dealing a poker hand is random, from the machine to the dealer.

so why don't i win 11 percent of the hands dealt at a 9-handed table?

Typically the loosest player at the table will win the most pots. This could be a LAG or a call station. As a tight player, your power is folding - so you do not get to realize your 11% of hands that would have been weak vs weaker or pure suck outs.

You profit on your meager 7~9% of pots because you invest small in losing pots and claim big in winning pots.

LOL. Yeah, I was just being sarcastic. Never even really thought about until the other night when I had folded for three straight orbits without winning a pot.

How many years should it take someone who plays poker fulltime(40 hrs/wk) to win at least a table share of a bad beat jackpot. Qualifying hand is Aces full of tens beaten by quads or better, with both whole cards having to play.

I was then thinking of multipliying the answer by 9 to get the average of winning the biggest prize(bad beat) but this is wrong since jackpots are hit without a full table all the time.

Any other information missing?

there are no odds for me hitting a bad beat. it's infinite, because i will never get so much as a table share.

Back to the ILCD at LATB "AA" count question. Here are the odds of him getting AA from 0 times to 78 times (assuming 78 hands in telecast)

Aces count Percent Odds
0 70.21% 1 in 1.424
1 24.89% 1 in 4.018
2 4.36% 1 in 22.96
3 0.50% 1 in 199.4
4 0.04% 1 in 2,339
5 0.00% 1 in 34,772
6 0.00% 1 in 628,756
7 0.00% 1 in 13,448,390
8 0.00% 1 in 333,368,534
9 0.00% 1 in 9,429,567,095
10 0.00% 1 in 300,652,863,899
11 0.00% 1 in 10,699,704,862,283
12 0.00% 1 in 421,600,310,991,459
13 0.00% 1 in 18,269,346,809,629,900
14 0.00% 1 in 865,685,971,902,462,000
15 0.00% 1 in 44,636,932,926,220,700,000
16 0.00% 1 in 2,494,000,061,909,470,000,000
17 0.00% 1 in 150,444,519,863,571,000,000,000
18 0.00% 1 in 9,766,562,273,110,540,000,000,000
19 0.00% 1 in 680,403,838,360,034,000,000,000,000
20 0.00% 1 in 50,741,981,165,833,100,000,000,000,000
21 0.00% 1 in 4,041,861,258,381,880,000,000,000,000,000
22 0.00% 1 in 343,203,657,729,268,000,000,000,000,000,000
23 0.00% 1 in 31,010,901,930,537,400,000,000,000,000,000,000
24 0.00% 1 in 2,977,046,585,331,590,000,000,000,000,000,000,000
25 0.00% 1 in 303,217,707,765,254,000,000,000,000,000,000,000,00 0
26 0.00% 1 in 32,724,628,083,344,500,000,000,000,000,000,000,000 ,000
27 0.00% 1 in 3,738,159,438,751,270,000,000,000,000,000,000,000, 000,000
28 0.00% 1 in 451,511,022,406,035,000,000,000,000,000,000,000,00 0,000,000
29 0.00% 1 in 57,612,806,459,010,200,000,000,000,000,000,000,000 ,000,000,000
30 0.00% 1 in 7,760,092,298,560,540,000,000,000,000,000,000,000, 000,000,000,000
31 0.00% 1 in 1,102,579,780,753,810,000,000,000,000,000,000,000, 000,000,000,000,000
32 0.00% 1 in 165,152,375,670,358,000,000,000,000,000,000,000,00 0,000,000,000,000,000
33 0.00% 1 in 26,065,353,203,626,100,000,000,000,000,000,000,000 ,000,000,000,000,000,000
34 0.00% 1 in 4,332,640,932,513,840,000,000,000,000,000,000,000, 000,000,000,000,000,000,000
35 0.00% 1 in 758,212,163,189,923,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000
36 0.00% 1 in 139,652,100,754,981,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000
37 0.00% 1 in 27,065,907,146,322,500,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000
38 0.00% 1 in 5,518,804,481,542,840,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000
39 0.00% 1 in 1,183,783,561,290,940,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000
40 0.00% 1 in 267,110,136,906,673,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000
41 0.00% 1 in 63,403,511,444,689,200,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000
42 0.00% 1 in 15,833,741,776,998,100,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00
43 0.00% 1 in 4,160,755,478,066,720,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000
44 0.00% 1 in 1,150,746,086,505,310,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000
45 0.00% 1 in 335,070,184,011,840,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000
46 0.00% 1 in 102,754,856,430,298,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000
47 0.00% 1 in 33,202,662,984,039,900,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000
48 0.00% 1 in 11,310,326,487,466,500,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000,000
49 0.00% 1 in 4,064,177,317,829,630,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000
50 0.00% 1 in 1,541,584,499,866,410,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000
51 0.00% 1 in 617,734,931,732,182,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000
52 0.00% 1 in 261,736,578,482,080,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000
53 0.00% 1 in 117,378,788,657,733,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000
54 0.00% 1 in 55,778,400,370,154,600,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000,000,000,000,000,000,000
55 0.00% 1 in 28,121,610,186,619,600,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000,000,000,000,000,000,000,000
56 0.00% 1 in 15,063,401,630,398,000,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000,000,000,000,000,000,000,000,000
57 0.00% 1 in 8,586,138,929,326,860,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000
58 0.00% 1 in 5,217,101,558,962,410,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000
59 0.00% 1 in 3,385,898,911,766,600,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000
60 0.00% 1 in 2,352,308,717,648,380,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000
61 0.00% 1 in 1,753,776,832,824,510,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000
62 0.00% 1 in 1,407,147,999,983,900,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000
63 0.00% 1 in 1,218,941,954,986,060,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000
64 0.00% 1 in 1,144,180,181,746,910,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000
65 0.00% 1 in 1,168,698,328,498,630,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000
66 0.00% 1 in 1,305,346,133,061,550,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000
67 0.00% 1 in 1,603,400,166,777,270,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000
68 0.00% 1 in 2,180,624,226,817,080,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000
69 0.00% 1 in 3,310,187,576,308,330,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0
70 0.00% 1 in 5,664,098,741,683,140,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000
71 0.00% 1 in 11,059,152,793,136,300,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000,000,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000
72 0.00% 1 in 25,025,282,891,897,100,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000,000,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000
73 0.00% 1 in 66,984,340,540,644,500,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000,000,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000
74 0.00% 1 in 218,101,012,800,338,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000
75 0.00% 1 in 899,666,677,801,396,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000
76 0.00% 1 in 5,014,142,284,279,780,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000
77 0.00% 1 in 42,469,785,147,849,700,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000,000,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000,000,000,000,000,000
78 0.00% 1 in 728,781,513,137,101,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000

