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Thread: Chances of winning if I know my first card is a 10?

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    Chances of winning if I know my first card is a 10?

    Hey all, I was at a casino where a guy was playing heads up and was dealt a 10 on a 14 when he said he gave the sign to surrender. Pit boss came looked at tape and then stated that his hand signs are ambiguous but that they will let him surrender and the 10 would be the next hand dealt.

    I couldn't believe what I heard. I wasn't playing yet just watching at that point. I asked for confirmation and the dealer said yes. The next card is a 10. I immediately through down the max bet. The guy glanced at me. I then threw my chip to the dealer and immediately pointed to 1st base. The guy was in 2nd base so he started grumbling and left to smoke a cig.

    I asked the pit boss now for confirmation that my first card will indeed be the 10 and she said yes. Indeed I got the 10 and then another 10 and beat the dealers 18 and won the max bet then walked away.

    My question is that I know I'm at some sort of advantage if i know my first card is a 10... but does anyone know exactly what that is? Just curious. I think this was a major casino error.

    Sent from my SM-G935S using Tapatalk

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    Senior Member Bodarc's Avatar
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    Last edited by Bodarc; 02-10-2017 at 12:54 AM.
    Play within your bankroll, pick your games with care and learn everything you can about the game. The winning will come. It has to. It's in the cards. -- Bryce Carlson

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    Chances of winning if I know my first card is a 10?

    13 per cent! The casino just tried to be fair, sometimes they aren't so fair, so enjoy!
    So if you bet 100$ you will win 113$, your 100 plus the casinos 13.

    Sent from my iPad using Tapatalk

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    Quote Originally Posted by gm7lp View Post
    My question is that I know I'm at some sort of advantage if i know my first card is a 10... but does anyone know exactly what that is? Just curious. I think this was a major casino error.
    What you found was a pit boss, who has a low level of knowledge about the game and made an error. What they did was to follow the "you can not back up the cards" rule and put the card in play. You were correct to place max bet with a 13% edge (has some high variance to go with it).

    The guy who was heads up is the one that should have attempted to stopped the play since you took his card. I would have max bet and immediately asked the pit boss to make this table private.
    Luck is nothing more than probability taken personally!

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    Quote Originally Posted by Stealth View Post
    What you found was a pit boss, who has a low level of knowledge about the game and made an error. What they did was to follow the "you can not back up the cards" rule and put the card in play. You were correct to place max bet with a 13% edge (has some high variance to go with it).

    The guy who was heads up is the one that should have attempted to stopped the play since you took his card. I would have max bet and immediately asked the pit boss to make this table private.
    Thanks all for the advice. The max bet was a thousand. And I went ahead and made the easiest thousand in blackjack so far^^

    Sent from my SM-G935S using Tapatalk

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    Senior Member Joe Mama's Avatar
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    There was still a 40+% chance of dropping a grand.

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    Better than when a 6 is the first card out and the house insists on dealing it.

    But yeah, 13% advantage. Still high variance but very much worth it.

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    My experience has been that the 10 would be the next card to be played but only to finish that hand. If no one called for it and the dealer couldn't use it, the card would then be burned. The pit boss probably allowed the surrender as a good will gesture because the guy was playing alone. It may have been a different story if others were playing at the table, depending on the outcome.

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    I think it's safe to say that the guy was not the best blackjack player. That may have figured into the goodwill gesture. They knew the guy had no advantage.

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    Anyone have numbers of the variance of playing a hand given that one card is a 10 (as well as an ace)? I've seen the EV numbers in so many places but I'm curious what the SD is like. I'd imagine you can't just take the 1.13 figure since that's average per hand for the distribution of all possible hands and outcomes. Knowing one of your cards is a face, what's the N0 like? two or three? less than 10? Probably much less with an ace.

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    Quote Originally Posted by NotEnoughHeat View Post
    Anyone have numbers of the variance of playing a hand given that one card is a 10 (as well as an ace)? I've seen the EV numbers in so many places but I'm curious what the SD is like. I'd imagine you can't just take the 1.13 figure since that's average per hand for the distribution of all possible hands and outcomes. Knowing one of your cards is a face, what's the N0 like? two or three? less than 10? Probably much less with an ace.
    I don't have the exact value, but, clearly, the variance when starting with an ace is much higher than for any other hand due to the higher probability that the hand receives the 3:2 payout. Although your edge with the ace is 52%, because of the higher variance, I think I remember the optimal bet's being something like 43%.

    James Grosjean wrote an article on "When your first card is an ace," if you want to look for it.

    Don

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    Quote Originally Posted by DSchles View Post
    I don't have the exact value, but, clearly, the variance when starting with an ace is much higher than for any other hand due to the higher probability that the hand receives the 3:2 payout. Although your edge with the ace is 52%, because of the higher variance, I think I remember the optimal bet's being something like 43%.

    James Grosjean wrote an article on "When your first card is an ace," if you want to look for it.

    Don
    I'd imagine 'optimal' refers to full kelly in this case. So using the kelly approximation formula x = edge/variance we get a variance of 1.2093.

    I might look for it. Out of interest of course. If only there was something beyond a one off chance to be had.

    Thanks Don

  13. #13


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    My guess for X

    Quote Originally Posted by NotEnoughHeat View Post
    Anyone have numbers of the variance of playing a hand given that one card is a 10 (as well as an ace)? I've seen the EV numbers in so many places but I'm curious what the SD is like. I'd imagine you can't just take the 1.13 figure since that's average per hand for the distribution of all possible hands and outcomes. Knowing one of your cards is a face, what's the N0 like? two or three? less than 10? Probably much less with an ace.
    Don already answered for the A.

    For a first-card X, I would guess the s.d. would actually be lower than the usual 1.13, since using B.S. we'd never split or DD, so the only result larger than 1 in magnitude would be the roughly 1-in-13 chance of a BJ.

    Dog Hand

    Update:

    When I got back to my computer, I ran a 400-million-round CVData sim for a heads-up player on a 6D, H17, DAS game with 75% pen. The player flat-bet and played straight B.S. but used HiLo tags. In the sim, I used the "MRI Slice" option to consider only those hands where the player's first card was an X (FCX). The S.D. for a FCX was 1.00, and varied very little with the TC. His IBA on FCX hands was +13.99%.

    Hope this helps!

    Dog Hand
    Last edited by Dog Hand; 02-21-2017 at 06:15 AM. Reason: Added CVData Sim results

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