What's the correct play here?

It the last hand of the semi-final round of a blackjack tournament. The winner of the table advances into the finals. The minimum bet is 100 and the maximum bet is 5,000.

Player 1 has 7,250 and is first to act.
Player 2 has 7,000.
1) How much should Player 1 bet and why?

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Player 1 bets 225.
2) How much should Player 2 bet and why?

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Player 2 bets 500.
Player 1 is dealt A-A and acts first.
Player 2 is dealt K-3.
The Dealer shows a Q.
3) What should Player 1 do and why?

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Player 1 splits aces and receives A-3 and A-A.
4) What should Player 1 do and why?

 

You did not state the rules of the games in terms of splitting and doubling after splitting. Here are quick answers:
1) Player 1 should bet 225
2) Player 2 bet should bet 505
3)Player 1 should split to cover for potential double by player 2.
4) Player 1 should re-split the aces as he lost the low already, so better to maximize chances of winning.

 

You can split pairs (or tens) up to 4 times. In the case of aces, when you split you only get 1 card and do not have the option of hitting again. Your only option, if given another ace as in the example here, is to split again, stand, or double down. You cannot split for less. The minimum chip value is 25. We're working with a 6-deck shoe. Dealer hits soft 17.

 

1) I agree.
2) Why 505? How was this calculated?
3) Player 1 captured the high and low on the first split. I agree that splitting again would cover the potential double by Player 2, but Player 1 would no longer have the low. How did you calculate that abandoning the low and opting for the high was the optimal play given that one of Player 1's hands is a 14 (a statistical loser against the Dealer's 10), and Player 2 has a 13?
4) I disagree. As the hand stands now, Player 1 has not "lost the low". Player 1 has 225 x 2=450 bet with 6,800 remaining while Player 2 has 500 bet and 6,500 remaining. As it stands now Player 1 has both the high and the low. How did you calculate that splitting again would "maximize" Player' 1's chances of winning?

 

I guess I made "too" quick answers, trying to simulate immediate decisions we face at the tables. Let me see if I can redeem my self here. 1) it is easy in a two persons race, taking the low is slightly better than taking the high. 2) Player 2 has several options that ran into my head when I first read this. a) Bet 500 to cover a win for player 1 plus the 250 he is behind plus a chip, b) bet 975 to cover a double win for player 1, or c) bet 2050 to cover a 4 split double win by player 2. My best guess would be 975.
3) Player 1 has 2 aces (12) and player 2 has 13. Player 2 is likely to try to win his hand over the dealer's 10. It is better for player 1 to split so he can get both the low and high as you pointed out.
4) Player 1 should stand, as respliting will not cover a double down for player 2 and will make him lose the low, as you already pointed out. If the dealer busts then player 1 wins. Same thing if player double down and busts. If dealer makes a hand player 1 wins. The only time player 2 wins is with a double down and winning over the dealer.

 

Hi and welcome to the forum! I read your blog about the tournament. Congratulations on your win and your impressive placement in the second tournament. Two final tables in a row is a great accomplishment.

With regard to your questions, these are my 1-minute-or-less-thoughts. We often try to do this here in order to simulate the time limits that may be imposed at a live table. We can then rethink the situation later to come up the with optimal play(s):

1. Yeah, this is a typical situation and taking the low is the way to go unless your read on your opponent tells you that he might go all in regardless of your bet, in which case you would go all in yourself, essentially matching his bet. Sometimes, you can induce this by saying out loud something like "well I guess we both bet it all and see what happens". If you are in doubt, however, just take the low.
2. Once player 1 has taken the low, player 2 should take the high. But, as Ken said, he might as well bet enough to cover every situation. Since it's the final hand and player 1 already has the low, this can be done without any cost at all. At a minimum, player 2 should bet enough to cover player 1's double, in order to protect himself from exactly what you did to him. So at least 705. I would probably just push out a max bet, for simplicity.
3. If you just play out your A-A by hitting it, then player 2 will advance by winning his hand. If you split it, then player 2 will have to win while you lose or push or push while you lose. My gut says that forcing him to create a swing is the higher percentage play. I would split those aces.
4. Player 2 already has a stiff hand, which requires a dealer bust for success, and has player 1's single bet covered high and low. Splitting again cannot cover player 1's double, so I don't see any value in that. I would stand.

