Thinning the field involves the notion that sometimes it is better to have fewer opponents even though you may have the advantage over each of them. It's unclear how this arose, but by looking at the hands that are often "protected" this way, which often involve high pocket pairs, it may be from an overemphasis on bolstering the win rate of these hands. Often, people feel entitled to some degree when they get these strong hands dealt to them. Although it is normal for even the strongest starting hands to get beaten fairly regularly, they often feel cheated when this happens, and want to prevent this, regardless of whether it decreases their overall profit ratio with these hands.
In any case, today we'll look at whether this is ever a good idea. The philosophy of thinning hands runs deep in the poker establishment though, almost to the point that arguing against it is seen as almost heretical. As you will see though, there's no arguing with the numbers, and the doctrine of thinning the field, which holds that sometimes it is preferable to be in a hand with fewer opponents, and seek to get rid of hands to which we have the advantage, is neither supported by common sense nor mathematics.
It is true that there are some cases where our win rate will take precedence. If you are down to your last chips, whether in a tournament or cash play, then whether you win or lose the hand will obviously be of higher concern. In the overwhelming majority of cases though, it is not win rates that we seek, it is profit maximization, and this must be our exclusive focus.
In seeking to thin the field, it is true that there are benefits to raising certain amounts. Whether raises are appropriate isn't the topic today though, and they certainly have their place in profit maximization. However, this is not what is being addressed here, as we are focusing on the preference toward lesser opponents as being held as a benefit.
For starters, wanting to thin the field is counterintuitive, when we realize that it is loose games which we seek. We normally want players in our hands with weak holdings, and attempting to thin the field will serve to eliminate the weakest. This cannot be a good thing, as our very profit is a function of the advantage we have over our opponents, whereby we can entice them to place or call bets at a mathematical disadvantage to us.
Let us look at the numbers though. We'll take the almighty pocket aces, which a lot of people agree need to be "protected" by thinning. The thinking is that we don't want these weaker hands getting lucky against us, so we'll cut them down and increase our win percentage with them. However, if in doing so we decrease our expected value in terms of profit, then it's obviously going to be a mistake to seek this goal.
In these example, we'll take the winning percentage with a hand versus a certain amount of opponents, with hands played out to the end, with one bet per round, and see which amount of opponents provides the most profit per hand.
Opponents Win % Net Gain
1 85 3
2 74 5
3 64 7
4 56 7
5 50 8
6 44 8
7 39 9
8 35 9
9 31 9
As we can see, the amount we win as the opponents increase doesn't go down, it goes up. Here's the kicker though. This example is against all random hands, where in reality the hands we'll be eliminating are the worst ones of the bunch, where the better hands will be kept. The first hand we eliminate, in other words, isn't going to be an average hand, as in the above example, it's going to be one of the worst ones. And the next will be one of the worst ones left, and so on. This will skew the results even further toward not running the weaklings out of the pot.
Again, the reasoning behind this is that we need to have a preference for keeping people in the pot if we have an advantage over them. This means that we are the favorite to win a bet with them that we will beat their hand, so we want to bet with them. Again, this is why we want to play against bad players, who will call us down with inferior hands. We don't want these inferior hands to fold, as better players would tend to.
Now, as was said, this is independent of the natural folding that will occur as we bet and raise to the degree that it is desirable to do in order to make the most money with our particular hand. However, it is making the most money that we need to focus on, not running people out of the pot so we can pat ourselves on the back and rake in the chips, a strategy which will have us raking in less chips in fact.
In any case, today we'll look at whether this is ever a good idea. The philosophy of thinning hands runs deep in the poker establishment though, almost to the point that arguing against it is seen as almost heretical. As you will see though, there's no arguing with the numbers, and the doctrine of thinning the field, which holds that sometimes it is preferable to be in a hand with fewer opponents, and seek to get rid of hands to which we have the advantage, is neither supported by common sense nor mathematics.
It is true that there are some cases where our win rate will take precedence. If you are down to your last chips, whether in a tournament or cash play, then whether you win or lose the hand will obviously be of higher concern. In the overwhelming majority of cases though, it is not win rates that we seek, it is profit maximization, and this must be our exclusive focus.
In seeking to thin the field, it is true that there are benefits to raising certain amounts. Whether raises are appropriate isn't the topic today though, and they certainly have their place in profit maximization. However, this is not what is being addressed here, as we are focusing on the preference toward lesser opponents as being held as a benefit.
For starters, wanting to thin the field is counterintuitive, when we realize that it is loose games which we seek. We normally want players in our hands with weak holdings, and attempting to thin the field will serve to eliminate the weakest. This cannot be a good thing, as our very profit is a function of the advantage we have over our opponents, whereby we can entice them to place or call bets at a mathematical disadvantage to us.
Let us look at the numbers though. We'll take the almighty pocket aces, which a lot of people agree need to be "protected" by thinning. The thinking is that we don't want these weaker hands getting lucky against us, so we'll cut them down and increase our win percentage with them. However, if in doing so we decrease our expected value in terms of profit, then it's obviously going to be a mistake to seek this goal.
In these example, we'll take the winning percentage with a hand versus a certain amount of opponents, with hands played out to the end, with one bet per round, and see which amount of opponents provides the most profit per hand.
Opponents Win % Net Gain
1 85 3
2 74 5
3 64 7
4 56 7
5 50 8
6 44 8
7 39 9
8 35 9
9 31 9
As we can see, the amount we win as the opponents increase doesn't go down, it goes up. Here's the kicker though. This example is against all random hands, where in reality the hands we'll be eliminating are the worst ones of the bunch, where the better hands will be kept. The first hand we eliminate, in other words, isn't going to be an average hand, as in the above example, it's going to be one of the worst ones. And the next will be one of the worst ones left, and so on. This will skew the results even further toward not running the weaklings out of the pot.
Again, the reasoning behind this is that we need to have a preference for keeping people in the pot if we have an advantage over them. This means that we are the favorite to win a bet with them that we will beat their hand, so we want to bet with them. Again, this is why we want to play against bad players, who will call us down with inferior hands. We don't want these inferior hands to fold, as better players would tend to.
Now, as was said, this is independent of the natural folding that will occur as we bet and raise to the degree that it is desirable to do in order to make the most money with our particular hand. However, it is making the most money that we need to focus on, not running people out of the pot so we can pat ourselves on the back and rake in the chips, a strategy which will have us raking in less chips in fact.
