The domino karma punished me for my hubris on this hand

Game situation: 6-3 in our favor, Darrell Morgan (my partner) bid 36 and opponent passed

I bid 41

Now to be fair I could have let Darrell Morgan play his 36

In retrospect I should have done that but I was feeling it

So I bid 41

Chase (the opponent to my left) had all 3 of the 3s not in my hand

Only 5.2% chance that one of your opponents has the other three.

NO!!! (The dominos said)

We got the decisive mark the next hand bidding 31 (much more reasonable)

In the spirit of not always touting hands that I win I will post this one as a hand that I lost and ought to have played differently

I went 84 in sixes and the opponent to my left said "will three of them hurt you?" and was not kidding.Br> He had all 3 of the other sixes including the 6:4 and I was set

Sooooo

What I should have done is called follow me and led my doubles first giving him 3 chances to toss just a single
six off and he would not survive my parade of sixes at the end. I'd still bid 84 but I should have played it that
way to maximize my chances of winning even in the unlikely (but not zero) event that I am 3 trumped.

only 5.3% of the time will you be set due to an opponent having the other 3.
But you should never (or at least almost never) go in 6s on a mark bid - always go in No Trump.

The total number of possible hands in 42 is the number of combinations choosing 7 out of 28, or commonly referred to as "28 choose 7".
Using the formula for combinations, the result is 1,184,040. You can do that in Excel as COMBIN(28,7). Similarly, once you have your hand
(that is, a specific 7 dominoes), the number of hands possible for your opponents and partner is "21 choose 7", or COMBIN(21,7) = 116,280.
Now you have to count all the hands that have all three of the other trumps and then divide by the number of possible hands.
To do that, it's "3 choose 3" (because you have to have those specific 3) times "18 choose 4" (because there would be 18 dominoes left out
of the 21 after you take out the 3 and you need 4 more to fill your hand). So, that is COMBIN(3,3)*COMBIN(18,4)= 1*3060,
which means there are 3060 hands out of the 116,280 possible that would meet the criteria. So the odds of any one player having all three is 3060/116280,
which is equal to 0.0263 (or 2.6%). Since there are two opponents, you multiply that by 2 to get 0.0526, or 5.26% (rounded up to 5.3).
You can put this in a spreadsheet as =2*COMBIN(3,3)*COMBIN(18,4)/COMBIN(21,7). Then of course you can subtract that from 1 to get the odds
of getting all your trumps if you start with the top two and two others (but not the third one), resulting in 0.947, or 94.7%.