If you’re going to play a lot of poker, it’s good to know things about pot odds and expected value and the like. What amazes me is the ineptitude with which these things are demonstrated by the “experts”, eager no doubt to cash in on advertising revenue when people come to their sites for advice on how to play.
A real example, and how web sites talk about it – the flush draw, Texas Hold’Em:
You have A-10 of clubs, with 8C 7C 2H on the board after the flop.
PokerTips.org says: You have a 35% chance of making your flush on the turn or the river. Close, but not quite.
aintluck.com says: Your odds are 47:9 for getting the club on the turn or river, or about 5.2:1 – roughly 16.13%. Where do they even get this shit??
Reality: There are 4 of 13 clubs accounted for; that leaves 9 clubs out of 47 unknown cards, or a 19.15% chance of a club on the turn (38:9, not 47:9). If you don’t get a club on the turn, that’s 9 out of 46 or a 19.57% chance of a club on the river. So your odds are actually 38.72% for the flush by the end of the game.
Now, as to the strategy, both web sites in question are giving the wrong advice according to the common wisdom. PokerTips.org is suggesting a raise on the wild assumption that the 4 people who bet before you will also call your raise. aintluck.com suggests a fold on the basis of their striking inability to calculate ratios (see above).
But the common wisdom is also wrong. Let’s say you’re heads up with a pot of 100, and your opponent throws 100 more at you. You’re in a good spot here, says the common wisdom! 38.72% amounts to winning odds of about 1.58:1, meaning if you call this bet of 100, your pot odds of 3:1 put you in a winning position. In fact, the usual expected value calculation here would be as follows:
EV = (P.win * Profit) – (P.loss * Loss)
EV = (0.3872 * 200) – (0.6128 * 100)
EV = 16.16
It’s not a huge edge, but the math says you go for it. Call the bet. But this is what pisses me off: statistics work because they take *ALL* of the information you do have into account. Are we really doing that? Now, let’s say that you call that bet, and the turn comes up 6 of diamonds. You now have a 19.57% chance of hitting your flush on the river, or winning odds of 4.11:1. With the pot now at 300, your opponent ups his opening bet and throws 150 at you. Now your pot odds are 3:1 against inferior winning odds, and your expected value is -32.58. That’s a fold!
So what? What’s the important lesson here? Again, statistics are only accurate if you feed in *everything* you know. And part of what you knew back there after the flop is that if the next card wasn’t a club, you’d be folding before you saw the final card! Meaning that final card can’t be considered a chance to make your flush – you either make it on the turn or you don’t make it at all.
The reality: with these pot odds, the turn is your only chance to make your flush, meaning the equations above – post-flop – would have been as follows:
EV = (0.1915 * 200) – (0.8085 * 100)
EV = -42.55
Which means that even though you still had two more cards coming, you actually should have folded after the flop when that guy first threw his 100 at you.
Would I fold in this situation? Probably not. I usually don’t, but that’s not a mathematically sound decision, contrary to what so many experts seem to suggest.
CONCLUSION: Newcomers should be wary of websites purporting to teach correct poker strategy. The math isn’t complex, but it is apparently beyond the grasp of most of these people. In my opinion the best poker strategy is to cultivate a keen sense of your opponent’s psychology. But I’m just an amateur. I don’t give strategy advice, ’cause I don’t think that much of myself as a player. The only advice I can really give is that the other guy’s advice is probably horse shit.