Odds of flopping…

Flush: 0.84%

Two pair: 2% Trips: 1.35%

Full house: 0.09% Quads: 0.01% Straight: 1.31% ——-

Total: 5.6% (1 in 18 times, 17:1)

However, most of the time you will be flopping draws instead of big hands with SCs, and that’s where things get complicated. Let’s separate this into two categories: combo draws and regular draws.

**COMBO DRAWS**

Odds of flopping…

20 outer (OESD + FD + pair): 0.077%

17 outer (Gutshot + FD + pair): 0.153%

15 outer (OESD + flush draw): 1.424%

14 outer (Pair + flush draw): 1.450%

13 outer (Pair + straight draw): 1.147%

12 outer (Gutshot + flush draw): 2.664%

————————

Total: 6.9% (1 in 14 times, 13:1)

These draws are all hands that can be played profitably after the flop; either you are a favorite against an overpair, or getting AI on the flop is +EV when you take some fold equity (and thus taking down dead money) into account.

Combining these big draws with good made hands, you’ll have a relatively “big hand” on the flop 12.5% of the time, or 1 in 8 (very close to how often you will flop a set with an overpair). However, since a set is a near-invincible hand and you still have to improve with these draws, you can’t say that you also need about 7:1 odds to call with a suited connector. Your average equity on the flop with these made hands and combo draws against an overpair is 66% (the made hands go from 75%-99%; the combo draws range from 45%-65%); compare this with sets, where your equity is generally 90+%.

**REGULAR DRAWS**

Odds of flopping…

9 outer (flush draw): 5.2%

8 outer (straight draw): 8.0%

—————–

Total: 13.2% (1 in 7.5 times, 6.5:1)

These are your standard draws; when you flop a hand with which you can continue, it will most frequently be one of these. These draws improve to a flush or straight on the river about 1 time in 3.

**Summary**

– you have a 5.6% (1 in 18, 17:1 chance) of flopping a good made hand

– you have a ~7% (1 in 14, 13:1) chance of flopping a strong (12+ outs) combo draw

– you have a ~13% chance (1 in 7.5, 6.5:1) chance of flopping a standard OESD or FD

Adding these all together, you will flop a hand you can continue

with on the flop 25% of the time (1 in 4). However, only half of the time will these hands be immediately profitable (i.e. +EV to shove it in); the other half, you’ll have your standard old OESD or FD which requires playing some poker.

**So, a question from me to all you math-heads: How do you combine these preflop odds with the odds of hitting your hand postflop to figure out the implied odds required to call with SCs preflop?**

If you don’t like numbers, skip the rest of the post; what follows is how I calculated everything.

**tl;dr math**

Made hands:

I calculated the odds of flopping a straight myself; with 65s, for example, there are four flops that give you a straight (789, 478, 347, 234). The odds of hitting each of those flops are 12/50 * 8/49 * 4/48; multiply that by 4 flops, and you get 1.31%.

**Combo draws**

All examples assume you have 6c5c.

OESD + flush draw + pair (20 outs ZOMG):

You need a flop of 87(6/5), 7(6/5)4, (6/5)43, with two clubs each. 8c 7c 6/5x: 2/50 * 1/49 * 5/48 * 3 = .0255%

Multiply by 3 to get odds for all three flops = 0.07653%. Not very high.

Gutshot + flush draw + pair (17 outs):

You need a flop of 98(6/5), 97(6/5), 8(6/5)4, 7(6/5)3, (6/5)42, (6/5)32 with two clubs.

9c 8c 6/5x: 2/50 * 1/49 * 5/48 * 3 = .00255%

Multiply by 6 to get odds for all six flops = 0.153%.

OESD + flush draw (15 outs):

You need a flop of 87x, 74x, or 43x with two clubs; in addition, you can catch ultra-deceptive flops of 973 with two clubs or 842 with two clubs.

Odds of flopping 87x with two clubs, where x does not complete a flush or straight and does not pair your hand:

87x: 7c 8c x = 2/50 * 1/49 * 27/48 * 3 = 0.138%

7c 8x xc = 1/50 * 3/49 * 10/48 * 6 = 0.153%

7x 8c xc = 3/50 * 1/49 * 10/48 * 6 = 0.153% Total = 0.444%

Total for all 3 flops = 1.332%

973: 9c 7c 3x = 2/50 * 1/49 * 3/48 * 3 = 0.0153% *3 for 9c 7x 3c/9x 7c 3c = 0.0459%

*2 for 842 = 0.0918%

Total odds of flopping 15-outer: **1.424%**

Pair + flush draw (14 outs):

Two clubs and one of your hole cards: 6/50 * 11/49 * 10/48 * 3 = 1.68%

Since we already counted pair + FD + OESD and pair + FD + gutshot, subtract 0.07653 and 0.153 to get **1.45%**

Pair + straight draw (13 outs):

using 65s, possible flops are 87(6/5), 7(6/5)4, (6/5)43 8/50 * 4/49 * 5/48 * 3 = 0.408%

Multiply by 3 for all three flops = 1.224%

Since we already counted pair + FD + OESD, subtract 0.07653 to get **1.147%**

Gutshot + flush draw (12 outs):

You need a flop of 98x, 97x, 84x, 73x, 42x, 32x (where each flop has two clubs).

Same calculation as OESD + flush draw; 0.444% per flop * 6 flops = **2.664%**

So, **total odds of flopping a combo draw** = 0.07653% (20 outs) + 0.153% (17 outs) + 1.424% (15 outs) + 1.45% (14 outs) + 1.147% (13 outs) + 2.664% (12 outs) = 6.915% = 1 in 14 times (13:1)

**Regular draws**

OESD (8 outs):

There are five flops you can catch an OESD with: using 65s as an example, there’s 87x, 74x, 43x, 973, and 842.

Odds of flopping 87x (where x does not pair your hand and does not complete a straight):

8/50 * 4/49 * 34/48 * 3 = 02.94%

Subtract 0.442% for the times it makes an OESFD (which we already counted) = 2.498%

Multiply by 3 for the odds of 87x/74x/43x: 7.494%

Odds of flopping 973: 12/50 * 8/49 * 4/48 = 0.33%

Multiply by 2 for the odds of 973/842: 0.65%

Subtract 0.0918 since we already counted double gutshot + FD: = 0.558%

Total odds of flopping non-combo OESD = **8.05%**

Flush draw (9 outs):

Two clubs + a blank that does not complete a flush or pair your hand:

11/50 * 10/49 * 33/48 * 3 = 9.26%

Subtract 1.424 and 2.661 since we already counted the times where the flush draw gives you an OESD, and you get 5.175% non-combo flush draws.

So, your total chances of flopping a standard 8 or 9 out draw are 8.05% (OESD) + 5.175% (flush) = 13.225% (1 in 7.5, 6.5:1).

I calculated the average equity of made hands/combo draws against overpairs by taking the weighted average of each:

0.077 / 12.5 * 65.556 (0.077 / 12.5 = %age of time you flop oesfd+pair, 65.556% = equity of 6s5s on 9s8s6x board against AcAd)

+ .153 / 12.5 * 57.677

+ 1.424 / 12.5 * 56.26

+ 1.45 / 12.5 * 50.71

+ 1.147 / 12.5 * 45.86

+ 2.664 / 12.5 * 47.78

+ 0.84 / 12.5 * 97.17

+ 2 / 12.5 * 74.55

+ 1.35 / 12.5 * 87.78

+ 0.09 / 12.5 * 91.414

+ 0.01 / 12.5 * 99.899

+ 1.31 / 12.5 * 96.717