here is something i found about implied odds with sc

A recent thread about using the 5/10 rule to call preflop raises with PPs and suitedconnectors got me thinking about the kind of implied odds required to call preflop raiseswith SCs; people tend to arbitrarily use things like the 5/10 rule, even though I've neverseen any mathematical description of the kind of odds you need to call these raises. I'mgoing to attempt to solve that problem (but I still need some help!).I'll list the conclusions first, and leave the tl;dr math for the bottom for those of you thatwant to peruse it. I also encourage math-head-types to check my math to make sure Ididn't mess anything up.There are two kinds of hands you can flop with SCs: Good made hands (most of whichcan be made by calling with ATC, which of course we don't do) and draws. First, madehands, stolen off some page I googled:

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, andthat's where things get complicated. Let's separate this into two categories: combo drawsand 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 afavorite against an overpair, or getting AI on the flop is +EV when you take some foldequity (and thus taking down dead money) into account.Combining these big draws with good made hands, you'll have a relatively "big hand" onthe flop 12.5% of the time, or 1 in 8 (very close to how often you will flop a set with anoverpair). However, since a set is a near-invincible hand and you still have to improvewith these draws, you can't say that you also need about 7:1 odds to call with a suitedconnector. Your average equity on the flop with these made hands and combo drawsagainst an overpair is 66% (the made hands go from 75%-99%; the combo draws rangefrom 45%-65%); compare this with sets, where your equity is generally 90+%.

REGULAR DRAWS

126

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 willmost frequently be one of these. These draws improve to a flush or straight on the riverabout 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 FDAdding 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 immediatelyprofitable (i.e. +EV to shove it in); the other half, you'll have your standard old OESD orFD which requires playing some poker.

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

If you don't like numbers, skip the rest of the post; what follows is how I calculatedeverything.

tl;dr math

Made hands:I calculated the odds of flopping a straight myself; with 65s, for example, there are fourflops that give you a straight (789, 478, 347, 234). The odds of hitting each of thoseflops 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.

127

Odds of flopping 87x with two clubs, where x does not complete a flush or straight anddoes 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 0.07653and 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)438/50 * 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 astraight):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%

128