How to Play Marginal Hands

[gmanko]

A couple weeks back I posted a couple of topics on preferred pot size and number of opponents that got me to thinking that maybe my problem was how I was playing my marginal hands (top pair with a poor kicker, middle pair, and underpairs) in pots with many players. (Note: I am not by any means not still bitter that I am only getting 1/5 the number of flopped sets that I should, or that I get rivered almost every time I possibly could).

I decided to take a break and not play again until I could learn how to play these hands properly. I could not find any books, articles, or posts so I did the math myself (so there may be some subleties here that are not accounted for, for example these guidelines probably need to be adjusted if 3 to a straight or flush flops).

I determined the following probabilities using 3rd grade math for any time you have a pair (split or pocket) on the flop.

For board overcards:
3 possible matching cards in other players hands
(12% per opponent per overcard)

For cards that match your pair or a board pair:
2 possible matching cards (8% per opponent)

Pocket pairs that beat your pair, or make a set
(approximately .5% per each per opponent)

These probabilities can quickly be added to see if you have a better than 50% chance of having the best hand.

Implications for Multiway Pots:

A pocket pair with one board overcard is probably good unless you have 4 or more opponents, and should be bet.

Top pair with a weak kicker is most likely good unless you have 6 or more opponents, and should be bet.

Middle pair with a good kicker is most likely good unless you have 4 or more opponents, and should be bet.

Middle pair with a poor kicker is most likely good unless you have 3 or more opponents, and should be bet.

A pocket underpair with a pair on the board is most likely good unless you have 3 or more opponents,
and should be bet.

In any of these situations, if you bet and are raised or check-raised, you most likely will have to fold,
especially if there are other players to act behind the raiser.

If there are more opponents than recommended, you should probably fold if someone bets into you, or check and
fold if someone bets behind you.

Keep in mind that these guidelines were developed without regard to possible draws. If an opponent is capable
of raising with a draw, you may need to adjust your play. If there is a possible or very strong draw on board
(two or three to a flush or outside straight), you may need to discount your chances.

Implications for Heads-Up play:

In general, you should bet any pair into a single opponent on the flop, including pocket underpairs.
Even with three overcards there is still a better than 50% chance that you have the best hand.

Even if you have two overcards, there is still better than an even-money chance that your opponent has nothing,
and he may even fold a small pair.

If you raised before the flop, unless there is a plausible draw on the board it may be worth betting when you have
a single overcard on the flop as a bluff, since your opponent most likely doesn't have a hand, either
(in this case you will most likely have to fold if raised, though).

If you have any pair, continue to bet after the flop, make your opponent show aggression before slowing down.

If your opponent bets into you and you have any pair, there can be as many as three board overcards before you have
a better than 50% chance of being beat (the fourth one goes over), excluding made hands. If your opponent is a mouse,
you might want to consider folding lower than middle pair, though.

Examples (no raises pre flop unless specified):

You raise QQ in BB
Flop is AT4
The chance that one opponent has you beat is
12% for the ace,
.5% each for KK (unlikely), TT (unlikely) and 44
a miniscule fraction for AA (very unlikely)
= 13.5% per opponent
If 2 Opponents limped in
x2 = a 27% chance that you are beat
>> You should bet out.
If 4 Opponents limped in
x2 = a 52% chance that you are beat
>> You should check.

You check with A2 in BB
Flop is AT4
The chance that one opponent has you beat is
8% for another ace with a better kicker,
.5% each for TT (unlikely) and 44
= 9.0% per opponent
If 4 Opponents limped in
x4 = a 36% chance that you are beat
>> You should bet out
If 6 Opponents limped in
x4 = a 54% chance that you are beat
>> You should check

You call with KTo on the button
Flop is AT4 (middle pair, best kicker)
The chance that one opponent has you beat is
12% for the ace,
.5% each for QQ (unlikely), JJ (unlikely), and 44
a miniscule fraction for AA and TT (very unlikely)
a minuscule fraction for T4 (unlikely)
= 13.5% per opponent
If 3 Opponents limped in
x3 = a 40.5% chance that you are beat
>> You should bet out.
If 4 Opponents limped in
x2 = a 52% chance that you are beat
>> You should check.

You check with T8s in the BB
Flop is AT4 (middle pair, poor kicker)
The chance that one opponent has you beat is
12% for the ace,
4% for a ten with a better kicker (8%/2, an 8 is about the median kicker for this flop)
.5% each for QQ (unlikely), JJ (unlikely), and 44
a miniscule fraction for AA and TT (very unlikely)
a minuscule fraction for T4 (unlikely)
= 16.5% per opponent
If 2 Opponents limped in
x2 = a 33% chance that you are beat
>> You should bet out.
If 3 Opponents limped in
x3 = a 49.5% chance that you are beat
>> You should check (this is a very vulnerable hand, considering straight you may be in bad shape).

