odds geniuses stud hi low

[sircorbett]

What are the odds of first 5 cards for 2 players being a flush??


Transcript for game #14429229636 requested by sircorbett (donaldcorbett001@yahoo.com)
*********** # 1 **************
pokerstars Game #14429229636: 7 Card Stud Hi/Lo Limit ($0.04/$0.08) - 2008/01/09 - 03:39:28 (ET)
Table 'Amelia IV' 8-max
Seat 1: sircorbett ($1.62 in chips)
Seat 2: EdwardBlake ($1.80 in chips)
Seat 3: kid okra ($1.84 in chips)
Seat 4: picoagi ($1.86 in chips)
Seat 5: cellman972 ($1.13 in chips)
Seat 6: kydn123 ($1.32 in chips)
Seat 8: worcaholicPD ($3.48 in chips)
sircorbett: posts the ante $0.01
EdwardBlake: posts the ante $0.01
kid okra: posts the ante $0.01
picoagi: posts the ante $0.01
cellman972: posts the ante $0.01
kydn123: posts the ante $0.01
worcaholicPD: posts the ante $0.01
*** 3rd STREET ***
Dealt to sircorbett [Ts 9s 7s]
Dealt to EdwardBlake [5h]
Dealt to kid okra [6h]
Dealt to picoagi [Kd]
Dealt to cellman972 [3s]
Dealt to kydn123 [Ac]
Dealt to worcaholicPD [8d]
cellman972: brings in for $0.02
kydn123: calls $0.02
worcaholicPD: folds
sircorbett: calls $0.02
EdwardBlake: calls $0.02
kid okra: folds
picoagi: folds
*** 4th STREET ***
Dealt to sircorbett [Ts 9s 7s] [Js]
Dealt to EdwardBlake [5h] [Jd]
Dealt to cellman972 [3s] [8c]
Dealt to kydn123 [Ac] [9c]
kydn123: bets $0.04
sircorbett: calls $0.04
EdwardBlake: calls $0.04
cellman972: calls $0.04
*** 5th STREET ***
Dealt to sircorbett [Ts 9s 7s Js] [5s]
Dealt to EdwardBlake [5h Jd] [Ah]
Dealt to cellman972 [3s 8c] [Th]
Dealt to kydn123 [Ac 9c] [Tc]
EdwardBlake: checks
cellman972: checks
kydn123: bets $0.08
sircorbett: raises $0.08 to $0.16
EdwardBlake: calls $0.16
cellman972: folds
kydn123: raises $0.08 to $0.24
sircorbett: calls $0.08
EdwardBlake: calls $0.08
*** 6th STREET ***
Dealt to sircorbett [Ts 9s 7s Js 5s] [Qd]
Dealt to EdwardBlake [5h Jd Ah] [Jc]
Dealt to kydn123 [Ac 9c Tc] [7d]
EdwardBlake: checks
kydn123: bets $0.08
sircorbett: calls $0.08
EdwardBlake: calls $0.08
*** RIVER ***
Dealt to sircorbett [Ts 9s 7s Js 5s Qd] [4c]
EdwardBlake: checks
kydn123: checks
sircorbett: bets $0.08
EdwardBlake: calls $0.08
kydn123: calls $0.08
*** SHOW DOWN ***
sircorbett: shows [Ts 9s 7s Js 5s Qd 4c] (HI: a flush, Jack high)
EdwardBlake: mucks hand
kydn123: shows [5c 7c Ac 9c Tc 7d 3d] (HI: a flush, Ace high)
kydn123 collected $1.44 from pot
No low hand qualified
*** SUMMARY ***
Total pot $1.51 | Rake $0.07
Seat 1: sircorbett showed [Ts 9s 7s Js 5s Qd 4c] and lost with HI: a flush, Jack high
Seat 2: EdwardBlake mucked [7h Jh 5h Jd Ah Jc 2d]
Seat 3: kid okra folded on the 3rd Street (didn't bet)
Seat 4: picoagi folded on the 3rd Street (didn't bet)
Seat 5: cellman972 folded on the 5th Street
Seat 6: kydn123 showed [5c 7c Ac 9c Tc 7d 3d] and won ($1.44) with HI: a flush, Ace high
Seat 8: worcaholicPD folded on the 3rd Street (didn't bet)

 

[viking999]

To simplify, I'm going to assume it's heads up. I'm also assuming that the two flushes are different suits.

P(flush in first 5 cards) = P(first card) * P(second card) * P(third card) * P(fourth card) * P(fifth card)

P(player 1 flush in first 5 cards) = 1 * 12/50 * 11/48 * 10/46 * 9/44
P(player 1 flush in first 5 cards) = 0.002446

P(player 2 flush in first 5 cards) = 39/51 * 12/49 * 11/47 * 10/45 * 9/43
P(player 2 flush in first 5 cards) = 0.002039

P(both getting a flush in first 5 cards) = P(player 1 flush in first 5 cards) * P(player 2 flush in first 5 cards)

P(both getting a flush in first 5 cards) = 0.002446 * 0.002039
P(both getting a flush in first 5 cards) = 0.000004987

Or about 0.0004987%.

Or about 1 in 200,000.

 

[sircorbett]

odds

wow i wasnt sure how you would figure that out but it looks correct,thank you,