In a game of blackjack today, I doubled down on hard 16.

It’s one of the worst plays you can make and – against a dealer’s ten, as it was – is one of the very few plays that has a expected loss of more than your original bet.

You would actually lose less money over the long term by forfeiting your bet before seeing any cards than by doubling down on 16 against a 10.

Of course, today the long term was irrelevant. This was the free Summerfest blackjack tournament that was included with my free room at Paris and, as you have hopefully realised, I was pretty desperate.

With five hands to go, the chips were counted down and I had 1,350 – second out of the four remaining players. The leader had 2,700.

Two ladies at the table didn’t appear to realise the objective was to finish with more chips than anybody else and seemed content to just make sure their play money lasted all the way to the final hand. One had just 300 left, and decided that the way to catch up with the leader in five hands or less was by betting 100 at a time.

She’d left herself absolutely no way to win, and that’s exactly what I was trying to avoid.

Hand 11 of 15: The chip leader, not content to sit on his massive lead and find out if I would go broke trying to catch him, bet 300. Although I could have bet the minimum 25 and hoped he would lose significant bets on the next four hands, he would only need to win one more hand (or to suddenly realise that he coast to victory) to put the game out of my reach. I had no choice but to bet the maximum 500.

He doubled down on a 12 with the dealer showing a 10 and I began to wonder whether letting him self-destruct would actually have been the best strategy. He bust, but I also lost the hand with a dealt 18, leaving me with 850 compared to his 2,100 and with four hands still to play.

Hand 12 of 15: He bets 500. Perhaps he really did want to lose. But even so, I didn’t think there was time for him to donk it all off and also made a maximum bet. Ploppy had a 14 and hit a miracle 7 for 21, which couldn’t lose as the dealer showed a 9. Even if the dealer also pulled a 21, he was ending the hand on 2,100 chips – but more than likely it would be 2,600.

If I win, I’m looking at 1,350, a deficit of 1,250 – 2.5 times the maximum bet – with just 3 hands left to play. And if I lose, I have 350 chips left to fight for a meaningless second place.

So, despite having a 16, I doubled down. And, unsurprisingly, I bust out of the tournament.

Give me a pen and paper and a few minutes and I’m fairly confident that I’d be able to work out the optimal play in the end stages of a blackjack tournament. Or, at least, be able to satisfy myself that any particular decision is not a huge error.

However, under tournament conditions, having to track the number of chips left for your opponents in your head, working out all the possible scenarios and having just ten seconds to act, it’s a totally different matter.

There’s actually no reason you should have the pressure of only ten second to make an important decision, but my table had a real bitch for a dealer. She’d already hissed at the lady to my left for not making clear enough hand signals (they were just fine if you ask me) and scolded me for the heinous crime of riffling my chips. Then she decided she’d had enough of this shit so started putting clocks on players indiscriminately.

God help you if it takes a few seconds to be absolutely sure in your head that 3 + 2 + 4 + 3 + A + 3 is indeed 16, and not 17. You’ve already wasted enough of her precious time by hitting 4 times in one hand and not busting yet.

Ten seconds? That wasn’t in the rules… what is this, an online turbo tournament?

She clearly didn’t want to be there, and letting her deal was a horrible advert for blackjack at the Rio, which is surely the point of running these promotional tournaments instead of just having a prize draw.

Anyway, here’s a pop quiz from a situation in the previous day’s tournament for anyone who actually read this far. I finished second, losing by a single chip 2,375 to 2,400. In the final hand, there were just two of us left and I thought my opponent’s stack was 175 less than mine (although it turned out I was actually only 125 ahead). How much do you bet here (minimum 25, maximum 500) to give yourself the best chance of winning, and is it affected by a lack of confidence in the chip counts?

Disclaimer: you know I don’t play blackjack….

Well the obvious (but probably incorrect) answer is that, since you each stand to lose the hand 57% of the time, you should bet anything between the minimum and the difference in the stacks. I don’t really see how any further strategy is involved – in a single-hand situation the longer strategy of gaining more chips is irrelevant, you’re basically taking a gamble as to who wins or loses.

So if you bet the minimum and he bets the maximum, so what? If he wins the hand he wins.

If you bet the maximum he has to bet the minimum and hope you lose, which actually gives him favourable odds. So that’s Bad.

If you bet the difference in stacks (the obvious answer) you can afford to lose and (assuming he loses too) you’ll still be ahead; however it makes no difference from just betting the minimum because if he wins he’ll still win. So essentially whatever you bet is irrelevant – you’re just betting enough so that you still win if either you both lose or you win and he loses – that gives you the best odds.

You both lose = 57%*57%=32.49%

You lose, he wins = 24.51%

You win, he loses = 24.51%

You both win = 18.49%

So playing the odds, you should go for the outcome where he loses (32.49+24.51), not the one where you win (18.49+24.51).

The complexities of doubling or splitting then become irrelevant since his maximum bet is beside the point – if he wins, he wins anyway.

I bet the minimum and he bet 200 (you have to bet in sequence so he got to see my bet first, which is a huge advantage when you are so close on the last hand). This meant that my result was irrelevant, I just needed him to lose.

I think I agree with you that this is a sound strategy. When it gets interesting is when I have good position and see his 200 chip bet first. Then (assuming I am confident of the exact difference between us) I could bet 150 which means I still win if we both win or both lose, and if he pulls a blackjack I can still double down to try to get there.

I like Geoffs thinking here, based on the general odds of winning a hand relying on the opponents loss seems like a sound strategy. Of course the chip leader would account for this I presume.