Everyone folds, what is the BB's range of hands?

[ZeeJustin]

Is anyone here capable of calculating the weighted range of hands the BB has in a full game where everyone folds? Any standard opening guide, including the middle road of the ones given in HEFAP would work just fine. To simplify, it would be best to assume each player uses the same hand-opening chart (which heavily depends on position), and no player ever mixes it up.

[Siegmund]

An exact calculation would be very difficult.

This looked like a fun problem to spend an hour simulating this afternoon, though, so I did.

The results will vary slightly with what range of hands you play. For my simulation I used the following:

10-handed table;
First 3 seats: play 66,T9s,QTs,KTs,A8s,ATo,KQo, or better
Middle 3 seats: play 22,98s,QTs,KTs,A5s,ATo,KJo, or better
CO/Button: 22,87s,QTs,K9s,Axs,Axo,KT,QT,JT, or better
SB: 22,87s,QTs,Kxs,Axs,Axo,Kxo,QT,JT or better

Ran it until I had 100,000 deals folded to the big blind. Results:

10.8% of deals folded to the big blind

Probability that the big blind:

Is suited: 23.3% (vs. random 23.5%)
Is paired: 5.9% (vs. random 5.9%)

Holds an ace: 18.5% (vs. random 14.9%)
king: 16.3%
queen: 15.7%
jack,ten: 15.5%
nine,eight: 14.4%
2-7: 13.6-14.1%

Specific hands:
AA: 139:1 (instead of 220:1)
KK: 177:1
QQ: 201:1
small pair: 250:1
AKo: 81:1 (instead of 110:1)
A2o: 95:1
72o: 123:1

Uncertainties in the above are about 0.1% for probabilities of suited/holding specific cards, about about 0.03% for specific hands (i.e., A2o between 92:1 and 98:1)

Would be happy to tweak the parameters a bit or extract particular bits of information for you if there's something else along these lines you're interested in.

[ZeeJustin]

This is perfect. Thank you. I think this is very interesting and useful.

[Filip]

I agree, i kinda liked the 250:1 for small pairs.

[pzhon]

Thanks for carrying out this experiment. It is much nicer to see actual data than the constant assertions that bunching doesn't matter.

[Dynasty]

[ QUOTE ]
Thanks for carrying out this experiment. It is much nicer to see actual data than the constant assertions that bunching doesn't matter.

[/ QUOTE ]

Bunching doesn't matter because people don't play according to charts. People play T4s and 65 UTG. You're deceiving yourself by using this information.

[Robk]

there are 3 games on pokerstars right now with players/flop < 20%. do you think anyone is playing T4s or 65 under the gun?

[ZeeJustin]

[ QUOTE ]
there are 3 games on pokerstars right now with players/flop < 20%. do you think anyone is playing T4s or 65 under the gun?


[/ QUOTE ]

Go easy on him. He plays live more than he plays online. It's a whole different world out there.

[pzhon]

[ QUOTE ]

Bunching doesn't matter because people don't play according to charts. People play T4s and 65 UTG. You're deceiving yourself by using this information.

[/ QUOTE ]
That a few people don't behave exactly as modelled does not mean everyone is playing random hands. The bunching effect may not be exactly as shown in the experiment, but it should be about as large. If you ignore this information you are deceiving yourself.

It complicates things to take into account bunching, but that does not mean it isn't useful. In NL, I often run into situations like the following: After a few limpers, I raise in the CO with AK. The button reraises, and the blinds and limpers fold. The correct action depends on many factors, including the types of hands the players in front of me would limp/fold. Axs and KJo are much more likely than T4s.

[Jman28]

[ QUOTE ]

10-handed table;
First 3 seats: play 66,T9s,QTs,KTs,A8s,ATo,KQo, or better
Middle 3 seats: play 22,98s,QTs,KTs,A5s,ATo,KJo, or better
CO/Button: 22,87s,QTs,K9s,Axs,Axo,KT,QT,JT, or better
SB: 22,87s,QTs,Kxs,Axs,Axo,Kxo,QT,JT or better

[/ QUOTE ]

I'm a bit confused as to how this is useful if we assume EVERYONE folds to the BB because the hand is then over.

Wouldn't a calculation of say, everyone folding to you in the SB be better so that you can have a better idea of the BBs hand?

-Jman28

[Siegmund]

[ QUOTE ]

Bunching doesn't matter because people don't play according to charts. People play T4s and 65 UTG. You're deceiving yourself by using this information.

[/ QUOTE ]

It's up to the user to decide if you think any adjustments are called for. It is still a small effect compared to the difference in the range of hands you put a TP vs. a LA raiser on.

Notice, incidentally, that the looser the table is, the *stronger* the effect is (but the less frequently the table will fold around to a steal situation). Tight players will fold AT and 72 alike, and leave lots of every rank in the deck. Someone who plays any face card will fold rarely, but *if* he folds you *know* that two spot cards have been folded.

If you have someone at your table who plays any two cards, well, it's a non-question, because it won't ever BE folded around.

You'll notice in my experiment that the effect on aces is quite large compared on other ranks. In real life I see people playing a lot more suited kings and queens than the charts say to.

I reran the test with two people at the table who would play any suited king or queen. The effect: A: 18.5% K: 16.8% Q: 15.9%; chance of being suited, 23.7%. And if in addition the cutoff will play any king, suited or not: A: 18.4% K: 17.3% Q: 15.8%.

In other words, no one player at the table can push these percentages by more than 0.5% no matter how weird his starting hand selection is. The impact of how many ace-rag and king-rag hands people play can be quite significant. The impact of other kinds of looseness like playing suited connectors out of position is smaller, since it is spread out over several ranks instead of concentrated somewhere obvious.

[gergery]

That's amazing. When I read ZJ's title, I immediately thoughts "the same as a random hand, because bunching is an extremely small effect." It's still pretty small, but definitely larger than i expected.

-g

[TStoneMBD]

wow this is some excellent information sieg. ty