Tournament Vs. Cash Game Play and Direct Pot Odds: Rule of 4/Rule of 2
Poker is a game of mathematics, and the ability to utilize the math to make players make errors that, over time, make them unprofitable and you profitable. In a cash game, these percentage point differences can be the difference between a yearly profit of $10,000 and $100,000. In a tournament, however, you can’t (unless it’s a rebuy tournament) pull a wad of bills out of your pocket and rebuy; if you bust, you’re done. The reason I bring this up stems from a classic example of the differences in thinking between a cash game player and a tournament player. Take a look at the following examples.
You’re in the first hand of a cash game, blinds $5/$10. You have $1,000 in chips. You look down at two queens in the big blind, but before you can begin to think of what to do with the hand, the man under the gun declares himself all-in for $1,000. Everyone folds to you, and as the small blind folds, the man flips over AKs, thinking the hand is over, and immediately realizes his error, putting his cards back under his protector. Do you call?
You’re in the first hand of a tournament, blinds $5/$10. You have $1,000 in chips. You look down at two queens in the big blind, but before you can begin to think of what to do with the hand, the man under the gun declares himself all-in for $1,000. Everyone folds to you, and as the small blind folds, the man flips over AKs, thinking the hand is over, and immediately realizes his error, putting his cards back under his protector. Do you call?
You probably noticed that the two paragraphs are verbatim except for a single change, the terms, “cash game” and “tournament” switched. The thing is, even with the correct pot odds to call, it may actually be correct to fold the queens in one situation! Let’s discuss this paradox of thinking. In the cash game, the call is automatic; your queens are a 54/46 favorite, and the 4% advantage you’re given makes this a +EV play every time. 54% of the time, you double up; 46% of the time, you grumble and fish out another $1,000 from your pocket. In a tournament, though, the decision is based on a number of factors. Are the blinds escalating quickly? Are you one of the better players at your table? Is the outcome of this tournament going to affect you critically financially? Is the tournament important or prestigious to you? If this happened at the WSOP Main Event, for example, are you willing to bust out in the first hand as only a 54% favorite? A professional’s opinion of this situation depends on the player, but a large majority are going to be tossing those ladies in the muck. Facing a slightly favorable coin flip for a double up, or folding and having 99% of their stack intact to play their normal, profitable game, professionals realize that doubling your starting stack is nice, but not critical to making deep runs in tournaments in the early stages.
Having touched on odds briefly in the previous paragraph, we now turn our attention fully onto pot odds. Direct pot odds are the odds you are being given in comparison to the amount of money in the pot. An easy way of visually understanding this is with the following:
Pot Size- $150
Cost To Call- $50
Pot Size After Calling- $200
Your Pot Odds- $200:$50 or 4:1
Now that you have an understanding of how to calculate pot odds, you can use them to help make decisions on hands based on your pot odds. We’ll start with a basic example, and work up to some more complex examples later in the article.
You’ve limped into a pot with J10o that contains $100 with 3 other players. You flop an open ended straight draw (9h 8s 2c) and your opponent bets $25. the other two players fold to you. You both have about $1,100 in your stacks.
What are your odds? The pot after your opponent bets stands at $125. If you call, the pot will contain $150, so your pot odds are $150:$25, or 6:1. What does that mean? Basically, if you think your hand has a 1:6 chance of either currently being or being able to draw to the best hand on the next card 16.6% of the time, you should call.
What are your odds of improving your hand? Well, first of all, we should be completely certain that we do NOT have the best hand. The only hands we technically beat right now are 107 and 76, but we’ll discard them for the purposes of this question. We know that a 7 and a queen give us the nuts, so those are each 4 clean outs, so we currently have 8 outs. What about if we hit a jack or 10? We’re not as certain that those count as outs, so we’ll count them as roughly 2.5 outs each, to discount the times our opponent is holding hands like 22, J9, or 98. That means we have an estimated total of 13 outs. How do we know the probability of reaching these outs by the turn or river? We utilize a concept known as the Rule of 2/4.
Rule of 2- With one card to come, multiply the number of outs you have left by 2. This gives you a rough estimate of the probability your hand will improve in a single card. In our first example, the probability our hand will improve by the turn is 13*2=26%.
Rule of 4- With two cards to come, multiply the number of outs you have left by 4. This gives you a rough estimate of the probability your hand will improve with two cards. In our first example, the probability our hand will improve by the river is 13*4=52%.
