"How much do I have to raise?"

Last night I was playing at Mandalay Bay. My most profitable hand of the night, by far, was this: A straightforward player open-raised from second position to $10. I was one off the button, but by the time it got to me the player to my left had his cards in hand, cocked, ready to muck, so I knew I effectively had the button for this hand. There had been two callers ahead of me. I had 8-10 offsuit. I decided to take a flier here.

Good thing I did. The flop was 8-8-6. Bingo! The pre-flop raiser's range was already pretty much defined as being either a big pair or a big ace, because of his unimaginitive style. I hoped for the pair, of course, because with something like A-K he'd likely fire once, then give up unless he improved on the turn. He bet $20. One middle-position player called, as did I. No need to tip my hand yet, nor chase away the guy in the middle, who probably had some middling pair. Turn was an offsuit 3. Original raiser fired another $25. Middle guy bowed out. I decided to milk it further, and smooth-called him again. Let him think I'm on a draw with something like 4-5 or 5-7, or perhaps have pocket 9s or 10s and don't credit him with a bigger pair.

River was the case 8, giving me quads--and, if my assessment was right, giving my opponent a full house for which he would pay dearly. He bet $25 again. I raised to $75. He called so fast that I wished I had pushed for more, but oh well. I showed my 8-10. He flashed his pocket jacks before disgustedly throwing them away.

He had arrived with a friend, who was sitting on his left. I overheard pieces of their subsequent conversation. He said, roughly, "Once he flops trips, I can't blame him for playing it the way he did. But why would he call the $10 in the first place? What I want to know is, how much do I have to raise to get rid of the people with crap hands like that?"

Of course I don't call every pre-flop raise with junky speculative hands. But I do sometimes when the situation seems favorable for trying to hit a well-concealed monster, as here. I had a player whose range I could narrow down to just a few possibilities, one who I believed would pay me off if I hit (he had bought in for the max, so was plenty deep to be worth trying to bust), with position, with a solid table image that would make my actual hand unthinkable, and with a couple of other people having called ahead of me to start swelling the pot. That is what I consider a nearly perfect alignment of the stars to try to hit the big one.

I wonder if my opponent really thought through his question and its answer. If his goal is to be extremely confident that he will drive away all the junk hands that might call and draw out on him, then he could, of course, open-shove. But in that case he'd only get called by the hands that had him in terrible shape: K-K, and A-A, maybe Q-Q if somebody was feeling brave. When nobody had one of those, he'd win the $3 in blinds. Win $3 or face an 80% chance of losing $300--not a pleasant pair of prospects. He could be less drastic and raise to, say, about $50, but the effect would be essentially the same. He'd shoo away all the speculative hands, get raised by the bigger pairs, and have to fold, so his choice would be losing $50 or winning $3. Again, not exactly optimal poker.

Actually, the whole premise of his question is wrong. You do not want to chase away all of the opponents who have lesser starting hands that you hold. You want at least some of them to call your raise and stay in. Their failed attempt to improve to better than what you have is what generates the profit from big pairs.

So how about the other extreme, just limping in? Well, that tends to start a cascade effect that nets you seven or eight opponents and a small pot, which, again, is hardly the optimal situation. There has to be a happy medium.

Mike Caro addressed this a few years ago in what was for me an eye-opening Bluff magazine column titled, "The flawed concept of thinning the field," available online here. For every hand there is a mathematically optimal number of opponents, in terms of maximizing profit--and it is rarely just one, though that's the situation that usually makes post-flop play easiest. Whatever the theoretically optimal number of opponent is, however, that's not always the number you actually want in real-world situations. You prefer keeping in weaker players and driving out the stronger ones. All else being equal, you would also prefer keeping in the ones on whom you have the positional advantage and shooing away those who are behind you. Like with most things in poker, the number of opponents that you want when you're holding a strong starting hand depends on a bunch of different variables.

