surrendering

Just a quick question. does one surrender when the chance of winning that hand is less then 25%. Because if you always lose 1/2 your bet every time for that hand thats like winning 1 out of 4 times for that hand...is this right?

Yes you surrender when your chance of winning the hand is less than 25% because it will be more advantageous to do so.

For instance, suppose the probability of winning a certain hand is 20%, that means that your net loss would be 80%-20%=60%, that is why it would be better to surrender because your net loss is only 50%.

In practice however the correct play is determined by calculating the expectation value of each action using combinatorial analysis and or simulations.

To expand on this point, this is because winning and losing one unit are not the only possibilities -

You might push (unless you have a stiff total for which the best non-surrender play is to stand).

You might double down, winning or losing 2 units (or again perhaps pushing).

If you have a pair you might split (and maybe resplit), potenially winning or losing a number of units. (Or again pushing, if the result balances the wins and losses).

The EV calculation is simply the sum of every possible outcome, each one weighted by its probability.

So if winning and losing do happen to be the only possibilities, and they are 25% and 75%, then the EV is (.25 * +1) + (.75 * -1) = -0.5, the same as surrender.

But the probability of winning could be <25% and surrender might not be the best option, because of the other possible outcomes besides losing.

An easy way to figure in the pushes: Count each push as 1/2 of a win.

Example: Your chance of winning is 20%, chance of losing 70%, chance of push 10%.
Win ---------- 20
1/2 of push ---- 5
___
Total ------ 25 (the cutoff point at which it doesn't matter whether you surrender or not)

Extreme example: Chance of winning: 0, chance of losing 50%, chance of a push 50%. Nothing gained or lost by surrendering, even though you have ZERO chance of winning!

Yes I like it, but as i said the best thing is to calculate the EV for each playing decision and pick the one with the highest EV, to choose surrendering the other actions (hitting, standing, splitting) must have an EV less than -50%.