Out Play Your Opponents by Using PokerStove

Part 7: So when do we need to manually perform hand removal?

I can think of two situations where manual hand removal is necessary. The first is when calculating fold equity. Let's revisit this example from page 4.

We are facing a short stacker (40 BB) who is raising UTG at 6max with 55+/ATs+/KQs/AQo+. We have decided to flat with 8 8 and the flop comes 9 7 6. He bets 8BB into a 9BB pot (28 BB back). Is it profitable for us to shove 36BB in order to win the 17BB pot?

We determined that Villain has 7.8% of hands in his range by putting his range into PokerStove. This range, however, includes hands like 7 7, which is impossible given the board. In order to determine our true fold equity, we'll have to be a little more careful. So let's remove any hands that include 9 8 8 7 or 6.

We now see that Villain's range is only 6.8% of hands. Because of our hand and the board, we have actually removed 12.8% of his hands. His calling range is now 3.4% of hands, meaning that our fold equity is actually 50%, a fair bit higher than the 43.5% we came up with the first time around. Note that the equity calculation is still the same since PokerStove performs the removal automatically when calculating equity:

Thus our equity when called remains the same, but our fold equity improves. This means that our shove in this spot is actually:

Shove/fold: .5 * 17 = 8.5

Shove/call/win: .5 * 45 * .356 = 8.01

Shove/call/lose: .5 * -36 * .644 = -11.59

By removing the impossible combos, we calculated our true fold equity. It turns what looked to be a +1.9 BB shove into a +4.9 BB shove!

Another time when we need to perform combination removal is when we are making range vs. range calculations. Take a look at the above example, and let's say that we want to calculate our entire range's equity against Villain's equity. Let's say that the shortstacker is instead 125 BBs deep, so that our button flatting range preflop includes JJ-22, 76s+, T8s+, suited broadways, and A5s+. In this particular instance, we have 8 8, but we're curious how our entire stacking off range fares against Villain's stacking off range.

Again, Villain's range is 66+,AcKc,AcQc,AcJc,AcTc,KcQc. Let's say that our stacking off range is top pair or better, pair + open enders, and flush draws. But we know that the 8 and 8 are not in Villain's range because we have that hand. So the final calculation is (we are Hand 0):

We have to remove the cards manually because we don't want to consider them Dead (we want them in our range), but there is no other way for PokerStove to know that the hand is not in Villain's range. It still is not necessary to remove Board cards from Villain's range because that happens automatically.

Knowing our range's equity against our opponent's range can be important when trying to make a balanced play. Removing our blockers doesn't make a big difference in this case, but having a hand like QQ on a KJT flop cuts Villain's chances of having the nuts in half.

In practice, these situations come up somewhat rarely. Manually removing your cards and the board cards from an opponent's range is almost always unnecessary.