I have a few questions/thoughts that I'd like some input on.
First of all, I made a statement today saying that Euchre is a game of probabilities, and was told I was wrong and "play style" had a huge impact. What am I missing? Isn't the entire game just a lot of decisions being made on the probabilities of each card in your hand winning the next trick, which guides your decision on which card to play next based on it having the highest probability of winning?
Second of all, I am stuck thinking about a specific hand and the actual probabilities of each outcome. I'm pretty sure I've been euchred going alone on this exact hand in the past, and just want to see the numbers laid out to help me wrap my head around why this is not a good choice.
My Hand:





I am pretty sure a

Is there an easy way to calculate my odds of taking all if I go alone?
Odds of getting at least 3?
Odds of getting Euchred?
Odds of getting all if I bring my partner?
Odds of getting Euchred if I bring my partner?
How much does taking my partner with me actually benefit me? I feel the only benefit would be if he had




So that I don't have to ask in the future, does anyone have a good breakdown for how I would just calculate the probabilities for myself in the future?
Sorry if this is to out there. Maybe this would make more sense to post in a math forum!

Thank you all for any and all input!