Re: Some Notes for the misinformed
Sure, let's take your strategy at the 1-5 card game. Just to be clear, here's how I interpret your strategy:
Going first:
1: Check/fold
2-4: Check/call
5: Bet/raise forever.
Going second:
1: Check behind or fold to a bet.
2-4: Check behind or call a bet.
5: Bet or raise forever.
Here is my counter strategy that has +EV over yours:
Going first:
1-3: Check, fold to a bet.
4: Bet, fold to a raise.
5: Bet (raise forever, but that will never come up given your strategy)
Going second:
1-3: Check behind, fold to a bet.
4: Bet, fold to a bet.
5: Bet.
It should be fairly obvious that the person going second has a positional advantage, so I'll show the hand chart for your strategy going second. Suffice it to say that your EV is even worse going first.
The BB code eats extra whitespace, so I'm not sure the best way to display the table. The columns are:
My card / Your card / Result
1 / 2 / You win $1 (check/check)
1 / 3 / You win $1 (check/check)
1 / 4 / You win $1 (check/check)
1 / 5 / You win $1 (check/bet/fold)
2 / 1 / I win $1 (check/check)
2 / 3 / You win $1 (check/check)
2 / 4 / You win $1 (check/check)
2 / 5 / You win $1 (check/bet/fold)
3 / 1 / I win $1 (check/check)
3 / 2 / I win $1 (check/check)
3 / 4 / You win $1 (check/check)
3 / 5 / You win $1 (check/bet/fold)
4 / 1 / I win $1 (bet/fold)
4 / 2 / I win $2 (bet/call)
4 / 3 / I win $2 (bet/call)
4 / 5 / You win $2 (bet/raise/fold)
5 / 1 / I win $1 (bet/fold)
5 / 2 / I win $2 (bet/call)
5 / 3 / I win $2 (bet/call)
5 / 4 / I win $2 (bet/call)
Note that while you win 10 out of the 20 combinations, you only win more than the ante when you have the 5 and I have the 4. In the case where you're going first, you will never win a bet from me; I'll only bet when I know I'm going to win. If you add up the results, you'll see that across the 20 possible hands, you'll win $11 and lose $15 for an EV of -$4/20, or -0.20. The rate for you going first is -$5/20, or -0.25. Combining the two gives your strategy a total EV of -0.45/hand versus my counterstrategy. As you can see, your theory that you should "break even" on your hands 2-4 is false; while you win 6 of the 12 hands, you only win $6 on your wins, and lose $11, far from breaking even. And you don't make more than the ante when you hold the nuts, so you aren't covering up the difference there. So, the "correct" strategy isn't as simplistic as that.
|