Re: The value of information (slightly retarded)
Just a few quick thoughts...
Knowing that exactly a single 3 is coming obviously dramatically increases the value of 33. It also significantly increases the value of any 3x, which now becomes ~12% to flop 2 pair or better. 42 goes up in value, as do A2, 45, A4 and A5.
Further, knowing how many 3s are coming alters the odds of your other hands hitting the flop, and this knowledge can be used to increase the EV of these hands because you could play them more correctly than other players.. For example, the odds of non-33 pocket pairs making a set is lower if you know a single 3 is coming (~9% instead of ~12%). Conversely, if you know that zero 3s are coming the odds of making a set go up slightly.
The value of connectors that do not use a 3 in their straight drops significantly if a 3 is coming, and any flush/straight type hands lose nearly all their value if you know that two or more 3s are coming.
I'm sure there are many more ways to adjust one's play in order to best take advantage of this extra information than those in this quick post, but I think it's clear that when used properly this extra information should improve one's winrate fairly dramatically.
M
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