, and they do not take into account even half of the things they should. It also goes without saying that if at least one UtH or Buzzard has already been played (in combo or not in combo), the probabilities will be much lower.
Probabilities
The simplest case is that the deck contains no Tracking, and the player does not mulligan. In this case, MikeR is almost right. Suppose the hunter has so far seen x distinct cards. The probability that there is a starving buzzard and an Unleash the Hounds among these x cards (assuming 2 of each in the deck) is equal to the probability that there is a buzzard, plus the probability that there is an UtH, minus the probability that there is a buzzard or an UtH. This comes out to
You can check this answer is correct by verifying that it gives 0, 0, 1, and 1 when you plug in x=0,1,29, and 30, respectively.
With Mulligan
Let s be the size of the starting hand, and suppose the hunter threw away k cards in the mulligan. Let x be the number of cards drawn so far, including the starting hand, but NOT including the cards thrown away. Assume that the player will never mulligan away either of UtH and Buzzard.
For each card thrown away in the mulligan, there is a chance of approximately
(x-s)/(30-s)that that card is drawn sometime again in the x cards, and a chance of(30-x)/(30-s)that it isn't. (This would be exact, except that if one card is shuffled in among thex-scards, the next card is more likely to be among the30-scards, as it cannot be in the same place as the first. Nevertheless, this difference should be negligible for x not too low or too high.) We can therefore approximate the effect of the mulligan quite well by saying that the number of cards x is increased by(30-x)/(30-s)for each card thrown away. Then the probability we obtain iswhere
r = k*(30-x)/(30-s).With Tracking
In almost all cases, the effect of Tracking will be equivalent to "draw 3 cards", for purposes of finding the combo. The only case where it is not equivalent is when BOTH (a) the hunter so far has neither of UtH and Buzzard, AND (b) both UtH and Buzzard are picked up among the 3 cards. Unfortunately, unlike with discards from Warlock cards like Soulfire and Doomguard, cards discarded from Tracking are not visible to the opponent, or else one could deal with these special cases just by watching the discard. But, erring on the side of overestimating the chances the hunter has the combo, I will assume that this case is negligible, and thus Tracking always increases the total number of cards drawn/seen by 3.
Actually, things get a bit complicated here. Supposing that the hunter will always play Tracking if he/she has it (to try and fish for the combo), the fact that the hunter has not played Tracking would have to be factored into the probability above, and it has not. On the other hand, if the hunter does play tracking, then that may decrease the chances that he/she has the combo, because he/she is probably fishing. However, I will sweep this objection under the rug and say it is covered by the large Caveat at the start of this answer. In general, it shouldn't be far off to assume that playing Tracking increases the value of x by three.
Summary:
In order to compute an approximate probability that the hunter has UtH+Buzzard in his/her hand, at any given moment, first compute or take note of
x, the total number of cards drawn so far in the game by your opponent. Include the cards in the starting hand and cards drawn from Tracking or other card draw. Do not include the coin or cards drawn on the mulligan. An easy way to compute this is to subtract the opponent's remaining deck size from 30.
s, the size of the hunter's starting hand, not including the coin.
k, the number of cards thrown away on the mulligan.
r, defined to be equal to
k*(30-x)/(30-s).Then compute the probability using the formula we found:
Here are particular cases of this formula.
Here's a plot of the probability:
Dotted lines indicate starting with 3 cards (going first), and solid lines indicate starting with 4 cards (going second). Red, Blue, Green, Orange, and Purple indicate 0,1,2,3, and 4 cards tossed in the mulligan, respectively.
As you can see, it turned out that starting with 3 versus 4 cards made hardly any difference. You can also see how the effect of the mulligan is very apparent in the early game, but becomes less significant later when you are more likely to redraw the cards you tossed away. (What appears to be error in the green, orange, and purple lines for low values x may actually be correct; note that x has to be at least equal to s for the probability to be meaningful, so the probability need not be 0 when x=0. If there is any error, it is due to the approximation in the mulligan, and it should be virtually insignificant.)
Was this worth the work? Probably not. The probability is reasonably close to linear, and since we are only looking for a general heuristic, we might as well just say the probability is
x/30. If you use this formula, add(k/2)to x, where again k is the number of cards tossed in the mulligan. This is plenty of accuracy for the kind of thing you might need it for, and it has the large advantage of being easy to compute in your head.