Risk Averse Betting

Two games.

First, player has 80% chance of winning and 20% chance of losing.

Second, player has 95% chance of a tie, 4% chance of winning and 1% chance of losing.

Is the kelly bet equal in both games?

In my estimation ties do nothing except postpone the inevitable outcome so the cases are equivalent except case 2 will be spread over a larger amount of time.

Depends - is this a one-off instance, or if it's a tie will a further round be played? The Kelly application could be different in each case as if you're intending to play more than one hand/round (whatever) you'd need to calculate the overall likelihood of losing and adjust accordingly (in my opinion).

Growth Rate

I would think the Kelly bet is the same but the growth rate is much faster in the game without the tie.:joker::whip:

Thanks.

Pushes are good in blackjack when you have a losing hand. It's different in blackjack because when you push out of a bad hand the next hand is not likely to have a similar house advantage.

Knowing this, I wonder if it changes how people would conventionally kelly bet blackjack.

I think most importantly it would affect hit/stand decisions on plays such as 16v10. Let's say your put in a situation where standing and hitting would have equal EV if you were to play the hand 10000 times. It would be enormously better to hit in this situation because if you push out of it, the push acts as a free escape out of the bad hand.

Do current indices take this effect into calculation?