Preflop madness, and the associated math

[mbraudel]

(Apologies in advance for the long question.)

Last night I had a table on Party that went mad for a little while.

Every hand was capped before the flop by the same four players. Sometimes, a fifth person would join in the foolishness.

Post-flop, play was normal.

Which means that while the cost of seeing a flop was abnormally high, the overall pot size wasn't increased in proportion to the cost of see a flop.

With that many people making that many mistakes before the flop, a smart player should -- I think -- be able to turn a profit.

The question is, since it's very expensive to see a flop, can we calculate how tight a player should get? Can we figure out that we should only play hands that have a certain probability of winning, and then perhaps map that to starting hand groups?

Assumptions:
It costs four small bets to play a hand.
The pot will have 20 small bets (10 BB) in total before the flop.
5 more small bets go in on the flop.
4 big bets go in on the turn.
2 big bets go in on the river.
Total is 18.5 BB for the final pot.
Two players see the showdown.

To see a flop costs us 2 BB. To see the turn costs us half a BB. To see the river costs us 2 BB. To see the showdown costs us another BB.

Total of 5.5 BB cost to play a winning hand.

Of course, we can drop out at any point if we don't feel our hand is worth continuing with. So the cost to play a losing hand can be lower.

In order to take into account the times when we won't play past the flop (or turn, or river), somehow you need to adjust the effective cost of playing a winning hand.

But my limited math skills were exhausted several paragraphs ago, so help! Please!

(And thank you for a fun forum. I'm almost exclusely a lurker, but I learn a lot by reading your conversations.)

[Mike Haven]

i regret that i have no idea of the mathematics you wish to see, but, in general terms, you're going to pair roughly half of the time you take the flop, so, forgetting the times you play on without a pair, it's going to cost you 2bb for half your hands and 5.5bb for the other half

if you win 13.5bb for a cost of 7.5bb you need to win about half your completed hands to make a profit

loosely speaking, you would like to end up with a pair on the flop that will win close to 50% of the time against four "random" hands

playing any two tens or higher seems reasonable to me in the circumstances of the game you give