Mathematical Explanation

Flatliner · #1 07-12-2004, 01:13 PM

I understand that if a person is holding suited cards and two cards of the same suit come on the flop, the probability of making the flush on the turn OR on the river is 1.86 to 1. Can someone please explain how this is mathematically determined?

Louie Landale · #2 07-12-2004, 01:41 PM

There are 5 cards you can see leaving 47 unknown in the deck; 9 are spades and 38 are not. The chances of making the flush = 1.0-changes of missing the flush. Chances of missing is easier to calculate.

To miss the flush you need to snag non-spade on turn AND river. Chances of a non-spade on turn are=38/47. "AND" means multiply. Chances of non-spade on river has one less card in the deck (the "miss" on the turn), or 37/46. So chances are 38*37/47*46 = 65%. Chances of making it = 100-65% = 35%. Odds are 65:35 = 65/35 = 1.86:1.

You need to force yourself through one or two of these. After you believe you DO understand it, then trust the various odds-charts.

- Louie

We CAN calculate the chances of making it directly. That would be chances of making on turn OR (plus) chances of making on river, MINUS chances of catching runner-runner. That's a little sticky.

BruceZ · #3 07-12-2004, 01:56 PM

[ QUOTE ]
I understand that if a person is holding suited cards and two cards of the same suit come on the flop, the probability of making the flush on the turn OR on the river is 1.86 to 1. Can someone please explain how this is mathematically determined?

[/ QUOTE ]

Here is a link to 3 different methods to compute this.

Flatliner · #4 07-12-2004, 02:04 PM

Thanks for both of your replies. Definitely cleared things up.

Ed Miller · #5 07-12-2004, 02:59 PM

Chance of MISSING flush is (38/47)(37/46) ~= 0.65
Thus, chance of MAKING flush is 1 - 0.65 = 0.35

Leo Bello · #6 07-12-2004, 10:14 PM

You want to know where the 1.86:1 came. Weel easy:
You have a 4 flush so you have 9 outs. this means you have 9/47 of catching on the the turn and if you miss there have 9/46 to catch on the river. To get the odds of catching you should first figure the odds of missing.

38/47*37/46= 0.65, so the chance of catching are 0.65

1-0.65) or 0.65:0.35 or about 1.86:1

Got it? 0,65 (chance of missing : (1-chance of missing).