Raising as a Means of Cutting Down Opponents' Odds

To illustrate this important point, we'll examine a hand from five card draw poker. You have a pat flush; the player to your right has nothing at all, and the player to your left has two pair. For the purposes of this illustration, we'll assume you know exactly what both opponents have. We'll also assume the betting limit is a flat $10 but that somehow a $100 pot has been created before betting gets under way. With the cards out, we'll say the chances of the two pair improving to a full house are 9-lo-l against. In other words, the player behind you will improve to the best hand one out often times on average.
With absolutely nothing, the player to your right bets $10 in an attempt to steal that big pot. You know this player will fold instantly if you raise, and you are fairly sure the player behind you will fold too. However, if you just call the $10, the player behind you will also call. Consequently, you may win $120 plus perhaps another bet at the end if you call, whereas if you raise you'll most likely have to make do with the $110 already in the pot. Should you call or raise?
The answer, of course, is you should raise, but let's look at the problem logically. The opponent with two pair is a 9-to-1 underdog. If you call, there is $120 in the pot. He would be getting 12-to-1 from the pot for his call when the odds against his making the best hand are only 9-to-1. Therefore, if you call and he calls behind you, he is making the correct play, the play with positive expectation. He will lose $10 in nine hands out of ten on average, for a total loss of $90, but he will win $120 in one hand out of ten for a net profit of $30. He gains on the play, and according to the Fundamental Theorem of Poker, any time your opponent gains, you are costing yourself money.
On the other hand, when you raise, making it $20 for the two pair to call, you are cutting that player's pot odds from $120-to-$10, or 12-to-1, to $130-to-$20, or 61/2-to-l. Since the two pair is a9-to-l underdog and is now getting only 61/2-to-l from the pot, you have made it correct for the two pair to fold. If he plays correctly and does fold, you do better, as we shall see presently, than if you had played incorrectly and allowed him sufficient odds for a call. However, if the two pair plays incorrectly and calls after you raise, you do best of all, because when an opponent makes a mistake, you gain. What your raise did was to reduce correct odds for a call into incorrect odds for a call. The curious effect of this turnabout is that although you raised to drive the two pair out, you are rooting for him to call after you raise.
To prove this point, let's see what happens over ten average hands if:
1. You call, and the two pair calls behind you.
2. You raise, and the two pair folds,
3. You raise, and the two pair calls your raise.
If you call and the two pair calls, you will win nine out of ten hands. Assuming you check after the draw and don't pay your opponent off the one time he makes a full house, you will win $120 (the $110 already in the pot - not counting your own $10 call - plus the two pair's $10 call) nine times for a total of $1,080, and you will lose $10 once. Your net profit is $1,070.
If you raise and the two pair folds, you will win all ten hands, which at $110 per hand comes to $1,100. You win $30 more than you would if you called and the two pair overcalled.
If you raise and the two pair calls, you win $130 (the $110 already in the pot plus the two pair's $20 call of a double bet) nine limes for a total of $1,170 and lose $20 once for a net profit of $1,150. You win $80 more than you do when you call and the two pair overcalls and $50 more than when you raise and your opponent folds.
Taking the $1,100 profit as the norm (since both you and your opponent play correctly in that case), we can say you lose $30 over ten hands or $3 per hand when you play incorrectly and only call, and you win $50 over ten hands or $5 per hand when your opponent plays incorrectly and calls your raise. To repeat, when you raise to drive people out, you are actually raising to cut down their odds. If they fold, that's fine, but sometimes you have cut their odds to a point where you are rooting for them to call after you raise, In no-limit games you can control the odds you are giving your opponents by the amount you bet, and you frequently find yourself rooting for them to call your raise even though you would be rooting for them to fold if you had just called.
Of course, it is correct just to call, as I did in the no-limit hold 'em hand of Chapter Three, when you know your opponent will fold if you raise but would make a mistake by overcalling if he knew what your cards were. You want to give your opponent every opportunity to make a mistake since that mistake is your gain even if he happens to get lucky and win an individual hand because of that mistake. In poker as in any game of skill with an element of chance, you cannot play results. That is, you cannot judge the value of a play because of the way it works out in a specific instance. In backgammon, for example, it's possible for a player to make a mistake or a series of mistakes that results in a hopeless position from which he can extricate himself only by rolling double six. The odds against rolling a double six are 35-to-1. If the hapless player happens to roll that double six and go on to victory, you cannot say he played the game correctly, anymore than you can say a person who puts his money on number 20 on the roulette layout plays correctly when number 20 happens to come up. Both players were just very, very lucky.
To summarize this section, when you raise to drive people out, you are really cutting down their odds. So you should raise with what you think is the best hand only when opponents are getting good enough odds to overcall or when you think an opponent will call a double bet even though he shouldn't even call a single bet.