So you're saying there's a chance.

Indeed.

In before "LATB is rigged"

great man, thank you very much! i was able to do it for 5card plo also, very much appreciated!

I have partially covered the non-bolded questions in other answers in the thread - so I will just address the bolded one at the moment:

"Odds of flopping a flush draw with 2 suited cards"

Related: Odds of getting suited cards:
12 / 51

Odds of flopping a flush:
11*10*9/(50*49*48) = 990 / 117,600 = 0.84% ~= 1 in 119

Odds of flopping a flush draw:
There are 50*49*48 / 3! flops
= 19,600 flops

Number that include exactly two of your suit
= 11*10 / 2 orders * 39 other cards = 2,145

2145 / 19600 = 10.94% ~= 1 in 9.13

1. Odds of an Ace flopping when me an opponent both have an ace

2. If i flop top pair with ak on a 9 7 board, what is the chance he has top pair vs middle pair vs bottom pair?

3. With A10 suited, what are the odds i flop top pair, odds i flop a straight draw, odds of flopping top pair with the 10 being top pair, odds of flopping a ten with it being middle pair

Odds of KK running into AA and AA running into KK?

I can at least answer question 1...If we are assuming you and your opponent have exactly one ace each then there are 48 unknown cards and 2 of them are aces. The odds of you not flopping an ace are therefore 46/48 * 45/47 * 44/46 = 87.77%. Therefore the odds of you flopping an ace (or two) is 12.23% (1-.8777).

What are the odds bip ever answers my question from way upthread?

Lol!!
Slim

. Hey now! - This thread still has a pulse. What question did I miss?

So there is still hope for me yet!

I think I can tackle this question:

I'm going to work on the assumption that if one player has KK and the other has AA that it will always some how get to show down, and as a result, we will know that it happened.

If that's the case, it's just simply what are the odds that one player is dealt AA and someone else is dealt KK in the same hand.

There is a 1/13 chance to get one king, and a 1/17 after that to get a second king.
So, 1/221 chance to be dealt KK x 10 different people who can have the hand.
1/22.1, or 4.52% chance.

Once we assume that one player has KK the odds that someone else has AA is more common (since there are now 2 kings removed from the deck) but there are less chances (players) who can be dealt in.

