A philosophical question

Something which happened during last night's session really got me thinking about pot odds. I'm not sure whether my opponent made the right play or not. Here's what happened: on hand 37, I flopped top two pair, bet small, and reraised big when I got raised. The turn looked like a harmless card, so I went all in with my last $5,748. My opponent called, and ended up winning a pot worth $36,196 when he hit his flush draw on the river. Did he make the right play or not? Looking strictly at the situation he was in at the time, he needed to pay $5,748 to win a $36,196 pot, so he was getting pot odds of slightly better than 6 to 1. If he thought his hand had better than a 1 in 6 chance of winning, he should call here. Actually, I should say, the conventional wisdom is that he should call here. I've always had difficulty buying into this particular piece of conventional wisdom. What bothers me about it is that it doesn't take into account how much the player has paid into the pot before the current decision point. In this case, my opponent had already paid $11,200 into the pot. If he doesn't hit his flush draw, he's not losing just the $5,748 he paid to see the river card, he's actually losing $16,948. If he feels he has a 1 in 6 chance of hitting his draw, that means that five of the times, he's going to be losing $16,948. The sixth time, he's going to be winning $36,196. To me, this is clearly a losing situation for him: he's lost 5 x $16,948, or $84,740, and only won $36,196. However, according to the conventional pot odds wisdom, he's made the correct play. I'll have to mull this over some more.

I was actually a 75% favorite to win this hand, but ended up hitting the felt. I reupped for the max, stayed patient, and ended up making a nice profit on the night. My biggest win was on hand 66, when I won a pot worth $105,100 with a full house, aces full of tens.

During current Hold'em session you were dealt 67 hands and saw flop:
 - 6 out of 9 times while in big blind (66%)
 - 4 out of 9 times while in small blind (44%)
 - 29 out of 49 times in other positions (59%)
 - a total of 39 out of 67 (58%)
 Pots won at showdown - 5 of 12 (41%)
 Pots won without showdown - 0

delta: $65,947
cash game no limit hold'em balance: $4,746,545
balance: $7,195,953

A philosophical question

I've played enough sit and go tournaments now that I've seen a fair number of unusual things. I've had a four of a kind at least three times in sit and gos, which I'm sure is well above the expected frequency given the number of hands I've played. I've been rescued by long shot river cards to split pots when I should have hit the felt, and have also been done in by long shot river cards when I was the clear favorite. Actually, those last two circumstances aren't really that unusual, especially in tournaments. Another variety of quasi-unusual tournament event has brought up a philosophical question. At least three times, I've observed hands where two players hit the felt at showdown; I was on the losing end of this scenario in the second tournament I played last night. The PokerStars software informed me that I'd finished the tournament in 5th place, and the other player who'd hit the felt had finished in 6th. The practical question of what criterion the software used to decide who got which place is what led to my philosophical question. I can think of at least 3 different criteria for deciding:

1. the losing player who had more money at the start of the final hand than the other losing player did gets the higher tournament placement

2. the losing player who had position on the other losing player gets the higher tournament placement

3. the losing player who would have won the hand if he'd been heads up against the other losing player gets the higher tournament placement

I don't think there's any clearly correct answer, which is what turns this into a philosophical question. Personally, I lean towards #3.

buy_in entry_fee num_players num_hands place winnings

 50000       800           6        56     3        0
 50000       800           6         6     5        0
 50000       800           6         8     6        0
 50000       800           6        80     2   105000
 50000       800           6        32     4        0
 50000       800           6        39     3        0

delta: $-199,800
tournament balance: $905,090
balance: $6,035,821