Odds of Rainbow flop vs Suited flop

[Sid Lambert]

So, some friends of mine have been doing side bets for red vs black flops, or somebody gets paid if a 7 or a 9 is on the flop...then it started getting more complicated, rainbow vs suited flops...I wanted to run the calculations by everybody, see if its right...assuming you don't know anybody's hand...

so for suited flops it's:
3 cards, first suit doesnt matter,
12/51 chance the second card matches
11/50 chance the third matches
so multiplying those gives about 5.177% for a suited flop

rainbow flops:
first card doesnt matter
39/51 chance 2nd card doesnt match suit of 1st card
26/50 chance 3rd card doesnt match suits of 1st 2 cards
this gives about 39.765%

39.765 / 5.177 = 7.68

so 7.68 to 1 are the odds?...with all the other flops not mattering...so a 8:1 payout would be in favor of the person hoping for suited flops

EDIT: 2nd card for rainbow flop is 39/51, not 29/51...brainfart...thanks gumbie

[gumbie]

29/51 chance 2nd card doesnt match suit of 1st card

You mean 39/51 which gives us a 39.8% chance of a rainbow flop.

This intuitively seems higher than I notice. But maybe I don't notice the rainbow if the board is paired etc.

[Sid Lambert]

This intuitively seems higher than I notice. But maybe I don't notice the rainbow if the board is paired etc.

Yeah, also i feel like suited flops are super rare, but i guess 1 in 20 isn't that terrible...

thanks for the double checking...i thought something mite be a little off...

[golddog]

I think your suited calculations need to be multiplied by four.

1st card: 13/52 (rank not important, but suit is).
* 12/51 * 11/51. ~1.27%

Rainbow calcs seem o.k to me.

[Sid Lambert]

I think your suited calculations need to be multiplied by four.

1st card: 13/52 (rank not important, but suit is).
* 12/51 * 11/51. ~1.27%

Rainbow calcs seem o.k to me.

The above calculation is for finding the chances of a specific suited flop, such as hearts...the last fraction should be 11/50 if you wanted to do that...if you multiply your final answer by 4 (one for each suit), you'll find that it matches my answer...The reason being is that the first card of the flop can be anything, no first card would preclude a suited flop