(4/50*3/49)*9 remaining players at the table.
(4*3*9)/(50*49) = 108/2450 = 1/22.68, or 4.40%
1/22.1 * 1/22.68 = ~1/501.23 So about .2% chance.
Seems like 2 in every 1000 hands dealt.

(Assuming 30 hands per hour)
We should see this once every ~16.6 hours of play.
So, for the average grinder once every 2 days. Seems reasonable.


Alternatively, and likely more simply I guess I could just say odds that someone has KK is 1/13*1/17 odds that someone has AA (when someone else has KK) is still (4/50*3/49).
There are 10c2 combinations of hands at a 10 handed table.

((4/52)*(3/51)) * ((4/50)*(3/49)) * (10!/(10-2)!) = (4*3*4*3*10*9)/(52*51*50*49)=12960/637000=.0020345

100%.


..the question was:

Hey bip the great, what are the odds that none vs. at least one of a certain number of cards flop (obviously the former is 1-the latter and vice versa). So if I had a PP I could know exactly how likely it is that an overcard flops or if my opponent's range was heavily weighted to AK/AQ I could know how often we get a flop with no A/K/Q etc. Thanks buddy.

There is a little caveat here. If you really have specific cards you want to dodge, then your opponent also implicitly has those cards. So I will approach it like so:

"I have 88 and I know my opponent has two broadways.. what are the odds of the flop coming without a single broadway?"

So the table would be:
How many cards to dodge = number of ranks * 4 cards per rank - 2 cards of said ranks in opponents hand.

i.e. - I want to dodge an A or a K because his range is AK, then you have to dodge 6 specific cards. 2 ranks * 4 cards / rank - 2 cards in opponent's range = 6..

Odds of succesful dodge = (48-#to dodge)*(47-#to dodge)*(46-#to dodge)/(48*47*46)
Cards to dodge & the odds to successfully dodge
3 (A-rag range) 82.0%
6 (A/K) 66.4%
10 (A/K/Q) 48.8%
14 (A/K/Q/J) 34.6%
18 (A/K/Q/J/T) 23.5%

Hey bip here is a fun one I have been thinking about.. perhaps it can be solved quickly with pokertools or something. What are the fair odds to run a random NL holdem hand vs a random PLO hand AIPF?. The PLO hand has to follow PLO rules (using exactly 2) while the NL hand can use 0 or 1 or 2 obv.

This is a very cool question... give me some time to work on it.

I have finished the BBJ number crunching... Results tomorrow!

Part 1, BBJ equity of each BBJ eligible hand.

note: All numbers assume the most common BBJ situation:
- Quads or better losing
- All quads must be made with pocket pair (i.e. AK on AAAxx board does not count)
- Your best possible hand must use both your hole cards (i.e. 5s3s on 8s7s6s4sX board makes a straight flush with both cards, but not the best hand that one can play)
- BBJ are split 50% to losing hand, 25% to winning hand, 25% to remainder of table
- I do not factor in taxes or tips... do that math on your own

There are 59 BBJ eligible hole card combos. Pocket pairs and sutied connectors:
(AA-22,AK-32,AQ-42,AJ-52,AT-62,A5-A2)

Below is the "equity in dollars of getting dealt one of these hands" per $100,000 BBJ. Again, losing gets one 50% of BBJ, winning gets one 25% of BBJ... and I will not factor in the table share, as any two cards are eligible for table share.

I have to assume all BBJ eligible hole cards make it to show down.. not a terrible assumption except for some of the outlier runner-runner quad deuces and of course people generally folding 62 suited.. but these effects are not terribly drastic.

After you are dealt your hole cards, there are 50*49*48*47*46 / 5! boards and we are looking for a specific opponent hand(s) out of 45*44/2 possible hands. That would imply:
2,097,572,400 ways for the board and opponent cards to run out.

The math is easy for heads up. 10 handed, there are 10*9/2 ways for the necessary beat hands to get distributed.. BUT! multiplying the heads up odds by 45 ever so slightly exaggerates the BBJ possibilities. This is because we are double counting and even triple counting some weird corner cases where a table produces 3-way or 4-way BBJ. I AM GOING TO IGNORE THOSE CASES - if anyone is ever curious about that math it is a few posts back. It is rather negligible because it only applies to certain boards (boards where 3+ BBJ hands are possible) and the odds of it are quite low even on those hands.

