effective odds and implied odds

[DSL8266]

ok i have a question about these odds.I was reading theory of poker and it talks about effective odds and implied odds. If i have a suited card its around 8-1 draw to hit a 4 flush on the flop. now if theres a total of 5 people playing how does that justify the call preflop for my suited cards. because my pot odds is 4-1 to me. and the draw for that 4 flush is 8-1. Now through mathematical explanation in detail how would i calculate the effective and implied odds to justify that preflop call. please explain it for me in detail. Thank you so much.

[BruceZ]

If all you had were two suited cards, you would never have the right odds to make this call pre-flop in limit hold 'em. You would want to have at least suited connecting cards which can also flop a straight draw, and even then it's very marginal. You would like to have at least one high card in addition to your draw. If all you have are sooooted cards, then you have an 11.8% chance of floping a flush draw or a flush. Let's call it 10% for the sake of simplicity, and since you will not always win even if you make your flush, and when you lose with a flush it is very expensive. Then 90% of the time you will miss the flop and be done with your hand, having lost 1 small bet or -0.9 sb in expectation. The 10% of the time that you hit the flop you will pay at least another small bet to see the turn, but 38/47 of the time you will miss on the turn, so this will cost you another -(38/47)*10% small bets in expectation, ignoring the small percentage of the time that you flop a flush. Then you will usually have a large enough pot to see the river, so you will pay another 2 small bets for that, and that will miss 37/46 of the time, costing a total of -2*(38/47)*(37/46)*10%. So all together you will pay on average 0.9 + (38/47)*10% + (38/47)*(37/46)*10% = 1.11 small bets. You will only make a flush 1/3 of the time that you hit the flop or 1/3 of 10% = 1 time in 30. The other 29 times you will lose an average of 1.11 small bets or 31.2 small bets all together. This is how much you must make from your opponents all together when you make your flush to break even. You will win the 4 small bets that went in preflop, plus at least 1 more on the flop and 2 more on the turn for a total of 7. That leaves over 24 additional bets that you need to make up which is very unlikely.

If you repeat the above analysis for suited connectors, then you have about a 20% chance to hit the flop with a draw, straight, or flush (actually 21.4%), and you would still need to make 18 small bets from your opponents (total including pre-flop bets). This ignores the additional times you can win with a hand less than a straight, and the times you can win by bluffing and semi-bluffing, the chance of which improves with your position. It is also sometimes correct to raise in late position with these hands pre-flop to make the pot larger and tie your opponents to their hands.

[BruceZ]

The fact that we used 10% and 20% for the probabilities of hitting the flop instead of the exact numbers makes very little difference, EXCEPT in the final step where we compute how often we make the hand. Instead of 1 in 30 in the first case, if we do it accurately we find we make the flush 1 time in 21.5. This comes from 10.9% of flopping a flush draw, 35% chance to complete the draw, and 0.84% of flopping a flush, so we make a flush 1/(0.109*0.35 + 0.0084) = 1 in 21.5. This means we only have to make 20.5*1.11 = 23 small bets from our opponents, not 31.2. Still a lot.

For the suited connectors, we only have to make 13 bets from our opponents, not 18. It pays to be more conservative, however, because this doesn't take into account that you can lose many extra bets when you make your hand and lose. That is, your opponents get implied odds from you (reverse implied odds).

[DSL8266]

"1/(0.109*0.35 + 0.0084) = 1 in 21.5. This means we only have to make 20.5*1.11 = 23 small bets from our opponents, not 31.2. Still a lot. "

ok I am not that great with math so sorry if im annoying but i don't understand that calculation. What does that
" * " mean? is that a multiplication?
1/(0.109*0.35 + 0.0084) how does that equal 21. 5

[BruceZ]

What does that
" * " mean? is that a multiplication?

Yes.

1/(0.109*0.35 + 0.0084) how does that equal 21.5

0.109*0.35 = .03815
0.03815 + 0.0084 = 0.04655
1/0.04655 = 21.5

0.109 is 10.9% chance of flopping flush draw
0.35 is 35% chance of completing flush after flopping draw
0.0084 = 0.84% chance of flopping flush.

The rest of the calculation is the same as in the first post.