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Because of the size of the pot ($1000), you have favorable odds to call a $100 bet. However, you don’t have favorable odds to initiate fresh money into the pot yourself since you’re only getting one to one for fresh money while your chance to win the pot is one in three.
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Agree 100%.
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At any rate, I don’t think whether or not you should bet (or raise) depends on your “pot equity.”
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Now let's see how can we use it to help us decide whether or not to bet. Let's use a real life example from Texas Hold'Em. Let's say there are 4 hands: Th Jh, 9c 9s, As Ac, 6d 7d.
Let's say the flop is: 9h 8h 5c
Well, who would be profiting by betting and raising on this round of betting? Here is the calculation:
http://twodimes.net/h/?z=2052349
pokenum -h jh th - ac as - 9c 9s - 6d 7d -- 9h 8h 5c
Holdem Hi: 820 enumerated boards containing 5c 9h 8h
cards win %win lose %lose tie %tie EV
Jh Th 346 42.20 474 57.80 0 0.00 0.422
As Ac 13 1.59 807 98.41 0 0.00 0.016
9s 9c 270 32.93 550 67.07 0 0.00 0.329
7d 6d 191 23.29 629 76.71 0 0.00 0.233,
Let's the say size of the bet is $25. How much would everyone profit by putting in bets on the flop? Well, for each bet put in, the Jh Th returns on average 42%. So if everyone puts in one bet, the total would be $100, and the Jh Th would expect $42 of that on average. Thus, it is making $17 (42-25) of each bet that is put in. On the other hand, 6d7d has equity of only 23%. Thus, with each additional bet put into the pot, it is actually losing $2. So who should be betting and raising in this scenario? The big draw and the set both have greater than 25% equity, and will profit from all additional money that goes into the pot. The AA and the straight lose by putting additional money in the pot.
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However, it would be possible to relate whether or not you should
call to your pot equity. I don’t think of it in that way, but I guess one could come up with a mathematical relationship between the two.
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You can absolutely come up with a mathemetical realtionship between the two: EV=pot equity x total amount in pot (including your calls)-amount to call.
What I was trying to tell you before was that the top set example is exactly analagous to the hold 'em hand I just talked about above. In a four handed pot, it will be rare for top set, even on that board, to have less than 25% equity against three hands, thus it is making money by putting in bets on that round if everyone calls.
Is it just me, or isn't this all very basic?