Classes of hands to bet when you have position versus a tricky player.
- strong hands
- weak hands with no draws
- medium hands with strong draws
Classes of hands to check:
- medium hands with no draws
- weak hands with draws
Let’s say you have a pocket pair, and the flop comes with one overcard. For example, you have QcQs and the board is 2d7hAs. In this case, the linear strength of your hand is .856. Now consider two cases of the board pairing.
Board: 2d 7h As
Hand: Qc Qs
Strength: .856
Board: 2d 7h As 7c
Hand: Qc Qs
Strength: .784
Board: 2d 7h As Ac
Hand: Qc Qs
Strength: .903
Your hand becomes much stronger if the overcard pairs, and much weaker if an undercard pairs. This isn’t much of a surprise really. If someone held the ace, you were beat already. The second ace just means that there are fewer aces out there to beat you.
If you raise preflop with a big Ace, and you pair your ace on the flop or the turn, don’t go to war on the turn with just a pair of aces. If someone raises you on the turn, just call ‘em down. Your pair of aces is a naked hand. Everyone knows what you have, or at least strongly suspect it. So if they are raising you on the turn, they are representing strength to rival top pair top kicker.
This holds regardless of how good the player is. They can be the loosest nutiest bluffomatic, but when they raise you on an ace-high board be careful. Even nutcases have hands, and the nutcases who know what they are doing are just waiting for the opportunity to crack your AK wide open. Don’t give ‘em the satisfaction of going nutso with them.
Here is a graph I made this morning while playing around with some of my hand history data. The graph represents the frequency that a hand wins as a function of it’s hand strength when the pot is heads up on the river. All hands have been linearized to a value in the range of [0,1].
The red line represents situations where the hero bet the river, while the blue line represents situations where the hero check or called the river.
All things being equal all three lines would overlap exactly. That is to say, if you held a hand with strength .3, and your opponent held a random hand, your hand would win 30% of the time. But in poker, all things are not equal. Players cannot fold if you do not bet, and players cannot bluff if you do.
Notice that the “active” plot clearly demonstrates the value of bluffing with your worst hands. It’s also more likely that our hand is good if we feel confident enough to bet the river. When we have a strong hand which isn’t a lock passive river play is usually an indicator that we’ve been faced with opponent aggression.
So, when should you bluff, and when should you value bet? From the graph, it looks like passive play out performs active play for hand value in the range of roughly [.35,.55]. In other words, for the game conditions in this game, we should be betting the river or bluffing with almost every hand. In practice, this may not be true, but it is good to see that “first approximation game theory” seems to be verified by observed data.
Thanks to everyone who sent feedback. I was able to fix a lot of the interface issues that people mentioned. There were a lot of good ideas, but not all of them could be incorporated into this version in a timely manner. I’ve made PokerStove version 1.20 available. You can view the changelog.
The biggest fix is that entering text into the dialog boxes allows you to manipulate the hand distributions without going through the dialog interface. There are a lot of parsing options, but the guiding principle I used was that the interface had to “eat it’s own dogfood”. In other words, if the dialog produces the text, it can also parse the text. It can parse more than that, but that’s the baseline. Also you can copy paste text from one distribution to another and you get the expected behaviour.
The other big change that I added the ability to edit the interface based on the “Top N%” of hands.
If you find any (more) bugs, or related interface issues, please let me know.