ANYWAYS - the 10 handed odds are a fraction high.. good enough to answer the question "how much is this hand worth in terms of BBJ"

Head Up Equity (SB/BB for example)

Hand class / BBJ Losing Hand / BBJ Winning Hand / Equity per $100,000 BBJ

(counts are instances out of 2,097,572,400 that the hand accomplishes BBJ stuff)

AA 19,008 8,064 $0.42
KK 17,424 9,648 $0.44
QQ 15,840 14,088 $0.52
JJ 14,256 18,528 $0.61
TT 12,672 22,968 $0.70
99 11,088 24,480 $0.72
88 9,504 26,064 $0.73
77 7,920 27,648 $0.75
66 6,336 29,232 $0.77
55 4,752 30,936 $0.79
44 3,168 29,664 $0.74
33 1,584 28,392 $0.70
22 0 27,120 $0.65
AK 5,736 0 $0.07
KQ 7,840 0 $0.09
QJ 9,580 0 $0.11
JT 11,308 0 $0.13
T9 11,236 0 $0.13
98 11,236 4,324 $0.24
87 11,236 4,504 $0.24
76 11,236 4,508 $0.24
65 6,912 4,508 $0.19
54 6,912 4,532 $0.19
43 5,184 4,532 $0.17
32 3,456 4,520 $0.15
AQ 2,304 0 $0.03
KJ 4,068 0 $0.05
QT 5,796 0 $0.07
J9 5,724 0 $0.07
T8 5,724 0 $0.07
97 5,724 364 $0.08
86 5,724 368 $0.08
75 5,184 368 $0.07
64 5,184 368 $0.07
53 5,184 392 $0.07
42 3,456 392 $0.05
AJ 1,800 0 $0.02
KT 3,552 0 $0.04
Q9 3,480 0 $0.04
J8 3,480 0 $0.04
T7 3,480 0 $0.04
96 3,480 12 $0.04
85 3,456 12 $0.04
74 3,456 12 $0.04
63 3,456 12 $0.04
52 3,456 36 $0.04
AT 1,776 0 $0.02
K9 1,728 0 $0.02
Q8 1,728 0 $0.02
J7 1,728 0 $0.02
T6 1,728 0 $0.02
95 1,728 0 $0.02
84 1,728 0 $0.02
73 1,728 0 $0.02
62 1,728 0 $0.02
A5 1,728 0 $0.02
A4 1,728 12 $0.02
A3 1,728 356 $0.03
A2 1,728 4,140 $0.12


Conclusions:

So, the most valuable hand is pocket 5s.
Pocket Pairs are more valuable than suited connectors (>2x typically)
The most valuable suited connectors are 98,87,76
One+ gappers are not that valuable relatively.
If you are debating completing the SB at a $1/$2 game with a PP when BBJ is $200,000... you should do it as that hand is worth > $1 for BBJ.

Don't pass up that free EV It can almost buy a McDouble.

Rough 10 handed equity
(9 places for your opponent to be)

AA $3.77
KK $3.94
QQ $4.72
JJ $5.50
TT $6.29
99 $6.44
88 $6.61
77 $6.78
66 $6.95
55 $7.15
44 $6.70
33 $6.26
22 $5.82
AK $0.62
KQ $0.84
QJ $1.03
JT $1.21
T9 $1.21
98 $2.13
87 $2.17
76 $2.17
65 $1.71
54 $1.71
43 $1.53
32 $1.34
AQ $0.25
KJ $0.44
QT $0.62
J9 $0.61
T8 $0.61
97 $0.69
86 $0.69
75 $0.64
64 $0.64
53 $0.64
42 $0.45
AJ $0.19
KT $0.38
Q9 $0.37
J8 $0.37
T7 $0.37
96 $0.38
85 $0.37
74 $0.37
63 $0.37
52 $0.38
AT $0.19
K9 $0.19
Q8 $0.19
J7 $0.19
T6 $0.19
95 $0.19
84 $0.19
73 $0.19
62 $0.19
A5 $0.19
A4 $0.19
A3 $0.26
A2 $1.07

! I am impressed. Old Man Coffee is onto something. Most of those hands are worth more for BBJ reasons than for poker equity reasons!

"How are we ever going to win the BBJ if you keep raising?!"... that old lady is right!! 55 UTG at a $200,000 BBJ 10 handed is worth ~$14 in equity.. and you made her fold it!!

So if the BBJ is 500k+ I should complete every BBJ eligible hand from the SB every time?
Interesting.

Assume a heads up game, there are (52*51*50*49*48*47*46*45*44)/(8*5!) hole card and boards runouts. Below is a table of BBJ results and frequency:


Those are counts out of 1,390,690,501,200