Poker Evolver Community

[kem_fi]

Hi,

For analyzing opponent's hole cards, VPIP/PFR/AF are traditionally used. It would be interesting to see one more statistic: positional awareness. In the simplest form, it could be calculated e.g. from the fraction the opponent voluntarily puts money in the pot in each position compared to the last position, then doing linear regression y = kx + b (x being the position 0-1, 0=button, 1=ep) and reporting 1/k as positional awareness (higher is better).

When speculating opponent's hole cards, the user could then narrow the range when the opponent acts from early position, if the opponent is known to respect position.

While talking about the subject, I've also been thinking about the possibility to estimate the ranges of the opponent's hole cards in pre-flop by software, from hand histories. In the simplest form: 1. sort the 169 possible starting hands according to Sklansky or no-fold-em ranks, 2. calculate VPIP-like statistics for opponents for a) limping, b) open-raising or calling raises, c) re-raising (etc), 3. if the opponent does a+b+c with N%, assume he plays the top N% hands of 1; if the opponent does a+b with M%, assume top M%; and similarly for just a), 4. reduce the probability of cards in the player's hole.

This would be great for beginners, not so useful in the simple form for experienced players.

Obviously though, this can be extended in several ways:
- There can be several possible starting hand orders (e.g. opponent overvalues suited cards/small pairs/suited connectors/faces), and they can be mixed according to player statistics.
- Learn opponents' starting hand order from seen holes.
- Take position into account.
- Classify flop (X-high, paired, 2-suited, 3-suited) and calculate a joint distribution of player actions / holes / flop -> modify the range.
- Same thing for turn and river.

To take this further, it would perhaps be possible to construct a Bayesian model, where the opponents' hole cards were the uncertain parameters. Assume a beta-distributed prior (which can be calculated from hand histories; prior for unknown players can be calculated over all players; it can also be just an expert prior based on Sklansky ranks) and a binomial distribution for the likelihood. The posterior then gives a probability for each hole, and quantifies our uncertainty (variance of the resulting beta-distribution). I believe quantifying the uncertainty is difficult even for very experienced players; this could potentially be useful for hand analysis.

Once we have a Bayesian model, we can in theory take almost anything into account: a) adjust the hole card beliefs when opponents fold: it's unlikely they had anything good; b) the opponent is slow-playing/bluffing/tilting could be a latent variable; d) it's Saturday night, and the player is drunk; etc.

Anyway, just thinking aloud here Maybe you'll get some ideas.

[Ilkka]

Thank you for sharing your thoughts. What comes to the positional awareness stat, I think it could be of some value to players. At least on levels where you meet various types of players this stat would definitely help.

When playing with more experienced players though the stat loses it's meaning somewhat as experienced players are known to respect position. Of course you could still draw some conclusions on how much the position actually directs their play, but the scale would be more narrow.

Figuring out the hole cards of the players in the simple way that you explained might also work if presented the right way, and you made many good points on how this could be taken further.

I have my doubts on the Bayesian model though. Correct me if I'm wrong but wouldn't you need quite a few different models to benefit from all this? The player model should vary at least according to the table size and experience of individual players since otherwise the data from all different situations and from every player would force a general model to be unsuitable for the particular situation at hand. And to make these models more useful you'd need to adjust all these models quite a bit according to your own perception even if you had lot of data available.

After saying all this I still think you presented some very interesting thoughts and gave us many ideas. Thank you.