Taken from my blog
I've just written my blog post, about to start a session, and feel I need to go through a hand from yesterday to show myself I'm being stupid:
Poker Stars $0.05/$0.10 No Limit Hold'em - 6 players
DeucesCracked Poker Videos Hand History Converter
MP: $9.62
Hero (CO): $10.35
BTN: $8.86
SB: $13.67
BB: $10.00
UTG: $11.93
Pre Flop: ($0.15) Hero is CO with Q 
J 
1 fold, MP calls $0.10, Hero raises to $0.30, BTN calls $0.30, 2 folds, MP calls $0.20
Flop: ($1.05) 7 8 T 
(3 players)
MP checks, Hero checks, BTN bets $0.90, MP calls $0.90, Hero calls $0.90
Turn: ($3.75) K (3 players)
MP checks, Hero checks, BTN bets $3, MP calls $3, Hero ???
Easy fold right? Not if I'm in a gambling mood.
So let's make some assumptions to make this maths easy.
1. If I miss the river, I fold
2. If I hit my A or 9, we all go all-in and I win (even if its a 3rd spade)
3. Neither villain has an A or a 9, or a flush draw
4. Villains are unknowns
Next, let's work out my odds of hitting the river:
52 cards in a deck, 6 are out (my 2 + the board), so 46 left. There are 8 cards left that (given the rules) give me the nuts. My odds are 8/46.
How much money does the pot need to amount to on the river to make it worth while?:
Imagine I'm flipping a coin, and betting 'tails'. I have 1/2 chance of winning, therefore to be breakeven I need a prize of 2/1.
Here I have 8/46 chance of winning, therefore to breakeven I need a prize of 46/8 x $3 that I'm putting in.
Therefore, to win if all conditions are perfect, I have to win $17.25 when this happens.
Let's add up.. $3.75 on the turn, add the BTN and MP bets of 3 each = $9.75. Add the rest of their stacks ($4.6 +$5.42) = $19.77! PROFITABLE CALL!
BUT, that's if all conditions are perfect and we live in a rake free world. Now lets assuming that 1 of these has an A (non-spade), and the other has a flush draw.
Now there are only 6 cards out of 46 that help us (one A is taken, and lets say we play perfectly and fold on A of spades). We now need to win $23 to be breakeven.
Add onto this that both villains could fold, or we could split pot, or we could call down against a flush draw, and this soon gets to be really bad. To be honest, I really wasn't expecting the initial set of rules to bring a good decision around! But we are then relying on a lot of assumptions for everything to play out well.
FYI;
Spoiler
Turn: ($3.75) K (3 players)
MP checks, Hero checks, BTN bets $3, MP calls $3, Hero calls $3
River: ($12.75) A 
(3 players)
MP checks, Hero bets $6.15 all in, BTN calls $4.66 all in, MP calls $5.42 all in
Final Pot: $28.25
MP shows 7 A (two pair, Aces and Sevens)
Hero shows Q J (a straight, Ten to Ace)
BTN shows 8 8 (three of a kind, Eights)
Hero wins $1.45
Hero wins $25.53
(Rake: $1.27)
