Quote:
Originally Posted by DalTXColtsFan
To calculate the probability that nobody has a K, there are 10 cards in the other 5 players' hands. The probability that the first card is not a king is 46/50, then 45/49, 44/48 et al.
1 - 92% 46/50
2 - 84% 45/49
3 - 77% 44/48
4 - 71% 43/47
5 - 65% 42/46
6 - 60% 41/45
7 - 54% 40/44
8 - 49% 39/43
9 - 44% 38/42
10 - 40% 37/41
So there's actually only about a 60% chance that someone has a king.
...
Thoughts on this (over)analysis?
Don't tell Captain R that you did this calculation.
Quote:
Of course, this assumes that the other 5 villains all have random hands. Even at *this* table, they're not - they'll play just about any hand that has a K, but they won't play, for example, just about any hand that has a 3 or just about any hand that has a 5. The probability is probably closer to 65%.
In order for you to definitively shift that percentage up, you're ALSO assuming that they will NEVER bet any kings, which is probably a false assumption. You're also assuming that they never raise preflop, and all sorts of other things. So it gets dicey if you want to start fudging that number around, and it becomes less helpful the more you tweak it. Treat this number as what it is, a blind starting point for a rough estimate, and don't try to fine tune it. (If you really want to know how things change under various assumptions, you'll need to do simulations.)
Here's the thing: Even *IF* someone has a king 60% of the time, that means that 40% of the time they DON'T have a king. If you bet and get two callers, you're still making money because you've put in 1 bet and the field has put in 2, and you're winning 40% of the time (which is more than 33%). So it still shouldn't bother you to bet here.
Once you factor in the fact that it was checked to you, you've actually eliminated a lot of the chances that there are kings out there, and you're probably doing better than the estimate above.