During my first year of playing in Las Vegas, I experimented with different pre-flop opening raise amounts, trying to find the optimal balance between keeping-in and driving-out. What I eventually homed in on was a formula that I've never shared here before. For a $1-2 no-limit hold'em game, I start mentally counting with $6 if the under-the-gun player folds and $7 if he limps in. I then add $1 for every subsequent player who folds and $2 for every player who limps. So, e.g., if I'm fourth to act and there have been two limpers and one folder before me, the raise amount will be $10. If I'm on the button in a ten-handed game and everybody has limped in ahead of me, that's seven players, and the raise will be to $19. If I'm in the big blind and everybody has limped, it will go to $23. Those big raise sizes don't happen often. It usually works out to between $8 and $16. If I'm under the gun, I make it either $7 or $8, depending on my mood. If there is a straddle, I usually add $4 or $5 to the amount. If there is a raiser and I'm inclined to reraise, I don't use any formula, but fly by the seat of my pants. The formula is adjusted but similar for $1-3 games.*

The reasoning is that, all else being equal, you want to raise more when there are already more people in the pot, and you want to play bigger pots when you're in position than when you're out of position. My formula accomplishes both goals rather nicely. There isn't any perfect formula, and I have to tweak it some depending on the table's propensities, but I have found it to be a extremely useful way of balancing the competing considerations without having to expend a bunch of mental energy selecting a bet size when I really want to be paying attention to my opponents' reactions. It also has the advantage that it looks fairly random to opponents, because there is no way they can watch me over enough hands to deduce what the formula is. I have to say, it has served me well. It may sound overly complicated, but it's really quite simple and has become completely automatic for me.

Key, of course, is that the raise size does not depend on the hand strength. If I'm raising from the button, the raise will be the same whether I'm doing it with A-A, J-J, 2-2, K-Q, 7-8, or 2-4. Whether I raise is not subject to any formula, being completely situational, but the size of the raise is determinate. Of course, opponents don't know that, and they frequently assume that my variable raise sizes are reflecting different hand strengths. Occasionally a player who fancies himself sophisticated and attentive will even say out loud something like, "I noticed that you made it $10 when you had jacks and $15 when you had aces. I'm on to you!" Yeah--good luck with trying to use that, Skippy.

A necessary result of this scheme is that sometimes I'm stuck with a small initial raise from early position, and a whole bunch of callers. But, frankly, I'm OK with that. I don't really want to be playing from out of position through the whole hand anyway, so if I don't improve on the flop, the fact that I've put in only a small amount of money makes it psychologically easier for me to give up on the hand, which is probably how it should be.

I do not, however, have as a goal to drive out every opponent who has a junky, speculative hand, the way the guy from last night seems to want to do. In the long run, I pay my bills when weaker opponents with weaker starting hands keep putting money into the pot with little more than "that hope which springs eternal in the human breast." (Brownie points for the first reader who can identify both the proximal, popular source of that quotation and what classical work it was alluding to. It's cheating to use Google.)

The answer to his question is this, in a nutshell: You're asking the wrong question. What you seem to need more work on is recognizing when you're beaten, so that you stop throwing away additional money. If you can do that more consistently than your opponents, you will deny them the proper implied odds for chasing your jacks with their 8-10 offsuit and similar crap hands. At that point, you have the best of both worlds: You'll make money when opponents chase and miss, and lose the minimum when they hit. That, my friends, is profitable poker. (No, I don't claim to have perfected that technique--not by a long shot. Surely, though, I am at least somewhat better at it than the average tourist, or I couldn't be a long-term winning player.)

But as long as you're going to be what Phil Laak and Antonio Esfandiari derisively refer to as a "POW" (pay-off wizard), worrying about the correct amount of a pre-flop raise is, as the saying has it, like rearranging the deck chairs on the Titanic.



*Long after I had devised this scheme for myself, I became aware of similar formulas employed for tournament situations, phrased in terms of number of big blinds, depending on the number of limpers and folders that have gone before.