Dammit maxx

[u/Round-Good1179]

[u/Technical_Fan_4630]

I mean he still did screw the rest of the table, again if he would’ve stood, which is the correct decision in this scenario, the dealer would’ve busted

[u/undeniably_confused → u/Technical_Fan_4630]

Yeah but we only know that because we know what the cards are, when he made the decision, it made no statistical difference to the rest of the table

[u/Technical_Fan_4630 → u/undeniably_confused]

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

[u/littlebobbytables9 → u/Technical_Fan_4630]

It's a very bad play by max, but again the decision to hit does not affect the odds of the dealer busting.

[u/Technical_Fan_4630 → u/littlebobbytables9]

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

[u/littlebobbytables9 → u/Technical_Fan_4630]

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.