Betting for protection has a negative rep in the poker community. The concept of betting for protection is betting to fold out your opponent’s share of equity in a pot; i.e. you bet and they fold a gutshot instead of checking and giving them a chance to hit. I was recently reading the book Easy Game, and the author Andrew Seidman claimed betting for protection is a consequence of betting for value, not a reason for betting. I’m going to provide a mathematical argument for why betting for protection is very legitimate.
Say your opponent has a gutshot on the turn. They have 4 outs to the best hand, about an 8% chance to win on the turn. So if the turn pot is 17 bbs, then their share of the equity is 1.1 big blinds. However, their 8% share of the equity is worth more than 8% of the pot. When they hit the gutshot, they can value bet on the river for 2/3 pot and it ends up costing us an extra 11 bbs. So really their equity is 8% * 1.66 – so 1.8 bb’s. So their equity including their turn bet in a percentage of the pot is 13%. Say they have a 9 out draw and you plan to call a river bet no matter what card comes – now the value of their draw goes from 18% to 30%. Overall this is a moderate difference, but not necessarily enough to get you to bet solely for protection.
But what about if they have a gutshot on the flop and we plan to pay off turn and river bets when we check back? Assuming the pot will be 7 bb on the turn and 17 on the river, that means we have to pay an extra 17 bb to reach showdown. Now their 4 outs on the flop will be worth 24 bbs when they hit on the turn: 7 bb for the pot and 17 bb of value bets. They are going to hit their draw about 8% on the turn, so the value of their free card can be expressed as 8% * (24/7), so 27% of the pot on the flop. Say they have 6 outs, then it is worth 41% of the pot. If they have 8 outs, the free card is worth 54% of the pot. You might be giving up more than you realize when you check the flop back with a medium strength hand.
Let’s say we bet and our opponent has 6 outs to the best hand. Our opponent might fold with only 6 outs, but if they call they are putting in 5 bb to win 12 bb, so they are getting 2.4:1. Since we already determined our hand was worth 2 bets by checking the flop planning to call turn/river let’s say that when they hit they collect our turn bet, but when they miss they fold on the turn. So when they hit they win another 12 bb about, so their implied odds are 24:5, so about 4.8 to 1. Their odds to hit the turn are 7:1, so by betting we take them from having a situation where they are entitled to 41% of the pot or one where they have to either fold or make a -EV call. That means we are earning 41% of the flop pot versus their hand or more if they decide to call. In a 7 bb pot, this is 2.9 bbs, so that’s a great result for us.
Betting for protection is an important factor in determining what the best line for your hand is. The value of protection is higher on the flop than on the turn because the implied odds given to your opponents are better. When you start giving your opponent free cards you are giving them not only a chance to win the pot if they hit but also a chance to extract value bets from you. To make this a profitable trade-off you need to be pretty certain that they are going to bluff on future streets in a way that is advantageous for you.
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