A4s might be a 9-1 dog
First of all, great book Dave!
This is based on the section "If it is Raised Behind You" from page 76 of Dave's book.
Even though I agree with the point that a call of one raise is almost always automatic after limping in, here are a couple of 5 handed examples (assuming the SB will automatically call---this may or may not be the case depending on the blinds) where someone has AA and the A4s is about a 9-1 dog (or worse).
http://twodimes.net/h/?z=261634
pokenum -h as 4s - ah ad - 7s 7d - qh jh - 2h 2c
Holdem Hi: 850668 enumerated boards
cards win %win lose %lose tie %tie EV
As 4s 82700 9.72 759910 89.33 8058 0.95 0.101
Ad Ah 340146 39.99 502464 59.07 8058 0.95 0.404
7s 7d 152523 17.93 695710 81.78 2435 0.29 0.180
Qh Jh 147723 17.37 700510 82.35 2435 0.29 0.174
2c 2h 119518 14.05 728715 85.66 2435 0.29 0.141
In fact, the A4s doesn't even need to be in such dire straits as being up against AA. It's in rough shape even if just a dominating A and a single 4 (of course, this is pretty much as bad as being against AA) are out in the hole cards, and the straight & flush draws to the 4 are non-live. (Although, as we see below, the A4s is in fact slightly worse off under these conditions.)
http://twodimes.net/h/?z=261645
pokenum -h as 4s - ah ts - 7s 6s - kh 4h - 9s 9c
Holdem Hi: 850668 enumerated boards
cards win %win lose %lose tie %tie EV
As 4s 57994 6.82 752615 88.47 40059 4.71 0.091
Ts Ah 193231 22.72 628962 73.94 28475 3.35 0.243
7s 6s 112503 13.23 735690 86.48 2475 0.29 0.133
Kh 4h 168337 19.79 668272 78.56 14059 1.65 0.205
9s 9c 278544 32.74 569649 66.96 2475 0.29 0.328
And if you're against the AA *and* a 4...
While it's true that these examples are cooked up (and as I mentioned already, I agree that it's still good advice to call one more bet after limping in most of the time with any two cards), it just got me thinking when you made a statement so absolute as "...you are not a 9-1 dog". And when you are trying to teach people about poker by writing a book, I'd say that getting them thinking about poker is probably the best thing you could so, so well done! 8)
ScottyZ
This is based on the section "If it is Raised Behind You" from page 76 of Dave's book.
Even though I agree with the point that a call of one raise is almost always automatic after limping in, here are a couple of 5 handed examples (assuming the SB will automatically call---this may or may not be the case depending on the blinds) where someone has AA and the A4s is about a 9-1 dog (or worse).
http://twodimes.net/h/?z=261634
pokenum -h as 4s - ah ad - 7s 7d - qh jh - 2h 2c
Holdem Hi: 850668 enumerated boards
cards win %win lose %lose tie %tie EV
As 4s 82700 9.72 759910 89.33 8058 0.95 0.101
Ad Ah 340146 39.99 502464 59.07 8058 0.95 0.404
7s 7d 152523 17.93 695710 81.78 2435 0.29 0.180
Qh Jh 147723 17.37 700510 82.35 2435 0.29 0.174
2c 2h 119518 14.05 728715 85.66 2435 0.29 0.141
In fact, the A4s doesn't even need to be in such dire straits as being up against AA. It's in rough shape even if just a dominating A and a single 4 (of course, this is pretty much as bad as being against AA) are out in the hole cards, and the straight & flush draws to the 4 are non-live. (Although, as we see below, the A4s is in fact slightly worse off under these conditions.)
http://twodimes.net/h/?z=261645
pokenum -h as 4s - ah ts - 7s 6s - kh 4h - 9s 9c
Holdem Hi: 850668 enumerated boards
cards win %win lose %lose tie %tie EV
As 4s 57994 6.82 752615 88.47 40059 4.71 0.091
Ts Ah 193231 22.72 628962 73.94 28475 3.35 0.243
7s 6s 112503 13.23 735690 86.48 2475 0.29 0.133
Kh 4h 168337 19.79 668272 78.56 14059 1.65 0.205
9s 9c 278544 32.74 569649 66.96 2475 0.29 0.328
And if you're against the AA *and* a 4...
While it's true that these examples are cooked up (and as I mentioned already, I agree that it's still good advice to call one more bet after limping in most of the time with any two cards), it just got me thinking when you made a statement so absolute as "...you are not a 9-1 dog". And when you are trying to teach people about poker by writing a book, I'd say that getting them thinking about poker is probably the best thing you could so, so well done! 8)
ScottyZ
Comments
I will defend myself by declaring that there is still no way to fold A-4s for a single raise if you have entered the pot in the circumstances that I describe (after there have been two limpers in front of you). At a minumum you are getting 7.5-1 to see the flop (two limpers + the raiser + the small blind + your bet). There is no way you can be sufficiently certain that you are a horrible dog. Further, without doing the math, the implied odds have to be sufficient to at least take off the flop. If the raise does has A-A then you are going to skin him if you do hit the flop. This is not an adequate argument, of course, to routinely take A-4s up against A-A but with the extra equity of 7-5-1 pre-flop I think it's probably OK. Remember to fold if you miss the flop.
I guess what really piqued my interested was the situation where, in addition, you *knew* your opponent had AA. (For example, let's say you actually saw the BB's cards for some reason.) That got me thinking about whether ot not I would call one more bet with the A4s. I'd probably fold it in that case, but I found it interesting that calling even in one of the worst cases isn't too far off either.
I also remember one time I really did fold in this kind of a situation. I had limped in in a loose-passive game with 66, and it was raised behind me. A player folding after me accidentally exposed his cards and one card was a 6. So, I folded for one more bet when it came back around to me, although I would always call in the same spot without the additional information.
ScottyZ