Really don't have a point to make, just got to thinking how the Equity of a small pocket pair suffers when a third player is introduced. Notice how little the two big cards are harmed, yet the pair takes a serious beating in equity. So.... my conclusion is, and it's nothing earth shaking, that you shouldn't be playing small pairs unless you are HU, or have enough players already into the pot to justify the implied odds of hitting a set, (at least 5 players is my guess, i know its 8 to 1, but I'm talking implied). Also note that suitedness of the big cards directly affects the small pair more than the other hand.


equity (%) win (%) tie (%)
Hand 1: 42.9039 % 42.41% 00.49% { AcKc }
Hand 2: 32.3473 % 32.13% 00.22% { 3h3s }
Hand 3: 24.7489 % 24.19% 00.56% { random }


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1,546,210,512 games 3.675 secs 420,737,554 games/sec

Board:
Dead:

equity (%) win (%) tie (%)
Hand 1: 39.8233 % 39.32% 00.50% { AcKd }
Hand 2: 34.3192 % 34.11% 00.21% { 3h3s }
Hand 3: 25.8575 % 25.28% 00.57% { random }


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Small pcket pairs I reserve for hitting maniacs IF I'm third in (i.e good implied odds). They are OK one on one - but only OK - blind steal at their best...

The funny thing is why is 66 better than 55? I got a lot of showdown results on the pennies. and you can quite clearly see than 66,77,88 are better than 44,55.

I think its because of:

1] The str8 If 77 fills in a gapped str8 then the odds are against anyone else having the str8 (given the gap is in the right place). This is a very small effect.

2] The ability to take substantially take out ppl who play low pocket pairs for the trip.

Both of these are very rare events - but of course NL is about the management of rare events...

Low pp are generally a fold because they don't help in 1] and they are the victim in 2].

Equity HU:

equity (%) win (%) tie (%)
Hand 1: 49.3938 % 49.12% 00.28% { AcKc }
Hand 2: 50.6062 % 50.33% 00.28% { 3h3s }


It has equity there, and is actually the favorite, but we all knew that. 33 doesnt get equity vs AKs until it gets 6 handed, and then just barely, if you squint some.... Ok actually its just a tad under break even, but it could be higher, I didn't feel like waiting 20 minutes for that sim to complete.


equity (%) win (%) tie (%)
Hand 1: 29.8471 % 29.06% 00.79% { AcKc }
Hand 2: 16.4168 % 16.24% 00.18% { 3h3s }
Hand 3: 13.4604 % 12.61% 00.85% { random }
Hand 4: 13.4115 % 12.57% 00.84% { random }
Hand 5: 13.4351 % 12.59% 00.85% { random }
Hand 6: 13.4290 % 12.59% 00.84% { random }

So what does that say about the idea of raising with small pairs from early or mid position to try and get heads up? Guess it would depend on how likely your table is to get multiple cold-calls.

See here is why I don't like equity.

AK - This hand has 2 strengths, top pair top kicker and Bluffability (is that a word???). Your equity chart assumes you will go to the river as will the other 2 hands. If 33 misses the flop it will fold. So if you eliminate 33 from the equity calculation from the flop on it would be totally different. Same with the random hand.

33 - This hands strength lies completely on the flop. It is nothing before the flop (unless it is heads up but that is a different discussion). 33 only strength is in hitting another 3.

I disagree with 5 people to get the implied odds to look for a set, 3 is enough in my mind if 1 of them will call to the end. if 2 will call to the end you only need 2.

with 3 opponents (1 being the bb), you put in 1 bet preflop to win 3.5. if you hit your set and 2 opponents fold but another calls you down you effectively put in 1 bet to win 8.5 small bets.

thats right on the fringe of profitable, I'll assume the times he bets into you or raises a lesser hand cancel out the rare times he beats you.

If you can get 1 other opponent to throw in a bet on the flop now it is highly profitable.

Its hard to say these hands will win this often. In a real matchup AK vs 33 the 33 will probably win 1 out of 5 pots, not the 50 something% it is supposed to. However those wins will be bigger than 20% (more likely 33 will win 40% of the money exchanged in this matchup) because of the chance of both players having a hand when a 3 spikes.

yeah 33 is a slight favorite, but with more bets to come I'll take AK.

NL is a different story where the 33 is better because you can relieve someone of their whole stack. in NL 33 will win more money than AK in this matchup, again assuming not a lot of money went in preflop.

Notice how little the two big cards are harmed, yet the pair takes a serious beating in equity.

Unless we're talking about AA or KK, AK's "win condition" doesn't change that much with the addition of a third party. It still needs to hit an A or K with five cards to come and dodge one of two 3's; the only difference is that now it has to dodge the small chance that this random hand (say J5) won't catch two pair or trips when AK makes TP. In fact, I would think the difference between AK's chance to win vs 33 (49%) and AK's chance to win vs 33 AND J5 (42%) is roughly the chance that J5 will hit two pair (or trips). I'm not good with statistics, so would anyone know if 7% for two pair is the magic number here? It actually might be just a little higher, since we're assuming one of the community cards can only be an A or a K.

Conversely, 33's "win condition" changes much more dramatically with the addition of J5, because now he has to dodge a single A, K, J, OR 5 with five cards to come. That doubles the outs of his combined opponents and nearly halves his own chance to win. This makes sense, because where HU against AK, 33 still had a fair chance to win without improving, he now has very little chance to win without improving against AK AND J5. You can see this where when HU, 33 has approx. 50% to win, where 20% of that time 33 hits a set. That means 33 wins 30% of the time without improving. Now when up against AK AND J5, 33's chance to win is only 32%, but its chance of setting is still 20%; this means that 33 will only win about 12% of the time without improving.