from
PNL:
"Many novice players think about big bets in absolute terms when they should be thinking about relative price and pot odds. The classic example is a player who says something like, "No way would I call that much money on a draw."
For instance:
You have
A♣ 4♣
in the big blind in a 9-handed $0.50-$1 game with loose passive opponents. You have the short stack of $11. Eight players limp and you check. The pot is $9. The flop is
K♣ 6♥ 4♦. It is checked around. The turn is
Q♣, giving you the nut flush draw. The small blind check. You decide to check. The next player bets $10 and seven players call. What do you do?
You call all-in. the pot is $89, and the bet is $10, yielding pot odds of 8.9-to-1. The odds of hitting the flush on the river are 4.2-to-1. You are getting great value to draw to the nut flush, so do it.
Now, what happens when we change the dollar amount of the call?
Same
A♣ 4♣, except that everyone starts with $1,001. Nine see the
K♣ 6♥ 4♦ flop, which is checked around. The turn is the
Q♣. You check, the next player goes all in for $1,000 and 7 players call all-in. (Yes, we know this is far fetched.) What would you do?
Many players would fold, refusing to call a big bet on a draw. Those players are making a mistake of thinking in absolute dollars. Their thought process goes something like: "A thousand dollars is a lot of money. I am not going to risk it all on just a draw. After all, I'm going to lose it more than four times out of five."
It is a natural way to think. It is also wrong. If calling was a good value when it was $10, it' still a good value.
Don't think in terms of absolute dollar amounts. Instead, think in terms of value.
How much, on average, does folding cost? Assume, for simplicity, that your opponents' hole cards are random with regard to suits. Of the 47 unknown cards 9 give you a flush. If you call you expect to win 9 out of 47 times, or 19.1 percent of the time. The other 80.9 percent of the time you will lose $1,000.
After your call the pot becomes $9,009. Your equity in the pot after calling is $1,721.
$1,721 = (0.191)($9,009)
The call costs you $1,000, but you get $1,721 of value. That means that folding is a $721 mistake! In a game with $1,000 stacks, you simply cannot make many $721 mistakes and be a long-term winner. If you cannot or will not make that call (and others like it), you are likely to fold yourself into the poorhouse.
Stepping back for a moment, we acknowledge that
occasionally players can be correct to fold for that $1,000. Specifically, if you are underbankrolled, or prone to serious tilt, it might be right. If you had just $1,000 and no means to replace it, folding would be correct-- as would cashing out immediately and finding a smaller game. If you were in a super loose game and expected to make a ton of money later in the night, but had no means of rebuying, folding would also be correct-- as would bringing more money with you next time. If calling and losing would cause you to go on tilt, and possibly bluff off $4,000 later in the night, folding would again be correct-- as would working on your tilt control.
But make no mistake, choosing to fold when you are getting good value costs money. If you do it too often, in the long run you wont win as much as you should, and you may not be able to win at all. "
(pgs 21-24)
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This is a pretty good summation and example of the recent "debates" regarding pot odds and value. Here we have a situation where, when we compare the event odds of hitting the flush (4.2:1 against) to the money odds (8.9:1) needed to call, we come to a correct decision regarding our equity and positive expected value (call).
I really don't see how this is debatable in any ways (other than those already pointed/refuted out by the authors), or how you can dismiss "math" here. This is essentially how you should make ALL your poker decisions.
I should add that in a footnote the authors do acknowledge that pairing the board might result in losing to a full house, or that hitting another ace or four might also win you the pot, but that for this example those factors don't change the main point that folding is bad.
Of course this is an unrealistic scenario designed to make a point. However, scenarios less extreme, but for all purposes the same as this, occur in poker all the time. The fact is, you simply cannot pass on +ev opportunities when they present themselves. It's hard enough to come across them, and the edges in poker are slim enough that missing profit when it's available because of something like having too little bankroll just isn't winning poker, and it certainly isn't professional poker either.
