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Comment by leetcrew | Hacker News Reader

maybe this is just my ignorance showing, but really? people can just computer large factorials and binomial coefficients in their heads fast enough to participate in the game?

I had always thought that knowing the odds exactly just wasn't that useful because there was a lot of missing information and it was more important to read one's opponents.

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It's usually not anywhere near that complicated. To use an example from the article he folded a QJ against a QT with 89J on the board with no flush possibilities. In this case there are not very many hands that can be beating him: the pocket pairs AA, KK, QQ, JJ, 99, 88, stuff that makes two pair like J9, J8, 98, and the straights QT and T7. Overall this is going to be close to the chance when holding 77 that your opponent has a higher pair, which most professional players will "just know" is about 3-4% because they memorize tables of such facts[1]. This means he should believe he's a pretty substantial favorite and why the fold was so unexpected.

[1] https://poker.stackexchange.com/questions/1203/pocket-pair-s...

It is that complicated if you’re trying to factor accurate ranges, card removal and bet sizing. He’s obviously not doing this because he’s playing an exploitative style. In otherwords, he’s guessing perfectly based on his perceptions.

For the mathematically perfect, they spend hours studying solvers which takes considerable processing power to generate the trees. A human player can calculate aspects of it but they can really only memorize what the solver would do. And some high stakes online players are using custom software to augment their decisions.

Depending on the bet size, the solver could call the turn a % of times. And depending on blockers, unblockers and the bet sizing, the solver could advocate to call/raise/fold.

Unless you are playing at the absolute elite levels you do not need to perfectly calculate your own range or another persons. But yes, the better you get the more complicated the math is.

> It's usually not anywhere near that complicated.

Top pros play millions of hands and if you truly have a knack you remember... everything.

"Read one's opponents" isn't about reading a person's soul sitting across from you. That whole aspect of poker of picking up tells plays a much smaller role than simply understanding what hands your opponent is likely to have in each possible specific situation or knowing your opponents playing tendencies, such as how frequently do they raise, call, fold, and in what cases would they do those actions. Tells can still be important but most experienced players will have learned to control their emotions to the point where it's far more reliable to rely on your understanding of the game than to rely on some psychological meaning behind someone splitting an Oreo cookie before making a decision.

As far as computing "large factorials and binomial coefficients in their heads", I don't know what makes you think that that's what poker math entails. It's nearly all just basic statistics.

> As far as computing "large factorials and binomial coefficients in their heads", I don't know what makes you think that that's what poker math entails. It's nearly all just basic statistics.

honestly I've never played much poker, but I remember doing lots of poker odds problems from my discrete math class in undergrad.

In practice,

a) most situations that come up in poker just aren't that complicated -- if you're good at mental math, you can compute the exact odds for the most common situations in your head with some practice

b) there are some simplifications/heuristics you can apply if you're willing to be off by a small margin of error -- e.g. "if you have x outs, you have approximately 2x% to hit one by the river for each card remaining" is accurate enough for most players in most situations

c) this math ends up being extremely useful in practice, because "reading" someone (which is usually just logically deducing reasonable possibilities for what is in their hand) is only useful if you can then use the information to determine whether it is profitable to make/call a bet, which requires knowing your likelihood of winning.

Texas hold'em is straightforward to calculate odds for. There are 52 cards in the deck. Two are in your hand, and after the flop three are on the table, leaving 47 unknowns. That means if you have N outs (cards that will improve your hand), the chance of hitting one on the turn is N/47, which is about 2N per cent. Likewise the chance of hitting by the river is about 4N%.

The hard part is calculating the implied odds: there you need to play out scenarios of what your opponent might hold, and what cards would cause them to bet or call with a losing hand.

Tells are overrated in poker. It's all about implied odds and grinding it out.

There are a total of 169 starting hands and at most half are relevant. Most people you can put on a range of 40 or fewer hands. All the math you need can be inferred from about 100 things you need to memorize, most of which are fairly intuitive.

only recently have very powerful computers gotten better at poker than good humans. a phone probably can't do it yet. but a phone could be used as a way to do various kinds of digital spying or communicating with other people etc.

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