Poker player, coach and author Alexander Fitzgerald, together with Topher Goggin, is back with a new book aimed at poker's 'serious amateurs'. Improve Your Poker Now! from D&B Publishing is out today and available at Amazon.
The following exclusive extract is from the Core Hold'em Concepts chapter, in a section titled 'The Shocking Truth About (Some) Bluffs'...
Situation: In the middle levels of a low stakes online tournament. About half the field is still playing. Stacks are not short yet, but stealing the blinds is starting to become more valuable. Everyone folds to us in the small blind, where we find 
. Our hand clearly sucks. But what would happen if we raised?
Analysis: In most live tournaments, a hand begins with around 2.5BB in the pot from the blinds and antes. That’s still the amount in the pot when the action folds to us.
Say we make it 3bb. First, it is crucial to understand what this raise just cost us, because it is NOT the full 3bb. The only thing that matters is the additional 2.5bb we are putting in now. Our small blind sailed out of town long ago and belongs to the pot. Any time we are calculating odds, we only care about the chips we are betting now.
With that in mind, our expected value formula applies just as much to bluffing as to calling. We just need to ask what we are risking versus how much we could win, and that will tell us how often it must work.
We know we’re risking 2.5bb. What can we win? After our raise, the total pot will be 5bb. 2.5bb/5bb = 50%. If we can steal the pot more than half the time, it is instantly profitable compared to folding. This is true even if we just give up and muck our cards every time the big blind calls.
The question then becomes whether we can make the big blind fold that often. Your first inclination might be 'no', falling prey to the knee jerk feeling that 'the big blind always calls if I raise.' Don’t be so sure.
To keep us from winning, the big blind has to defend (i.e. call or raise) with half of all possible hands. That turns out to include some very questionable junk. Different people have different opinions on which starting hands comprise the top 50%, but any way you slice it, there will be some pretty gnarly stuff included. One plausible top-50% range includes hands as weak as J-4s, Q-2s, and J-7o. A different version gets rid of that garbage, but gets stuck with 6-4o and 4-2s instead.
Whatever 50% range you pick, if our opponent doesn’t call with every single junky hand in it, we immediately turn a profit. If they do call with all of those hands, then they have to play after the flop with a lot of garbage that will be in rough shape. That’s also unpleasant.
The lesson to learn here is not necessarily 'raise more often from the small blind' (though that’s probably good advice). We have only shown that raising is a profitable play, not that it is the most profitable play. The point is to think about all your options, and to do so through a lens of expected value. Countless scenarios exist where your competition has so many weak hands that they won’t call often enough to stop you from indiscriminately betting. The more you know about what your bets need to succeed – and what your opponents have to do to stop you – the easier it will be to recognize those spots.
Success rates based on bet size
Of all the mathematical applications of our expected value formula, the one we just used might be the most important. For any given bet size, you should be able to determine how often it must succeed to profit as a pure bluff. We know you are seeing these calculations a lot right now – that’s intentional. The more you see them, the more you’ll subconsciously know the answers without much effort when you play.
How often does a half-pot bet need to work? How about one-third pot? Two-thirds? What if you went wild and bet double the pot? Knowing the most common answers will dramatically improve your play.
Try one. If we fire a 500-chip bluff into a 1,000-chip pot, we are risking 500 chips to collect a total of 1,500 – the original 1,000, plus our 500.
500/1,500 = 1/3.
This, or any other, half-pot bet needs to win one-third (33%) of the time to profit as a bluff.
Here is a list of bet sizes worth knowing by heart:
- A 1/4-pot bet must work 1/5 (20%) of the time.
- A 1/3-pot bet must work 1/4 (25%) of the time.
- A 1/2-pot bet must work 1/3 (33%) of the time.
- A 2/3-pot bet must work 2/5 (40%) of the time.
- Betting the size of the pot must work 1/2 (50%) of the time.
What about betting double the pot? Now with 1,000 in the middle, we whip out a bet of 2,000 more. Crazy, right? Not necessarily.
If we fire 2,000 into a 1,000-chip pot, we’ll get 3,000 back when we win. That requires 2,000/3,000, or a 2/3 (67%) success rate to break even. That’s attainable. All but the toughest opponents will struggle to call a bet that large with anything but a monster, since calling incorrectly both costs a lot AND makes you feel stupid. It’s so much easier to just fold.
Many people think of overbetting as a high-risk, low-reward play that leads to disaster the first time it misfires. This shows that’s not necessarily true. Yes, it’s foolish to move all-in for 30,000 chips when the pot has 300 in the middle. But bets that are slightly larger than the pot can be extremely powerful plays when deployed at the right moment.
No-limit hold’em allows you to bet any or all of your chips at any time. Use that to your advantage. Small bets rarely need to win to make money. Overbets can be sufficiently scary to earn enough folds. Put your whole toolbox to work.