You call 88 in UG
Flop is AT4
The chance that one opponent has you beat is
12% for the ace,
12% for the ten
.5% each for KK, QQ, JJ, (unlikely), 99, and 44
a miniscule fraction for AA and TT (very unlikely)
= 26.5% per opponent
If the button raised and it is heads-up
x1 = a 26.5% chance that you are beat
>> You should bet out.
If 2 Opponents limped in
x2 = a 53% chance that you are beat
>> You should check.

You call 88 in UG
Flop is QQT
The chance that one opponent has you beat is
8% for a queen (since there are only two other queens in the deck)
12% for the ten
.5% each for AA, KK, QQ, JJ, (unlikely), and 99
a miniscule fraction for QQ and TT (very unlikely)
= 22.5% per opponent
If 2 Opponents limped in
x2 = a 45% chance that you are beat
>> You should bet.
If 3 Opponents limped in
x3 = a 67.5% chance that you are beat
>> You should check.

You call 88 in UG
Flop is QQ4
The chance that one opponent has you beat is
8% for a queen (since there are only two other queens in the deck)
.5% each for AA, KK, QQ, JJ, TT, (unlikely), 99, and 44
a miniscule fraction for QQ (very unlikely)
= 11.5% per opponent
If 3 Opponents limped in
x3 = a 34.5% chance that you are beat
>> You should bet.
If 4 Opponents limped in
x4 = a 46% chance that you are beat
>> You should bet.
If 5 Opponents limped in
x5 = a 57.5% chance that you are beat
>> You should check.

[gmanko]

I know this post got lost during the popular "How do you muck" discussion, so it is probably good that I have had a few days to go over my calculations (I should have used fourth grade math), and I made a few changes.

When you have middle pair, the chances that an opponent has top pair is actually almost 13% (12.9%: 3/47 + 3/46) instead of 12%.

When you have top pair with a poor kicker, the chances that another opponent also has top pair is closer to 9% (8.6%: 2/47 + 2/46) instead of 8%.

The chances that an opponent has a set is closer to 0.3% than 0.5% for other pocket pairs.

This changes some of the recommendations. For example, I would not bet top pair with a weak kicker into more than 4 opponents, the examples have top pair as aces, and it is often correct to keep a suited ace that beats your kicker (let alone the any acers who may have an A7o UG that beats your A4o in the BB), and when top pair is less than an ace you need to worry about overpairs.

Also, since you must have a better hand to call a bet than to make a bet, you should probably fold if you are "on the margin" with the recommended number of opponents. In the example above if you have top pair/weak kicker and four opponents and are bet into, you should probably fold because top pair/weak kicker is the MINIMUM betting hand (even if your opponent is misplaying a hand such as middle or bottom pair doesn't mean you should make a mistake also, plus someone else behind you may actually have the goods). With 3 opponents top pair with a weak kicker is a playable hand even if bet into.

[TommyO]

Interesting post but I don't know that I agree with the assumptions. When you calculate the odds that your small pocket pair is ahead when an ace flops you're assuming the opponent had random cards. More often than not, the players seeing the flop have above average cards. I don't know how you quantify this but I would think it would make your pocket pair less of a favorite than you make it out to be. Maybe the line between betting and checking moves from four opponents to three?

[gmanko]

Good point.

When I redid the calculations for all of the examples (not posted), a pocket pair with one board overcard did work out to a less than 50% chance of being beat when there are 3 opponents.

Also, if you have top pair/poor kicker, I reduced the number of opponents from 5 to 4 since many people will keep an ace, and you can run into overpairs if top pair is less than an ace.

[Stormwolf]

You forget that sometimes even if your a underdog to have the best hand(say against two/three opponents) you should STILL bet because you will be laying on yourself a very good price to pickup the pot(and also to know if your good or not and to not give free cards)

[gmanko]

Good, finally some discussion on this topic.

At what point would you suggest checking, when you are a 5-3 dog (60% chance you are beat), 2-1 dog (67% chance u are beat)?

[gmanko]

After mulling this over some more, I have a few more things to say.
Also, I am going to write another post about how to play these hands when there is a possible draw on the flop.

First, let me restate that in the original post, due to my miscalculation of the odds of another player having the same or higher pair (when matching a board card), some of the recommendations in the examples are off by one player. (I have a chart with corrections, but I am keeping that to myself for now<g&gt.

Second, I am going to stick to the odds quite rigidly. That is, I will bet out or raise with these hands (top pair porr kicker, middle pair good kicker, and middle pair good kicker) when there is less than a 50% chance that I am beat, and check or fold if there is greater than a 50% chance that I am beat (I would only check and call if I had odds to draw to 2 pair and/or a backdoor draw). I will play my hand strongly when I have the best of it, and dump them when I do not.

That being said, in last position I would add the option of betting with one more opponent than recommended if it is checked to you and you are last to act. In this situation you may have a better than even money chance of having the best hand. Note - this is only an option, for example I would tone it down against players who do a lot of check-raising.

Remember, these are marginal hands, if you are raised, and especially if reraised, you may have to fold on the flop (unless there is now enough money in the pot to justify drawing to 2 pair).