I have played a few rounds of Bluff with a new group of players and I am currently a little lost in the early game. What's a good strategy to come out ahead of the first rounds? Here is what I have thought about myself.
The other 4 players:
As far as I can tell, the other players are not trying to analyze the playing styles of their opponents early on, so I am not worried about being easy to read, at least not in the beginning. Most of them have played a lot more than me so they have a better feeling for the flow of the game.
What do I want to achieve:
The more I think about it the more obvious it gets. It looks like the early game revolves around not having to call a bluff or getting called. You want your opponents to call bluffs on each other because it is quite rare that you take any damage in that case (only if the exact amount has been bet). On the other hand you can earn nothing if you are involved in a challenged bet. That's why I feel that I have to create situations where I am not involved in the showdown. Is this line of thinking correct?
How do I achieve this goal:
It seems like it depends a lot on position. If I am the first to bet I have no information about the other players. There are 4 players in front of me so I want to make it easy for the next player to bet a larger amount while I don't want the betting to come back to me increased 4 times if noone calls a bluff.
In the first round there are 20 dices out there hidden from me. With the numbers 1 to 5 and a joker on each dice the chance for each number (incl. the jokers) is 1/3. On average there will be a little less than 7 rolls of a certain number out there, a little more than 3 of them will be jokers.
Lets say I rolled 1-1-2-3-J. What should I do? On average I expect 10 times
1, 9 times
2, 9 times
3, 8 times
4 and 8 times
5 (all of them incl. the jokers) and 4 times a Joker. If I start betting the average expected amount of any of those, it is better than a coin flip that I am right. But if I bet 10 times
1 and the next player has no
J it will be called immediately. Not what I want. Going for 8 times
4 feels less risky to get called, that's why I would prefer to take that route.
It might even be better to calculate the expected value and go down a certain amount to be even safer. If I reduce one from the expected value it will be even harder for the next player to call a bluff. If I go down even more it gets better and better. Where do you think is the threshold in a game of 5 players? I could obviously start by betting 1 times
1 but I can be pretty sure that the betting will be back at me for sure, if no one raises the bet significantly.
I guess the same thinking patterns will apply when I am the second to make a bet. If I am allowed to make the same bet that I would have made in first place, I will make that one. If I have to go higher, I am already lost again. What range of values can I bet and when am I forced to call a bluff? I prefer the bet because I might avoid an showdown in which I am involved, but if the amount I have to bet is too high I will be called by the next player.
Transition into middle and endgame:
I want to keep middle and endgame out of this question. Once a significant amount of dices has been lost or the number of players is reduced the psychological factor weights more and more compared to a mathematical approach.
Summing it up:
My main questions are:
- Is a mathematical approach viable as long as there are 5 players with almost all the dices left?
- How much do I have to factor the play style of my opponents into the equation at that stage of the game?
- What is a good betting strategy to avoid being involved in a showdown?