How do we utilize this knowledge? Without going into more advanced concepts (implied odds, payoff boards, obvious draws, etc.) and simply looking at the math, this becomes a clear call, and possibly even a raise if you’re a more aggressive player. Your odds of improvement are greater than the pot odds being given to you, and if you look at the rule of 4, if your outs are indeed 13, you’re actually the favorite in the hand against a single pair! You can happily call and take a card here, with correct odds to draw.
You’ve called a raise with A3h into a pot that contains $1,500. You flop the nut flush draw (6h 2h Kc) and your opponent bets $1,500. You have exactly $1,500 left in your stack, and will be all-in if you call.
What are your odds? This time, the pot contains $3,000 after the bet. If you call, there’s $4,500 in the pot, so your pot odds are $4,500:$1,500, or 2:1. This time, you need to have the best hand 33% of the time by the river in order to make the call.
What are your odds of improving your hand? With a nut flush draw, you have 9 outs if the board isn’t paired, as paired boards generally kill a few of your outs. This board is not paired, and contains very few two pair combinations; a set would kill the Kh, but we can discount that enough of the time to give yourself the full 9 outs. What about the 3 remaining A’s? Since he raised, he could very well have AA, AK, a set, or even A6/A2. I’m inclined to give an A about 1.5 outs here, because the evidence is a bit grim as to whether your ace is a valid out. Now, we use the Rule of 4 to determine the odds of improving our hand. (10.5*4=42%)
How do we utilize this knowledge? Since the odds that the pot is laying us (33%) are lesser than the odds we are being given by the Rule of 4 (42%) by a good margin, this is a call, even knowing that we are very likely behind. The dead money in the pot forces our hand into calling, here.
You raised preflop to $325 with 10d10c, and were called by the big blind, an extremely tight, but aggressive player, making the pot $700. You flop an over card (Kc 7h 5h) and the big blind shoves all-in for $500. If you call and lose, you’ll be down to $1,200, or 12 big blinds.
What are your odds and odds of improvement? First, you can puke a little bit. 
Now then, let’s take a look at your pot odds. It costs you $500 to win a pot of $1,700, meaning your pot odds are 3.4:1. You need to be winning this pot roughly 30% of the time by the river to justify a call now. But, what can we beat? This requires a bit of math on our part, and some good deduction skill on yours. This guy is tight, but is also a bit short, so he may be willing to move in here on the flop with just a flush draw. He could also be making this move with JJ or QQ, deciding to take a flop and shove any flop that seemed uncoordinated or if just one over hits. I still have to put the odds he holds a king here at around 70%. He also can be doing this with a set of 7′s or 5′s, but I only give him about 5% odds of holding that. The two play the same against your tens; you have 2 outs twice to improve, or about an 8% chance of improvement. Now, let’s look at the other two options; a smaller pair and a flush draw. The 66, and 88-99 possibilities seem a bit more plausible for a tight player than suited cards, so we can put that at around 20%, and the flush draw at 5%. The pairs have about a 8% chance of improving, using the rule of 4, and the flush draws (we’re going to assume that, since the player is tight, it can only be the nut flush) have 13 outs, meaning they have a roughly 52% chance of improving to beat you. Whew. We now have to compute the of each of your winning chances in all of the possible scenarios as a factor of 100.
He has a king, set, or JJ/QQ. 75% of the time, you win 8%. (.75*.8=.06) or 6%.
He has an under pair. 20% of the time, you win 92%. (.2*.92=.184) or 18%
He has a flush draw. 5% of the time, you win 48%. (.05*.48=.024) or 2.4%
How can we utilize this knowledge? The odds we have of winning this pot are about 26.4%, meaning we’re not quite getting the pot odds needed to make this call. It’s close, but a few other factors are working against us, here. The stack you have left if you fold, $1,700, is still a bit flexible at the 50/100 level; you have an M of over 11, and can maneuver a little and make some plays. $1,200 gives you an M of just 8, which gives your stack less resteal value and forces you to play more straightforwardly. Even given this information, I think I lean slightly towards calling, here.
Pot odds, while seemingly complicated, become natural as they are utilized more and more often in tournament play. Use them to get a better idea of whether or not a questionable decision is actually a profitable play. The Rules of 2/4 are immensely helpful in quickly calculating odds for drawing hands, as well. Keep honing them often enough and you can use them to add profitability to your game.