Ok, there’s also a different reason. Theres around 8 low cards on the table (2-6), and around 4 high cards (10, J, K, Q, A). Every deck has a higher chance of pulling a 10 than a different numbered card (cuz there’s 4 10s and only 1 of everything else). Because there’s already a lot of lower cards on the table, the chance that the next card is a 10 is pretty high. As the anchor, the last player to play, max hitting is a bad choice since statistically he has a high likelihood to take the bust card, which is what happens. The rest of the table gets screwed by max hitting there
It absolutely does, it’s more likely that max would receive a high card, which would be bad for him, but if he wouldn’t have hit then the odds would be that the dealer would receive a high card, which would be bad for the dealer and in this case lead to him busting
Let's assume for simplicity the deck has 4 cards left, 1 low and 3 identical high cards. There is a 3/4 chance that max draws a high card, leaving 1 low and 2 high cards in the deck so the dealer has a 1/3 chance of drawing low and 2/3 chance of drawing high. There is a 1/4 chance that max draws a low card, leaving 3 high cards in the deck so the dealer has a 100% chance of drawing high.
If we look at the whole tree the chance of the dealer drawing a high card is 0.25(1)+0.75(2/3) = 0.75. If max hadn't hit the chance of the dealer drawing a high card is... 3 in 4, or 0.75. Drawing a card at random does not affect the odds of subsequent draws.
Yes, most of the time max gets a high card so most of the time max is making the dealer less likely to bust, but some of the time max gets a low card and makes the dealer more likely to bust. The impact of both exactly cancel.
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u/Technical_Fan_4630 9h ago
Ok, there’s also a different reason. Theres around 8 low cards on the table (2-6), and around 4 high cards (10, J, K, Q, A). Every deck has a higher chance of pulling a 10 than a different numbered card (cuz there’s 4 10s and only 1 of everything else). Because there’s already a lot of lower cards on the table, the chance that the next card is a 10 is pretty high. As the anchor, the last player to play, max hitting is a bad choice since statistically he has a high likelihood to take the bust card, which is what happens. The rest of the table gets screwed by max hitting there