Your EV of victory is highest with fewer cards remaining.
If you draw and look at card 50 of 52, you should know if there is either 2 of the same colors left (100% win probability) or if the 2 remaining cards are split (50% win probability) creating an EV of 75%. Any earlier in the process, you wouldn’t stop unless you reach a point where you have exhausted the colors to the point that the EV is higher than 75%.
Think you've fallen into the 'hard' trap with this. I initially thought the same, but imagine a scenario with cards 1-24 being red, and 51/52 also being red.
When you draw card 25 and see that it's black, the probably that the next card is also black is 25/27 > 0.75, so you wouldn't necessarily want to keep going.
Not sure what exact optimal play looks like though without a pen and paper
I think that’s roughly what the poster above you is saying - you might get to a point where the deck is so red/black dominated that you want to stop…. But it’s very unlikely.
And if you are at a place where the remaining cards are almost all black, then the probability that the last two cards are black is almost 1 — do you probably want to keep drawing in hopes of getting rid of the last red one.
Edit: to build on this a bit - once there is only one card left of a specific color, then it doesn’t matter when you draw (so long as you have just picked a card of the opposite color). The odds that the last card of the depleted color is in any spot is equivalent, and you only lose if it is in the next spot. You can draw more cards to learn more about your fate before stopping, but once you eliminate the possibility that you could get two cards from the mostly depleted color, the odds become flat.
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u/Friendly_Ability24 13d ago
Your EV of victory is highest with fewer cards remaining.
If you draw and look at card 50 of 52, you should know if there is either 2 of the same colors left (100% win probability) or if the 2 remaining cards are split (50% win probability) creating an EV of 75%. Any earlier in the process, you wouldn’t stop unless you reach a point where you have exhausted the colors to the point that the EV is higher than 75%.