 

Thanks gronbog. I was second-guessing myself immediately after that round, so it's nice to review the hand and get input from others. The last time I played any serious blackjack was at the Playboy Casino in Atlantic City. As you can see from my blog, I'm a poker player now. I only entered the blackjack tournament because my entry fees were comped. I actually tried to hit the second A-A hand only to be told by the dealer that my options were stand of split. I also had to ask if I split aces and got 21 if it paid even money or 3-to-2. Ignorance of some of the basic rules of how to play blackjack might have had my opponents underestimating me at the tables. After reading Ken's tournament strategy guide I would have to say that a blackjack tournament has more in common with playing poker as position and bet-sizing are key.

 

There is also the option of doubling down on the aces. I think splitting is likely to be the better play, but I'm not entirely sure. I started to try and work out the numbers, but quickly realised it was beyond me!

Splitting the aces gives a high chance of a net push (which would keep you ahead of a push by player 2).
On the other hand, it presumably has a slightly lower chance of winning two bets, compared to doubling.

P.S. Welcome, alpaha1243.

 

You cannot double down on aces in all but very rare places

 

Are you talking about the post-split A,A hand? Because my comment was about the initial A,A hand. Surely you can double down on any first two cards in all but a few places (i.e. where thay have D9,D10, or D11 rules in place).?

 

Yes, I thought you were talking post split. Not sure there is an advantage of double down vs. splitting. I think splitting gets the same money out with better EV.

 

EV is not really a relevant concept; what matters is the probabilities of the various combinations of player1/player2 outcomes.

Like I said, doubling presumably gives a higher probability of winning two bets, compared to splitting, since it is easier to win one hand than to win two. (But then player 2 doesn't lose much [if anything?] by choosing to also double down, if need be, to take back the high. That is, they would probably want to stand after drawing one card to their total of 13, in any case. And if player 2 doubles, then it makes no difference whether or not player 1 wins their two bets.)

And as I also mentioned, the down side of player 1 doubling is that it increases the probability of player 2 winning the tournament by pushing while player 1 loses (since splitting the aces would have a good chance of giving at least one winning hand, and thus at least a net push for player 1).

So I suspect that splitting is the right play, but the complexities of trying to prove it make my head spin!

 

I'm new here, so let me start by playing Devil's Advocate. In the 1st part of the question I asked what was the correct bet for Player 1 at the start of the hand. It seems there is agreement that since betting is in $25 increments, that $225 is the correct bet. Why is $225 the optimal bet in this scenario?

 

I am also new but will answer any way
The chance of winning is smaller than the chance of losing (44% vs 48% for a given hand). The chance of both players win is 30%. The chance of both players lose is 31%. One one and the other lose is 12%. In a two persons player keeping the low gives 44% chance of winning the table vs 42% chance for keeping the high. Small difference but it is what it is.

 

Now you got my head spinning too

 

Ah, so it's math! Math has got to be the basis for calculating bet-sizing (as in question #1) and individual hand play. So there is only one correct answer for question 1: $225. All other answers are less than optimal.

That said, there should be similar answers, based upon math, for the remaining questions. Coming from a poker background, ALL of your play has its fundamentals based in math and knowing the numbers. While you may not be able to calculate it in your head at the tables, you can certainly review the hands afterward to see which is correct and to better prepare yourself for your next time playing.

 

Yes, the other questions all have math answers that can be calculated by computer simulations.

 

Not entirely. As Ken said, the $225 is optimal if you assume that whatever you do your opponent will in turn respond optimally. If, in poker terms, you can get a 'read' on your opponent, predicting how they will respond to various bets you might make, then that can change things.

Specifically, many people will match a max bet in this situation, giving you the high and the low and making you a massive favourite. You should seek out the previous thread(s) on this subject that Ken mentioned.

 

You mean that there's another optimal bet?