[JLD]

Pre-flop Bet Sizing and Target SPRs
Following through on your key advice on thinking about the hand from beginning to end at the start of the hand, I put myself on the button in a live $1-$2 game, two limpers from middle position, typical opponents for these stakes (loose/passive), and my cards are AQo. I first thought about what would happen with various raise sizes and what the pre-flop pot would likely look like (sorry about the table but couldn't cut and paste succesfully).

Pre-Flop...................# of........Pre-Flop
Action........My Bet......Callers........Pot
Call..............$2..........4.............$10
Min-Raise......$4..........4.............$20
3x Raise.......$6..........3.............$24
3x + 1 per.....$10.........2.............$30
3x + 1 per.....$10.........1.............$20
7x Raise.......$14.........1.............$28
8x Raise.......$16.........1.............$32
10x Raise......$20.........1.............$40


The first column is my action, the second is how much I bet, the third is how many callers I get, and fourth is the resulting pre-flop pot size. I get the blinds to call as well in the first two bets, only the BB and the original limpers in the third example, and then when I raise to $10 I only get 1 or 2 of the original limpers to call. The final three examples are larger raises where I think I only get 1 caller when I am behind (at these stakes I think I would get reraised by QQ-AA and sometimes AK and only called by a mid pocket pair or AK...making a raise this large a bad play with AQo).

With that information, I then considered what each of these raises and resulting pre-flop pots would mean for me if I had various beginning stack sizes.

STACK SIZE SPRS
Pre-Flop.......$40.....$100.....$200......$300.....$40 0
Action.......(20BB)...(50BB)..(100BB)..(150BB)..(2 00BB)
Call.............3.80.....9.80....19.80.....29.80. ....39.80
Min-Raise.....1.80.....4.80.....9.80.....14.80.....19. 80
3x Raise.......1.42.....3.92.....8.08.....12.25.....1 6.42
3x + 1 per....1.00.....3.00.....6.33......9.67.....13.00
3x + 1 per....1.50.....4.50.....9.50.....14.50.....19.50
7x Raise......0.93.....3.07.....6.64.....10.21.....13 .79
8x Raise......0.75.....2.63.....5.75......8.88.....12 .00
10x Raise.....0.50.....2.00.....4.50......7.00......9. 50

For beginning stack sizes under 100BB, it looks like raising 3x the BB plus 1 for each limper is the preferred pre-flop bet because it achieves the lowest SPR. Even if I only get 1 caller, I would rather face one opponent with a slightly higher SPR than 3 opponents with a lower SPR because my steal equity is better against one opponent.

As mentioned in the book, the difficulty begins when the beginning stack size reaches 100BB ($200) as the only way to get a low SPR is to raise more (and as mentioned above I think this raise amount is bad because I think I only get called by a better hand with limited steal equity). One alternative is to limp and get an SPR of 20. However, I still think the steal equity I have from the button at these stakes is sufficient to make raising the better play at 100BB. Furthermore, because most opponents at these stakes do not raise or check-raise unless they have two pair beat, I am not getting my whole stack in there unless I have a very strong hand as well.

This discussion relates to your hand example number 4 on page 226 where you suggest limping with KJs on the button after two limpers. I think it is close but in late position I think my steal equity is sufficient in low-limit NL games to raise with KJs on the button. In other words, the continuation bet still works in these games against 1 to 2 opponents on the flop. My hand is likely ahead of their range (or only slightly behind Ax or mid-pocket pairs) and they are playing fit or fold so that a continuation bet will win enough to justify the pre-flop raise. By doing this, it also improves the chances that I get action when I really do have a good over-pair.

So I feel like I am missing something, because despite what I learned from the book about the dangers of SPRs of around ten for TPTK type hands, I still think it is the better play to raise with AQo even with a beginning stack of 100BBs. Is this simply due to my estimation of the players at these stakes and my estimated steal equity (as you noted in footnote 61 on pg. 226) or in your opinion am I misestimating my steal equity in live or online games at these stakes ($1-$2 live/$0.10-$0.25 online)?