In last month’s article, we examined various snowing lines and discussed several important principles that will increase one’s overall snowing efficiency. This month we will examine a potential snow after the 2nd draw and analyze the situation from the prospective of both players involved.
Consider a hand where Villain opens from the cut-off and Hero defends the big blind with 238QK. Both players take two cards on the 1st draw and Hero improves to 2358(5). Hero leads out on the flop, is called, and both players take a single card on the 2nd draw. On the 2nd draw Hero obtains an Ace and check-calls his opponent’s turn bet. Hero draws one and Villain stands pat on the 3rd and final draw.
Before deciding how to react with various holdings that we may make, we should first think about Villain’s range. In this situation, second to act, Villain can have any made low from a Seven to a Jack along with some possible snows. Since there was no raise on the flop, we can possibly discount very strong seven lows as many players will raise after the 1st draw with a premium draw such as 2357.
Thus, when Hero makes 85432, 86532, and 87532 he should probably tend to lead out as checking simply allows Villain to check back the weaker portion of his range. Villain needs to bluff catch with some theoretical frequency and some opponents will simply always call with their entire pat range due to the size of the pot.
Assuming Hero checks 98532, T8532, and J8532 how should he respond to a bet from a Villain? If Villain has never shown any proclivity to snow in this situation, the decision is easy and many players are satisfied just taking the free card and the draw one “coin flip.” Hero should simply fold as there would be no bluffs in the range and Villain is almost certainly not value betting worse.
However, when our opponent has shown the ability to snow what is the approximate game theory optimal solution on how often we should call? A precise answer would require some advanced software that probably does not exist. However, we can probably get a general idea of what it is from viewing the situation from the perspective of our opponent. Relatively speaking our strategy should be such that our opponent does not unduly profit from his snows and on the whole make him somewhat impartial between drawing to and snowing his rougher draws.
Hand from Villain’s Perspective
After Hero checks the turn there are 3.25 big bets in the pot. Villain has 3678 with a paired Six after the 2nd draw and is deciding whether or not to snow. In this specific case, Villain has 42% equity should he decide to draw and while he would not have this exact knowledge he will probably realize that on average he is an equity underdog.
The pot does not end on the turn thus one must also consider the impact of the river betting if the choice is to draw. In this case with the inferior draw but with position, we can expect the betting on the river to be relatively neutral. One old website calculated river expectations assuming both players played optimally and a 3678 with position was shown to reap a .02 big bet advantage over a super smooth 2347 draw.
Thus, with a paired Six and our opponent holding 2358, our advantage would be slightly greater than .02 big bets. However, it would not be a materially large amount and thus for this purpose of this example will just assume a river expectation of zero. Therefore, the EV of drawing is simply equal to 3.25 big bets * 42% equity = 1.37 big bets.
Now let’s move onto an estimation of the EV of drawing assuming that Hero chooses to lead with any of the Eights, check-calls 98532, and check-folds everything else.
● Hero makes an Eight 25% of time and will lead with it. Villain folds river and loses turn bet.
● Hero makes a Nine 11.1% of time and check/calls. Villain loses two bets, turn and river.
● Hero makes a ten or worse 63.9% of the time. Villain wins the turn bet plus the 3.25 bets in pot for a total of 4.25 bets
● EV = (-1)*(25%) + (-2)*(11.1%) + (4.25)*(63.9%) = 2.24 big bets.
As we can see, under these assumptions the EV of the Snow is greater by 0.87 big bets (2.24 - 1.37). This is a somewhat substantial difference and is that large because Villain’s win percentage increased from 42% to 63.9% while in the process also charging Hero the turn bet. If the turn bet had induced a break from a T8532 that was made on the 2nd draw, the win is even bigger as T8532 would have patted had Hero checked and 3678 only has 36% equity against that hand.
If instead Hero check-calls both 98532 and T8532 (made on last draw) the resulting calculations would be adjusted as follows.
● Hero makes an Eight 25% of time and will lead with it. Villain folds river and loses turn bet
● Hero makes a Nine or Ten 22.2% of time and check/calls. Villain loses two bets, turn and river
● Hero makes a Jack or worse 52.8% of the time. Villain wins the turn bet plus the 3.25 bets in pot for a total of 4.25 bets
● EV = (-1)*(25%) + (-2)*(22.2%) + (4.25)*(52.8%) = 1.55 big bets.
When Hero is a bit stickier with his calls and includes T8532, the EV of the snow decreases yet Villain still does around 0.18 big bets (1.55-1.37) better snowing as opposed to drawing.
Concluding Thoughts
In the above example, we only looked at the mathematics of one specific situation yet we can probably draw some useful conclusions. While the results will vary among different hands and ranges it appears highly likely that the approximate breakeven hand to call down with is either a Ten- or Jack-low.
From the viewpoint of the snower, this play is very effective when used in the proper situations and not overdone. We should only snow the very worst of our one card draws such as one card Nines and very rough Eights. Pairing cards along the way increases the probability of success therefore when having seen multiple pairs or possibly trips of a rank we may even fare better snowing a hand such as 2578 as opposed to drawing.
The profitability of snowing is highly player dependent. If a player does not call with a low worse than a Nine, the play is printing money. Some players may not even call with their Nines while others will always call when they make at least a Jack thus choosing your targets wisely is crucial. Another important player read to carefully note is how your opponents handle made hands such as 86532 and 87532. If they tend to check-call these holdings, the expectation of a snow will decrease because an extra big bet will be lost when they make these hands.
When potentially being snowed in this situation, in theory you need to call with at least a Ten-low in order to prevent Villain from profiting way too much on his snows. However, we should keep careful notes on our opponents and look to play exploitatively. If an opponent never snows in this situation there is no need to keep flicking in the chips only to continually look at strong hands. Your opponent doesn’t know what you caught thus may never know you are folding hands as good as Ten-lows.
Against an unknown but possibly capable player it is generally a good idea to call down with at least a Nine-low. However, in all cases we need to be cognizant of the play throughout the hand in order to make the best decisions. If our opponent raised us on the flop and drew one, he probably has a very strong draw and thus few or no snows. His range will also usually be strong if he raised from early position and initially drew one card. We should be much more suspicious of Villains that originated from a steal position.
In the next issue, we will examine another possible snowing situation on the turn where one player was behind 2-1 on the 2nd draw yet decides to raise or check-raise and stand pat as a bluff.
