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by Richardb02 » Sun Jun 07, 2020 8:10 pm
One out of 12 = 1/12= 8.3%. Very reasonable compared to my calculations below!
I use a simple, but multi-step approach, to analyze the possibility of taking 4 points.
1st, count the single cards that can stop my Loner.
The Jd is in Partner's hand so it can not stop me.
The Kd and Ad as well as the Ac can stop me so:
3 single cards can stop me.
Additionally a guarded Ah can stop me.
That is a combination or a parlay.
I am simplifying that as equivalent to 0.25 single cards.
The chance of a single card can be calculated as 44%.
I round that off to 0.50, 50% probability that a single card can stop me. Also of my success!
(I justify rounding up because "Stoppers" can and are discarded as the hand is played!)
That means that 2 cards have a 0.50 x 0.50= 0.5^2 = 25% probability to take 4 points.
The 3rd card is expressed 0.50x0.50x0.50= 0.5^3 = 0.125 or a 12.5% possibility to take 4 points.
A 4th single card would be 0.5^4= 6.25%
But we aren't up against 4 cards, we are up against 3.25 equivalents!
That could be expressed as 0.5^3.25. The calculator on my phone gives me 10.5%.
But we don't have time to consult our calculator.
So interpolate between 12.5% and 6.25%, about 1.5% per parlay and I get 11% chance of success.
Now what? Know the magic number of single card equivalents to come at ahead.
Let's calculate an EV, the Expected Value of the hand.
I see a 10% possibility of being euchred, 11% getting 4 points and 79% getting 1 point. So:
0.10x-2+0.11x4+.79x1= -.2+.44+.79= 1.03. A positive EV.
So this hand is just above my breakeven point. I use it as my "Edge Hand" to go Alone.
This scenario has us down 6-9. My probability of winning is about 10% (my "guessimate").
So I see no logical reason to not go Alone!
That is my analysis.
But don't let all the details scare you.
Simply count up the single cards and the card combinations that can stop you and if it is 3.25 or less, go Alone. It is a simple and empowering approach to go Alone more often. In this scenario, it also snatched a victory from the jaws of defeat!
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. So bring your partner's Right bower along for the ride to help make sure you don't go set. That said, this a loner in around 99% of game textures out there where the vast majority play their cards instead of playing to win.